adjustment for non differential misclassification error in the generalized linear model it is well known that estimates of association between an outcome variable and a set of categorical covariates some of which are measured with misclassification tend to be biased upon application of the usual methods of estimation that ignore the classification error we propose a method to adjust for misclassification in covariates when one applies the generalized linear model in the case where one can observe some true covariates only through surrogates we combine a latent class analysis with the approach to incorporate multiple surrogates into the model we include discussion on the efficacy of repeated measurements which one can view as a special case of multiple surrogates with identical distribution we provide two examples to demonstrate the applicability of the method and the efficacy of multiple replicates for a covariate subject to misclassification in a regression framework

entropy stable high order discontinuous galerkin methods for ideal compressible mhd on structured meshes abstract we present a discontinuous galerkin dg scheme with suitable quadrature rules 15 for ideal compressible magnetohydrodynamic mhd equations on structural meshes the semi discrete scheme is analyzed to be entropy stable by using the symmetrizable version of the equations as introduced by godunov 32 the entropy stable dg framework with suitable quadrature rules 15 the entropy conservative flux in 14 inside each cell and the entropy dissipative approximate godunov type numerical flux at cell interfaces to make the scheme entropy stable the main difficulty in the generalization of the results in 15 is the appearance of the non conservative source terms added in the modified mhd model introduced by godunov 32 which do not exist in the general hyperbolic system studied in 15 special care must be taken to discretize these source terms adequately so that the resulting dg scheme satisfies entropy stability total variation diminishing bounded tvd tvb limiters and bound preserving limiters are applied to control spurious oscillations we demonstrate the accuracy and robustness of this new scheme on standard mhd examples

variational iteration method for autonomous ordinary differential systems in this paper a new iteration technique is proposed to solve autonomous ordinary differential systems in this method general lagrange multipliers are introduced to construct correction functionals for the systems the multipliers in the functionals can be identified by the variational theory the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary initial conditions some examples are given the results reveal that the method is very effective and convenient

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

piecewise homotopy perturbation method for solving linear and nonlinear weakly singular vie of second kind the purpose of this paper is to obtain the approximation solution of linear and strong nonlinear weakly singular volterra integral equation of the second kind especially for such a situation that the equation is of nonsmooth solution and the situation that the problem is a strong nonlinear problem for this purpose we firstly make a transform to the equation such that the solution of the new equation is as smooth as we like through modifying homotopy perturbation method an algorithm is successfully established to solve the linear and nonlinear weakly singular volterra integral equation of the second kind and the convergence of the algorithm is proved strictly comparisons are made between our method and other methods and the results reveal that the modified homotopy perturbation is effective

approximate quasi likelihood estimation in models with surrogate predictors abstract we consider quasi likelihood estimation with estimated parameters in the variance function when some of the predictors are measured with error we review and extend four approaches to estimation in this problem all of them based on small measurement error approximations a taxonomy of the data sets likely to be available in measurement error studies is developed an asymptotic theory based on this taxonomy is obtained and includes measurement error and berkson error models as special cases

application of he s homotopy perturbation method for nth order integro differential equations abstract in this paper he s homotopy perturbation method is proposed to solve n th order integro differential equations the results reveal that the method is very effective and simple

aerodynamic optimization algorithm with integrated geometry parameterization and mesh movement an efficient gradient based algorithm for aerodynamic shape optimization is presented the algorithm consists of several components including a novel integrated geometry parameterization and mesh movement a parallel newton krylov flow solver and an adjoint based gradient evaluation to integrate geometry parameterization and mesh movement generalized b spline volumes are used to parameterize both the surface and volume mesh the volume mesh of b spline control points mimics a coarse mesh a linear elasticity mesh movement algorithm is applied directly to this coarse mesh and the fine mesh is regenerated algebraically using this approach mesh movement time is reduced by two to three orders of magnitude relative to a node based movement the mesh adjoint system also becomes smaller and is thus amenable to complex step derivative approximations when solving the flow adjoint equations using restarted krylov subspace methods a nested subspace strategy is shown to be more robust than truncating the entire subspace optimization is accomplished using a sequential quadratic programming algorithm the effectiveness of the complete algorithm is demonstrated using a lift constrained induced drag minimization that involves large changes in geometry

the errors in variables problem considerations provided by radiation dose response analyses of the a bomb survivor data abstract some basic issues in the errors in variables problem are discussed in terms of considerations that arose in analyses of radiation effects on atomic bomb survivors the setting essentially involves generalized linear models for the response variables a very nonnormal distribution of the true covariable and multiplicative errors in the observed covariable consideration is given to distinctions between structural and functional modeling it is argued that careful attention to the apparent distribution of true covariables is critical in either case and a quasi structural approach to functional models is suggested the focus is on the case in which the expected response is linear in the true covariable and strong assumptions are tentatively made about the model for covariate errors for settings such as just described which differ from that of much of the classical work in the area it is emphasized that an attractive approach is based on weighted regression of the response on the expected value

