note on numerical solution of the fredholm singular integro differential equation with cauchy kernel by using taylor series expansion and galerkin method abstract we study the paper of maleknejad and arzhang 2006 with taylor series expansion and galerkin method for fredholm singular integro differential equation with cauchy kernel we point out a basic error in the paper due to the basic error our observations reveal that generally the suggested method should not be considered for a fredholm singular integro differential equation with cauchy kernel

a new efficient method for cases of the singular integral equation of the first kind various cases of cauchy type singular integral equation of the first kind occur rather frequently in mathematical physics and possess very unusual properties these equations are usually difficult to solve analytically and it is required to obtain approximate solutions this paper investigates the numerical solution of various cases of cauchy type singular integral equations using reproducing kernel hilbert space rkhs method the solution u x is represented in the form of a series in the reproducing kernel space afterwards the n term approximate solution u n x is obtained and it is proved to converge to the exact solution u x the major advantage of the method is that it can produce good globally smooth approximate solutions moreover in this paper an efficient error estimation of the rkhs method is introduced finally numerical experiments show that our reproducing kernel method is efficient

solving cauchy integral equations of the first kind by the adomian decomposition method a new approach is presented to resolve cauchy integral equations of the first kind in the general case by first considering a regularized integral equation and then transforming it into a canonical form suitable for applying the adomian decomposition method adm we obtain a decomposition solution f e of the regularized integral equation and prove the convergence of our new combined method as the regularization parameter e 1 the obtained solution is shown to be a sufficiently good approximate solution for the particular cauchy integral equation the proposed method has been tested for a variety of cauchy integral equations which are particularly important in engineering applications e g airfoil design etc

exponentially fitted runge kutta methods abstract exponentially fitted runge kutta methods with s stages are constructed which exactly integrate differential initial value problems whose solutions are linear combinations of functions of the form x j exp x x j exp x r or i r j 0 1 j max where 0 j max s 2 1 the lower bound being related to explicit methods the upper bound applicable for collocation methods explicit methods with s 2 3 4 belonging to that class are constructed for these methods a study of the local truncation error is made out of which follows a simple heuristic to estimate the value error and step length control is introduced based on richardson extrapolation ideas some numerical experiments show the efficiency of the introduced methods it is shown that the same techniques can be applied to construct implicit exponentially fitted runge kutta methods

contact between spheres and general surfaces abstract this work presents a mathematical model to establish the weak form and tangent operator contributions due to contact between spherical surfaces and general surfaces normal and friction components are included such as dissipative actions the main concern herein is the proper consideration of the kinematics of the spherical surface and its influence on contact forces including the appropriate description of the spherical motion by gap functions in normal and tangential directions this leads to the possibility of dealing with complex kinematics of rolling or alternating rolling sliding of the spherical surface mapping its motion on another general surface to achieve that the model is based on rotational and translational degrees of freedom used to map the motion of contacting surfaces one may employ such strategy for interactions between spheres and rigid or flexible bodies modeled using finite element meshes as examples parameterizations of rigid and flexible surfaces are proposed and used practical applications are shown with usage of beam and shell finite elements experiencing contact interactions

numerical evaluation of two dimensional cauchy principal value integrals a twelve point cubature formula has been constructed for the numerical evaluation of two dimensional real cauchy principal value cpv integrals some particular cases of this rule have been discussed and the truncation error associated with the rules have been analysed

on a transplant operator and explicit construction of cauchy type integral representations for p analytic functions we present a new technique for explicit construction of cauchy kernels and cauchy integral representations for a class of generalized analytic functions and p analytic functions

numerical solution of systems of cauchy singular integral equations with constant coefficients abstract this paper deals with the numerical solution of a class of systems of cauchy singular integral equations with constant coefficients the proposed procedure consists of two basic steps the first one is to consider a modified problem equivalent to the original one under suitable conditions the second one is to approximate its solution by means of a vector of polynomial functions such array is constructed by applying a quadrature type method based on gaussian rules that leads to solve a determined and well conditioned linear system the convergence and stability of the method are proved in weighted l 2 spaces some numerical tests are also shown