a numerical method for solving systems of linear and nonlinear integral equations of the second kind by hat basis functions abstract in this paper we use hat basis functions to solve the system of fredholm integral equations sfies and the system of volterra integral equations svies of the second kind this method converts the system of integral equations into a linear or nonlinear system of algebraic equations also we consider the order of convergence of the method and show that it is o h 2 application of the method on some examples show its accuracy and efficiency

a maximum principle preserving finite element method for scalar conservation equations this paper introduces a first order viscosity method for the explicit approximation of scalar conservation equations with lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension provided the lumped mass matrix is positive definite the method is shown to satisfy the local maximum principle under a usual cfl condition the method is independent of the cell type for instance the mesh can be a combination of tetrahedra hexahedra and prisms in three space dimensions

discontinuous galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction abstract we present a novel high order discontinuous galerkin discretization for the spherical shallow water equations able to handle wetting drying and non conforming curved meshes in a well balanced manner this requires a well balanced discretization that cannot rely on exact quadrature due to the curved mesh using the strong form of the discontinuous galerkin discretization we achieve a splitting of the well balanced condition into individual problems for the flux and volume terms which has significant advantages it allows for the construction of non conforming well balanced flux discretizations i e we can perform non conforming mesh refinement while preserving the well balanced property of the scheme more importantly this approach enables the development of a new method for handling wet dry transitions in contrast to other wetting drying methods it is well balanced and able to handle wetting drying robustly at any polynomial order without the introduction of physical model assumptions such as viscosity artificial porosity or cancellation of gravity we perform a series of one dimensional tests and analyze the properties of our scheme in order to validate our method for the simulation of large scale tsunami events on the rotating sphere we perform numerical simulations of the 2011 tohoku tsunami and compare our results to real world buoy data the method is able to predict arrival times and wave amplitudes accurately even over long distances this indicates that our method accurately captures all physical phenomena relevant to the long term evolution of tsunami waves

high order schemes entropy inequalities and nonclassical shocks we are concerned with the approximation of undercompressive regularization sensitive nonclassical solutions of hyperbolic systems of conservation laws by high order accurate conservative and semidiscrete finite difference schemes nonclassical shock waves can be generated by diffusive and dispersive terms kept in balance particular attention is given here to a class of systems of conservation laws including the scalar equations and the system of nonlinear elasticity and to linear diffusion and dispersion in either the conservative or the entropy variables first we investigate the existence and the properties of entropy conservative schemes a notion due to tadmor math comp 49 1987 pp 91 103 in particular we exhibit a new five point scheme which is third order accurate at least second we study a class of entropy stable and high order accurate schemes satisfying a single cell entropy inequality they are built from any high order entropy conservative scheme by adding to it a mesh independent numerical viscosity which preserves the order of accuracy of the base scheme these schemes can only converge to solutions of the system of conservation laws satisfying the entropy inequality these entropy stable schemes exhibit mild oscillations near shocks and interestingly may converge to classical or nonclassical entropy solutions depending on the sign of their dispersion coefficient then based on a third order entropy conservative scheme we propose a general scheme for the numerical computation of nonclassical shocks importantly our scheme satisfies a cell entropy inequality following hayes and lefloch siam j numer anal 35 1998 pp 2169 2194 we determine numerically the kinetic function which uniquely characterizes the dynamics of nonclassical shocks for each regularization of the conservation laws our results compare favorably with previous analytical and numerical results finally we prove that there exists no fully discrete and entropy conservative scheme and we investigate the entropy stability of a class of fully discrete lax wendroff type schemes

a computational method for solving nonlinear stochastic volterra integral equations in this paper an efficient method for solving nonlinear stochastic ito volterra integral equations nsivies is proposed by using new adjustment of hat basis functions and their stochastic operational matrix of integration the nsivie is reduced to a nonlinear system of algebraic equations also the error analysis of the proposed method is investigated and proved that the order of convergence is o h 4 finally numerical examples affirm the efficiency of the proposed method

the stability of numerical boundary treatments for compact high order finite difference schemes the stability characteristics of various compact fourth and sixth order spatial operators are assessed with the theory of gustafsson kreiss and sundstrom g k s for the semidiscrete initial boundary value problem these results are generalized to the fully discrete case with a recently developed theory of kreiss and wu in all cases favorable comparisons are obtained between g k s theory eigenvalue determination and numerical simulation the conventional definition of stability then is sharpened to include only those spatial discretizations that are asymptotically stable bounded left half plane eigenvalues many of the higher order schemes that are g k s stable are not asymptotically stable a series of compact fourth and sixth order schemes that are both asymptotically and g k s stable for the scalar case are then developed

a detailed evaluation of adjustment methods for multiplicative measurement error in linear regression with applications in occupational epidemiology it is often appropriately assumed based on both theoretical and empirical considerations that airborne exposures in the workplace are lognormally distributed and that a worker s mean exposure over a reference time period is a key predictor of subsequent adverse health effects for that worker unfortunately it is generally impossible to accurately measure a worker s true mean exposure we begin by introducing a familiar model for exposure that views this true mean as well as logical surrogates for it as lognormal random variables in a more general context we then consider the linear regression of a continuous health outcome on a lognormal predictor measured with multiplicative error we discuss several candidate methods of adjusting for the measurement error to obtain consistent estimators of the true regression parameters these methods include a simple correction of the ordinary least squares estimator based on the surrogate regression the regression of the outcome on the covariates and on the conditional expectation of the true predictor given the observed surrogate and a quasi likelihood approach by means of a simulation study we compare the various methods for practical sample sizes and discuss important issues relevant to both estimation and inference finally we illustrate promising adjustment strategies using actual lung function and dust exposure data on workers in the dutch animal feed industry

numerical solution of second kind fredholm integral equations system by using a taylor series expansion method in this paper we present a taylor series expansion method for a second kind fredholm integral equations system with smooth or weakly singular kernels this method reduce the system of integral equations to a linear system of ordinary differential equation after constructing boundary conditions this system reduce to a system of equations that can be solved easily with any of the usual methods finally we show the efficiency of the method using some numerical examples

a numerical solution for solving system of fredholm integral equations by using homotopy perturbation method abstract homotopy perturbation method is applied to the numerical solution for solving system of fredholm integral equations comparison of the result obtained by the present method with that obtained by taylor series expansion method k maleknejad n aghazade m rabbani numerical solution of second kind fredholm integral equations system by using a taylor series expansion method appl math comput 175 2006 1229 1234 reveals that the present method is very effective and convenient

an explicit residual based approach for shallow water flows we describe fully explicit residual based discretizations of the shallow water equations with friction on unstructured grids the schemes are obtained by properly adapting the explicit construction proposed in ricchiuto and abgrall 2010 57 in particular previous work on well balanced integration ricchiuto 2011 56 and preservation of the depth non negativity ricchiuto and bollermann 2009 60 is reformulated in the context of a genuinely explicit time stepping still based on a weighted residual approximation the paper discusses in depth how to achieve in this context an exact preservation of all the simple known steady equilibria and how to obtain a super consistent approximation for smooth non trivial moving equilibria the treatment of the wetting drying interface is also discussed giving formal conditions for the preservation of the non negativity of the depth for a particular case based on a nonlinear variant of a lax friedrichs type scheme the approach is analyzed and tested thoroughly the quality of the numerical results shows the interest in the proposed approach over previously proposed schemes in terms of accuracy and efficiency

superconvergent functional output for time dependent problems using finite differences on summation by parts form finite difference operators satisfying the summation by parts sbp rules can be used to obtain high order accurate energy stable schemes for time dependent partial differential equations when the boundary conditions are imposed weakly by the simultaneous approximation term sat in general an sbp sat discretization is accurate of order p 1 with an internal accuracy of 2p and a boundary accuracy of p despite this it is shown in this paper that any linear functional computed from the time dependent solution will be accurate of order 2p when the boundary terms are imposed in a stable and dual consistent way the method does not involve the solution of the dual equations and superconvergent functionals are obtained at no extra computational cost four representative model problems are analyzed in terms of convergence and errors and it is shown in a systematic way how to derive schemes which gives superconvergent functional outputs

a well balanced and entropy conservative discontinuous galerkin spectral element method for the shallow water equations in this work we design an arbitrary high order accurate nodal discontinuous galerkin spectral element type method for the one dimensional shallow water equations the novel method uses a skew symmetric formulation of the continuous problem we prove that this discretisation exactly preserves the local mass and momentum furthermore we show that combined with a special numerical interface flux function the method exactly preserves the entropy which is also the total energy for the shallow water equations finally we prove that the surface fluxes the skew symmetric volume integrals and the source term are well balanced numerical tests are performed to demonstrate the theoretical findings