mixed collocation methods for y f x y inline equatio abstract the collocation methods introduced here are based on linear combinations of trigonometric functions and powers the motivation is to provide better approximations for oscillatory solutions of initial value problems for differential equations of the special form y f x y the resulting methods for two or more collocation points are implicit runge kutta nystrom methods with coefficients which depend on both the fitted angular frequency and the steplength algebraic and trigonometric order conditions are considered and the stability properties of some methods are examined particular mixed collocation methods and other methods for the same class of problems are compared by applying them to a variety of test problems

solving singular integral equations using gaussian quadrature and overdetermined system abstract gauss chebyshev quadrature and collocation at the zeros of the chebyshev polynomial of the first kind t n x and second kind u n x leads to an overdetermined system of linear algebraic equations the size of the coefficient matrix for the overdetermined system depends on the degrees of chebyshev polynomials used we show that we can get more accurate solution using t 4 n 4 x than other t n x the regularization method using generalized singular value decomposition is described and compared to gauss newton method for solving the overdetermined system of equations computational tests show that gsvd with an appropriate choice of regularization parameter gives better solution in solving singular integral equations

explicit solutions of cauchy singular integral equations with weighted carleman shift existence and uniqueness of solutions as well as their explicit representations are obtained for singular integral equations with weighted carleman shift which cannot be reduced to binomial boundary value problems

an approximate numerical method for solving cauchy singular integral equations composed of multiple implicit parameter functions with unknown integral limits in contact mechanics abstract cauchy singular integral equations are widely used in physics and mathematics especially in solid contact mechanics the solution of cauchy singular integral equations composed of explicit functions has already been achieved in existing research however when dealing with the contact problem between two solid bodies with irregular surfaces described by implicit parametric functions difficulties arise when trying to solve the cauchy singular integral because it is composed of multiple implicit parameter functions moreover the integral limits are unknown and constrained by physical characteristics to solve this kind of problem an approximate calculation method with high accuracy will be provided in this paper specifically based on the quadrature method and taking the constraint function of the boundary as the convergence criterion both the integral limits satisfying the physical characteristics condition and the solution of the cauchy singular integral equations composed of multiple parameter functions can be derived by an iterative method finally five different examples are calculated using the new method and the absolute errors between the approximate values provided by the new method and the true values are analysed

mortar based frictional contact formulation for higher order interpolations using the moving friction cone abstract finite element discretizations including contact usually apply the standard nts node to segment element thus a coupling with higher order solid elements leads to inconsistencies in the transmission of contact stresses one can circumvent this using the mortar method which includes a weak projection of the contact constraints in this paper we present a penalty formulation based on the mortar concept for two dimensional large deformation frictional contact the discretization of the contact surfaces contains quadratic approximations which can be used within a quadratic approximation of the solid elements to obtain a simple and efficient matrix formulation the moving friction cone algorithm is applied

robust group analysis using outlier inference neuroimaging group studies are typically performed with the assumption that subjects used are randomly drawn from a population of subjects the population of subjects is assumed to have a distribution of effect sizes associated with it that are gaussian distributed however in practice group studies can include outlier subjects whose effect sizes are completely at odds with the general population for reasons that are not of experimental interest if ignored these outliers can dramatically affect the inference results to solve this problem we propose a group inference approach which includes inference of outliers using a robust general linear model glm approach this approach models the errors as being a mixture of two gaussian distributions one for the normal population and one for the outliers crucially the robust glm is part of a traditional hierarchical group model which uses glms at each level of the hierarchy this combines the benefits of outlier inference with the benefits of using variance information from lower levels in the hierarchy a bayesian inference framework is used to infer on the robust glm while using the lower level variance information the performance of the method is demonstrated on simulated and fmri data and is compared with iterative reweighted least squares and permutation testing

bayesian regression diagnostics with applications to international consumption and income data abstract three variants of friedman s consumption model are analyzed using houthakker s international consumption and income data and the bayesian regression analysis program brap the analysis is focussed on evaluating friedman s proportionality hypothesis various diagnostic procedures are discussed and applied using diffuse and informative prior distributions of the three models considered the logit transformation model is deemed most appropriate and results based on it suggest a departure from the proportionality hypothesis particularlyat low levels of income this result is at variance with houthakker s earlier conclusion that these data are in accord with the proportionality hypothesis