an efficient finite difference method for the shallow water equations abstract a high order explicit finite difference scheme is derived solving the shallow water equations the boundary closures are based on the diagonal norm summation by parts sbp framework and the boundary conditions are imposed using a penalty sat technique flux splitting combined with upwind sbp operators is used to naturally introduce artificial dissipation the scheme is tested against various benchmark problems where high order convergence is verified for smooth solutions a particular discretization of the source term is used leading to a well balanced scheme we also present an application a simplified incident wave simulation with wave channel interaction using a multi block setup experiments suggest that a bathymetry consisting of many spikes could provide a dispersing effect on an incoming wave

generalized conservative approximations of split convective derivative operators we propose a strategy to design locally conservative finite difference approximations of convective derivatives for shock free compressible flows with arbitrary order of accuracy that generalizes the approach of ducros et al 2000 1 and that can be applied as a building block of low dissipative hybrid shock capturing methods the approximations stem from application of standard central difference formulas to split forms of the convective terms in the compressible euler equations which guarantee strong numerical stability and near energy preservation in the inviscid limit a convenient implementation of the high order fluxes is suggested which guarantees improved computational efficiency over existing methods numerical tests performed for isotropic turbulence at zero viscosity show stability of schemes with order of accuracy up to ten and effectiveness of convective splitting of kennedy and gruber 2008 2 in providing extra stability in the presence of strong density variations numerical simulations of compressible turbulent boundary layer flow indicate suitability of the method for non uniform grids and overall support superior computational efficiency of high order schemes

new iterative methods for nonlinear equations by modified hpm a numerical method based on modified homotopy perturbation method hpm is proposed for solving nonlinear algebric equations it is shown that the proposed method has third order convergence to assess its validity and accuracy the method is applied to solve several test problems

a third order newton type method for nonlinear equations based on modified homotopy perturbation method in this paper we present a new iterative method for solving nonlinear algebric equations by using modified homotopy perturbation method we also discuss the convergence criteria of the present method to assess its validity and accuracy the method is applied to solve several test problems

iterated he s homotopy perturbation method for quadratic riccati differential equation abstract in this paper iterated he s homotopy perturbation method is proposed to solving quadratic riccati differential equation comparisons are made between adomian s decomposition method adm and the exact solution and the proposed method the results reveal that the method is very effective and simple

superconvergent functional estimates from summation by parts finite difference discretizations diagonal norm summation by parts sbp operators can be used to construct time stable high order accurate finite difference schemes however to achieve both stability and accuracy these operators must use s order accurate boundary closures when the interior scheme is 2s order accurate the boundary closure limits the solution to s 1 order global accuracy despite this bound on solution accuracy we show that functional estimates can be constructed that are 2s order accurate this superconvergence requires dual consistency which depends on the sbp operators the boundary condition implementation and the discretized functional the theory is developed for scalar hyperbolic and elliptic partial differential equations in one dimension in higher dimensions we show that superconvergent functional estimates remain viable in the presence of curvilinear multiblock grids with interfaces the generality of the theoretical results is demonstrated using a two dimensional poisson problem and a nonlinear hyperbolic system the euler equations of fluid mechanics

the homotopy perturbation method for nonlinear oscillators with discontinuities in the paper the homotopy perturbation method is applied to the nonlinear oscillators with discontinuities only one iteration leads to high accuracy of the solutions

a free energy stable nodal discontinuous galerkin approximation with summation by parts property for the cahn hilliard equation abstract we present a nodal discontinuous galerkin dg scheme for the cahn hilliard equation that satisfies the summation by parts simultaneous approximation term sbp sat property the latter permits us to show that the discrete free energy is bounded and as a result the scheme is provably stable the scheme and the stability proof are presented for general curvilinear three dimensional hexahedral meshes we use the bassi rebay 1 br1 scheme to compute interface fluxes and a first order implicit explicit imex scheme to integrate in time we provide a semi discrete stability study and a fully discrete proof subject to a positivity condition on the solution lastly we test the theoretical findings using numerical cases that include two and three dimensional problems

exactly well balanced discontinuous galerkin methods for the shallow water equations with moving water equilibrium hyperbolic conservation laws with source terms often admit steady state solutions where the fluxes and source terms balance each other to capture this balance and near equilibrium solutions well balanced methods have been introduced and performed well in many numerical tests shallow water equations have been extensively investigated as a prototype example in this paper we develop well balanced discontinuous galerkin methods for the shallow water system which preserve not only the still water at rest steady state but also the more general moving water equilibrium the key idea is the recovery of well balanced states a special source term approximation and the approximation of the numerical fluxes based on a generalized hydrostatic reconstruction we also study the extension of the positivity preserving limiter presented in 40 in this framework numerical examples are provided at the end to verify the well balanced property and good resolution for smooth and discontinuous solutions

asymptotology by homotopy perturbation method in the paper an heuristical example is given to illustrate the basic idea of the homotopy perturbation method so that homotopy perturbation method has made all that is necessary simple and all that is complex unnecessary

newton like iterative methods for solving system of non linear equations abstract homotopy perturbation method hpm is applied to construct a new family of newton like iterative methods for solving system of non linear equations comparison of the result obtained by the present method with newton raphson method reveals that the accuracy and fast convergence of the new method

discretely conservative finite difference formulations for nonlinear conservation laws in split form theory and boundary conditions the lax wendroff theorem stipulates that a discretely conservative operator is necessary to accurately capture discontinuities the discrete operator however need not be derived from the divergence form of the continuous equations indeed conservation law equations that are split into linear combinations of the divergence and product rule form and then discretized using any diagonal norm skew symmetric summation by parts sbp spatial operator yield discrete operators that are conservative furthermore split form discretely conservation operators can be derived for periodic or finite domain sbp spatial operators of any order examples are presented of a fourth order sbp finite difference operator with second order boundary closures sixth and eighth order constructions are derived and are supplied in an accompanying text file

a new family of iterative methods for solving system of nonlinear algebric equations abstract homotopy perturbation method hpm is applied to construct a new iterative method for solving system of nonlinear algebric equations comparison of the result obtained by the present method with that obtained by revised adomian decomposition method hossein jafari varsha daftardar gejji appl math comput 175 2006 1 7 reveals that the accuracy and fast convergence of the new method

covariance analysis in generalized linear measurement error models we summarize some of the recent work on the errors in variables problem in generalized linear models the focus is on covariance analysis and in particular testing for and estimation of treatment effects there is a considerable difference between the randomized and non randomized models when testing for an effect in randomized studies simple techniques exist for testing for a treatment effect in some instances such as linear and multiplicative regression simple methods exist for estimating the treatment effect in other examples such as logistic regression estimating a treatment effect requires careful attention to measurement error in non randomized studies there is no recourse to understanding and modelling measurement error in particular ignoring measurement error can lead to the wrong conclusions for example the true but unobserved data may indicate a positive effect for treatment while the observed data indicate the opposite some of the possible methods are outlined and compared

a numerical simulation and explicit solutions of the generalized burgers fisher equation we consider solitary wave solutions of the generalized burgers fisher bf equation u t pu ru x u x x qu 1 u r 0 in this paper by considering the decomposition scheme we first obtain the exact solutions of the generalized bf equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some values r 2 of the generalized bf equation

convergence of a residual based artificial viscosity finite element method we present a residual based artificial viscosity finite element method to solve conservation laws the galerkin approximation is stabilized by only residual based artificial viscosity without any least squares supg or streamline diffusion terms we prove convergence of the method applied to a scalar conservation law in two space dimensions toward an unique entropy solution for implicit time stepping schemes

a high order semi implicit discontinuous galerkin method for the two dimensional shallow water equations on staggered unstructured meshes a well balanced spatially arbitrary high order accurate semi implicit discontinuous galerkin scheme is presented for the numerical solution of the two dimensional shallow water equations on staggered unstructured non orthogonal grids the semi implicit method is derived in such a fashion that all relevant integrals can be precomputed and stored in a preprocessing stage so that the extension to curved isoparametric elements is natural and does not increase the computational effort of the simulation at runtime for p 0 the resulting scheme becomes a generalization of the classical semi implicit finite volume finite difference scheme of casulli and walters 2000 25 but with less conditions on the grid geometry the method proposed in this paper allows large time steps with respect to the surface wave speed gh and is thus particularly suitable for low froude number flows the approach is validated on some typical academic benchmark problems using polynomial degrees up to p 6

skew selfadjoint form for systems of conservation laws abstract hyperbolic systems of conservation laws augumented with an entropy inequality are studied it is shown that such systems can be written in a quasilinear skew selfadjoint form centered differencing of such a form under the smooth regime ends up with a systematic recipe for constructing quasiconservative schemes where the global entropy conservation is recovered employing the above formulation in bounded regions under the nonsmooth regime as well a local entropy decay estimate is also concluded examples of the shallow water and the full gasdynamics equations are explicitly treated

summation by parts projections and stability ii we have derived stability results for high order finite difference approximations of mixed hyperbolic parabolic initial boundary value problems ibvp the results are obtained using summation by parts and a new way of representing general linear boundary conditions as an orthogonal projection by slightly rearranging the analytic equations we can prove strict stability for hyperbolic parabolic ibvp furthermore we generalize our technique so as to yield strict stability on curvilinear non smooth domains in two space dimensions finally we show how to incorporate inhomogeneous boundary data while retaining strict stability using the same procedure one can prove strict stability in higher dimensions as well

multiplicative errors in variables models with applications to recent data released by the u s department of energy abstract in an errors in variables model the predicting variables are observed with errors traditionally the errors are assumed to be additive in this article i consider the case in which the error is multiplicative a situation that arises when analyzing some recent data released by the u s department of energy a consistent estimator is provided for regression coefficients by correcting the asymptotic bias of the least squares estimate it is shown that after being normalized by an estimate of its covariance is asymptotically normally distributed this can therefore be used to construct approximate tests and confidence sets for the results are essentially nonparametric

skew symmetric form of convective terms and fully conservative finite difference schemes for variable density low mach number flows the form of convective terms for compressible flow equations is discussed in the same way as for an incompressible one by morinishi et al y morinishi t s lund o v vasilyev p moin fully conservative higher order finite difference schemes for incompressible flow j comput phys 124 1998 90 and fully conservative finite difference schemes suitable for shock free unsteady compressible flow simulations are proposed commutable divergence advective and skew symmetric forms of convective terms are defined by including the temporal derivative term for compressible flow these forms are analytically equivalent if the continuity is satisfied and the skew symmetric form is secondary conservative without the aid of the continuity while the divergence form is primary conservative the relations between the present and existing quasi skew symmetric forms are also revealed commutable fully discrete finite difference schemes of convection are then derived in a staggered grid system and they are fully conservative provided that the corresponding discrete continuity is satisfied in addition a semi discrete convection scheme suitable for compact finite difference is presented based on the skew symmetric form the conservation properties of the present schemes are demonstrated numerically in a three dimensional periodic inviscid flow the proposed fully discrete fully conservative second order accurate scheme is also used to perform the dns of compressible isotropic turbulence and the simulation of open cavity flow

generalised summation by parts operators and variable coefficients abstract high order methods for conservation laws can be highly efficient if their stability is ensured a suitable means mimicking estimates of the continuous level is provided by summation by parts sbp operators and the weak enforcement of boundary conditions recently there has been an increasing interest in generalised sbp operators both in the finite difference and the discontinuous galerkin spectral element framework however if generalised sbp operators are used the treatment of the boundaries becomes more difficult since some properties of the continuous level are no longer mimicked discretely interpolating the product of two functions will in general result in a value different from the product of the interpolations thus desired properties such as conservation and stability are more difficult to obtain here new formulations are proposed allowing the creation of discretisations using general sbp operators that are both conservative and stable thus several shortcomings that might be attributed to generalised sbp operators are overcome cf nordstrom and ruggiu 2017 38 and manzanero et al 2017 39

a semi implicit semi lagrangian p adaptive discontinuous galerkin method for the shallow water equations a semi implicit and semi lagrangian discontinuous galerkin method for the shallow water equations is proposed for applications to geophysical scale flows a non conservative formulation of the advection equation is employed in order to achieve a more treatable form of the linear system to be solved at each time step the method is equipped with a simple p adaptivity criterion that allows to adjust dynamically the number of local degrees of freedom employed to the local structure of the solution numerical results show that the method captures well the main features of gravity and inertial gravity waves as well as reproducing correct solutions in nonlinear test cases with analytic solutions the accuracy and effectiveness of the method are also demonstrated by numerical results obtained at high courant numbers and with automatic choice of the local approximation degree

adjusting for measurement error to assess health effects of variability in biomarkers longitudinal studies of health effects often relate individuals biomarker levels to disease progression repeated measurements also provide an opportunity to assess within individual biomarker variability and it is reasonable to postulate that this measure might provide additional information about a particular outcome variable given the existing precedent for application of adjustment methods to account for measurement error in subject specific average levels of a covariate this concept motivates the application of such methods to incorporate variability as well in this paper we investigate the nature of the relationship between the decline of cd4 cell count induced by infection with human immunodeficiency virus and cd4 level and variability prior to infection we first describe the distribution of repeated cd4 measurements prior to infection using a model that accounts both for random average levels and random subject specific variance components based on this model we define true unobservable random variables that correspond to prior level and stability we perform a linear regression analysis using these latent variables as covariates by means of a full maximum likelihood approach we compare the resulting parameter estimates with those based on regressions employing sample based estimates of pre infection levels and variances and empirical bayes estimates of these quantities although the final inferences are similar to those based on the unadjusted analysis we find that the magnitude of association with prior level decreases while that with prior stability increases stratified analyses indicate that smoking status affects the relationship between prior cd4 level and initial cd4 decline we point out advantages associated with the maximum likelihood approach in this particular application

meshfree approach for solving multi dimensional systems of fredholm integral equations via barycentric lagrange interpolation abstract a highly accurate meshfree approach based on the barycentric lagrange basis functions is reported for solving the linear and nonlinear multi dimensional systems of fredholm integral equations fies of the second kind the method is an improved lagrange interpolation technique which possesses high precision and inexpensive procedure the systems of fies are handled with the barycentric formula and transformed into the corresponding linear and nonlinear systems of algebraic equations the stability of the solved integral equation systems is guaranteed by the numerical stability of the barycentric lagrange formula which is dominated by barycentric weights the convergence analysis and error estimation are included some computational results indicate that the method is simple and efficient

numerical complexiton solutions for the complex kdv equation by the homotopy perturbation method in this paper the homotopy perturbation method is extended to investigate the numerical complexiton solutions of the complex kdv equation by constructing special forms of initial conditions three new types of realistic numerical solutions are obtained numerical positon solution expressed by the trigonometric functions numerical negaton solution expressed by the hyperbolic functions and particularly the numerical analytical complexiton solutions expressed by combinations of the two kinds of functions all these numerical solutions obtained can rapidly converge to the exact solutions obtained by lou et al illustrative numerical figures are exhibited the efficiency of the proposed method

second order invariant domain preserving approximation of the euler equations using convex limiting a new second order method for approximating the compressible euler equations is introduced the method preserves all the known invariant domains of the euler system positivity of the density posi

output error estimation for summation by parts finite difference schemes the paper develops a posteriori error estimates of integral output functionals for summation by parts finite difference methods the error estimates are based on the adjoint weighted residual method and take advantage of a variational interpretation of summation by parts discretizations the estimates are computed on a fixed grid and do not require an embedded grid or explicit interpolation operators for smooth boundary value problems containing first and second derivatives the error estimates converge to the exact error as the mesh is refined the theory is verified using linear boundary value problems and the euler equations

stabilized non dissipative approximations of euler equations in generalized curvilinear coordinates we discuss stabilization strategies for finite difference approximations of the compressible euler equations in generalized curvilinear coordinates that do not rely on explicit upwinding or filtering of the physical variables our approach rather relies on a skew symmetric like splitting of the convective derivatives that guarantees preservation of kinetic energy in the semi discrete low mach number limit a locally conservative formulation allows efficient implementation and easy incorporation into existing compressible flow solvers the validity of the approach is tested for benchmark flow cases including the propagation of a cylindrical vortex and the head on collision of two vortex dipoles the tests support high accuracy and superior stability over conventional central discretization of the convective derivatives the potential use for dns les of turbulent compressible flows in complex geometries is discussed

discontinuous galerkin finite element methods for hyperbolic nonconservative partial differential equations we present space and space time discontinuous galerkin finite element dgfem formulations for systems containing nonconservative products such as occur in dispersed multiphase flow equations the main criterium we pose on the weak formulation is that if the system of nonconservative partial differential equations can be transformed into conservative form then the formulation must reduce to that for conservative systems standard dgfem formulations cannot be applied to nonconservative systems of partial differential equations we therefore introduce the theory of weak solutions for nonconservative products into the dgfem formulation leading to the new question how to define the path connecting left and right states across a discontinuity the effect of different paths on the numerical solution is investigated and found to be small we also introduce a new numerical flux that is able to deal with nonconservative products our scheme is applied to two different systems of partial differential equations first we consider the shallow water equations where topography leads to nonconservative products in which the known possibly discontinuous topography is formally taken as an unknown in the system second we consider a simplification of a depth averaged two phase flow model which contains more intrinsic nonconservative products

stable and accurate wave propagation in discontinuous media a time stable discretization is derived for the second order wave equation with discontinuous coefficients the discontinuity corresponds to inhomogeneity in the underlying medium and is treated by splitting the domain each homogeneous sub domain is discretized using narrow diagonal summation by parts operators and then patched to its neighbors by using a penalty method leading to fully explicit time integration this discretization yields a time stable and efficient scheme the analysis is verified by numerical simulations in one dimension using high order finite difference discretizations and in three dimensions using an unstructured finite volume discretization

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

on the use of the quasi likelihood method in teratological experiments this paper concerns the impact of litter effects on the inference of dose response relationships in teratological experiments with binary response kupper et al 1986 biometrics 42 85 98 concluded that when intra litter correlations are dose dependent the use of a common intra litter correlation likelihood based on the beta binomial distribution could lead to severe bias in estimation of the parameter beta which characterizes the dose response relationship we show here that the problems of bias and coverage probability for beta could still be substantial when one uses the likelihood with heterogeneous intra litter correlations we then examine through a simulation study the performance of the quasi likelihood method wedderburn 1974 biometrika 61 439 447 and recommend that this method with a common intra litter correlation parameter be used when the number of litters is small or modest

approximate analytical solution for seepage flow with fractional derivatives in porous media abstract in this paper a new and more exact model for seepage flow in porous media with fractional derivatives has been proposed which has modified the well known darcy law and overcome the continuity assumption of seepage flow a new kind of analytical method of nonlinear problem called the variational iteration method is described and used to give approximate solutions of the problem the results show that the proposed iteration method requiring no linearization or small perturbation is very effective and convenient

an entropy stable nodal discontinuous galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry we design an arbitrary high order accurate nodal discontinuous galerkin spectral element approximation for the non linear two dimensional shallow water equations with non constant possibly discontinuous bathymetry on unstructured possibly curved quadrilateral meshes the scheme is derived from an equivalent flux differencing formulation of the split form of the equations we prove that this discretization exactly preserves the local mass and momentum furthermore combined with a special numerical interface flux function the method exactly preserves the mathematical entropy which is the total energy for the shallow water equations by adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme that is the numerical scheme discretely satisfies the second law of thermodynamics finally with a particular discretization of the bathymetry source term we prove that the numerical approximation is well balanced we provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem

pseudo maximum likelihood estimation theory and applications abstract pseudo maximum likelihood estimation easily extends to k parameter models and is of interest in problems in which the likelihood surface is ill behaved in higher dimensions but well behaved in lower dimensions several signal plus noise or convolution models are examined which exhibit such behavior and satisfy the regularity conditions of the asymptotic theory for specific models a numerical comparison of asymptotic variances suggests that a psuedo maximum likelihood estimate of the signal parameter is uniformly more efficient than estimators that have been advanced by previous authors a number of other potential applications are noted

on modelling metabolism based biomarkers of exposure a comparative analysis of nonlinear models with few repeated measurements establishing and characterizing exposure biomarker relationships is an important problem in molecular epidemiology the problem is difficult due to several complicating features namely the biomarker response is a nonlinear function of exposure and unknown parameters variation in exposure and biomarker levels occurs both within and between subjects and errors tend to be heteroscedastic to overcome some of the statistical challenges in analysing such data it is common for the investigator to make several assumptions about the data structure for example it is common to assume that the natural logarithm of right skewed biomarker measurements lead to homoscedasicity and normality so the effect of outliers is minimized and gauss markov theory is applicable in this paper we compare a lognormal maximum likelihood estimator mle to generalized estimating equations gee for drawing statistical inference in a nonlinear model of a benzene biomarker benzene oxide albumin adducts as a function of benzene exposure we explore the characteristic properties of the lognormal mle under a certain type of model misspecification and compare its small sample performance to the estimating equation approach in simulation studies we show that the multiplicative lognormal model can lead to severe biases for modest deviations from the true outcome biomarker distribution furthermore the lognormal mle can exhibit very poor small sample properties even under the true model all methods are applied in a novel data analysis from a study of benzene exposed workers in china

convergence and error estimation of homotopy perturbation method for fredholm and volterra integral equations abstract in this paper an application of the homotopy perturbation method for solving fredholm and volterra integral equations of the second kind is presented discussed method consists in constructing the functional series sum of which determines the function giving the solution of considered problem conditions under which the constructed series is convergent are formulated and proved in the paper in general the composed series is rather fast convergent thanks to which calculation of few first terms ensures a very good approximation of the sought solution estimation of errors of approximate solution obtained by taking the partial sum of the series is also elaborated in the paper

iterative methods to nonlinear equations homotopy perturbation method is applied to construct a new iterative method for solving nonlinear algebraic equations the convergence of the new scheme is proposed an at least the cubic order of convergence is established several examples are presented and compared to other methods showing the accuracy and fast convergence of the new method

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

approximate solution of nonlinear differential equations with convolution product nonlinearities in this paper a new iteration method is proposed to solve nonlinear problems special attention is paid to nonlinear differential equations with convolution product nonlinearities the results reveal the approximations obtained by the proposed method are uniformly valid for both small and large parameters in nonlinear problems furthermore the first order of approximations are more accurate than perturbation solutions at high order of approximation

a skew symmetric discontinuous galerkin spectral element discretization and its relation to sbp sat finite difference methods this paper shows that the discontinuous galerkin collocation spectral element method with gauss lobatto points dgsem gl satisfies the discrete summation by parts sbp property and can thus be classified as an sbp sat simultaneous approximation term scheme with a diagonal norm operator in the same way sbp sat finite difference schemes can be interpreted as discontinuous galerkin type methods with a corresponding weak formulation based on an inner product formulation common in the finite element community this relation allows the use of matrix vector notation common in the sbp sat finite difference community to show discrete conservation for the split operator formulation of scalar nonlinear conservation laws for dgsem gl and diagonal norm sbp sat based on this result a skew symmetric energy stable discretely conservative dgsem gl formulation applicable to general diagonal norm sbp sat schemes for the nonlinear burgers equation is constructed