comparing probabilistic methods for outlier detection in linear models summary this paper compares the use of two posterior probability methods to deal with outliers in linear models we show that putting together diagnostics that come from the mean shift and variance shift models yields a procedure that seems to be more effective than the use of probabilities computed from the posterior distributions of actual realized residuals the relation of the suggested procedure to the use of a certain predictive distribution for diagnostics is derived two main procedures for outlier detection have emerged when using the bayesian approach the first of these confines itself to postulating a null model for the generation of the data and then seeks identification methods for outliers with no alternative model to the null entertained examples of work in the category are i use of the predictive distribution for detection ii using the posterior probabilities of various unobserved perturbations and iii looking at the change in a posterior of interest when some observations are deleted these methods will be discussed in 3 of this paper after the basic model is set out in 2 the second procedure takes into account an alternative model for the generation of a subset of the sample as examples various authors have proposed and utilized the mean shift model and the variance inflation model these methods are discussed in 4 of this paper we show in this paper that these procedures can be classified as those which identify outliers by looking at some functions of the predictive density ordinate and those that look at the posterior probabilities of the unobserved residuals the first seems to be effective in overcoming the problem of high leverage outliers in contrast to the latter where outliers are masked by high leverage these results are illustrated by examples in 5

bayesian sensitivity analysis with the fisher rao metric we propose a geometric framework to assess sensitivity of bayesian procedures to modelling assumptions based on the nonparametric fisher rao metric while the framework is general the focus of this article is on assessing local and global robustness in bayesian procedures with respect to perturbations of the likelihood and prior and on the identification of influential observations the approach is based on a square root representation of densities which enables analytical computation of geodesic paths and distances facilitating the definition of naturally calibrated local and global discrepancy measures an important feature of our approach is the definition of a geometric contamination class of sampling distributions and priors via intrinsic analysis on the space of probability density functions we demonstrate the applicability of our framework to generalized mixed effects models and to directional and shape data

bayesian influence analysis a geometric approach in this paper we develop a general framework of bayesian influence analysis for assessing various perturbation schemes to the data the prior and the sampling distribution for a class of statistical models we introduce a perturbation model to characterize these various perturbation schemes we develop a geometric framework called the bayesian perturbation manifold and use its associated geometric quantities including the metric tensor and geodesic to characterize the intrinsic structure of the perturbation model we develop intrinsic influence measures and local influence measures based on the bayesian perturbation manifold to quantify the effect of various perturbations to statistical models theoretical and numerical examples are examined to highlight the broad spectrum of applications of this local influence method in a formal bayesian analysis

normal singular cauchy integral operators with operator valued symbols abstract in this paper we characterize a class of normal isometric coisometric unitary hyponormal singular cauchy integral operators with operator valued or matrix valued symbols on vector valued or c n valued l 2 spaces

volume integral equations for electromagnetic scattering in two dimensions we study the strongly singular volume integral equation that describes the scattering of time harmonic electromagnetic waves by a penetrable obstacle we consider the case of a cylindrical obstacle and fields invariant along the axis of the cylinder which allows the reduction to two dimensional problems with this simplification we can refine the analysis of the essential spectrum of the volume integral operator started in a previous paper costabel et al 2012 and obtain results for non smooth domains that were previously available only for smooth domains it turns out that in the transverse electric te case the magnetic contrast has no influence on the fredholm properties of the problem as a byproduct of the choice that exists between a vectorial and a scalar volume integral equation we discover new results about the symmetry of the spectrum of the double layer boundary integral operator on lipschitz domains

reproducing kernel method of solving singular integral equation with cosecant kernel in the paper a reproducing kernel method of solving singular integral equations sie with cosecant kernel is proposed for solving sie difficulties lie in its singular term in order to remove singular term of sie an equivalent transformation is made compared with known investigations its advantages are that the representation of exact solution is obtained in a reproducing kernel hilbert space and accuracy in numerical computation is higher on the other hand the representation of reproducing kernel becomes simple by improving the definition of traditional inner product and requirements for image space of operators are weakened comparing with traditional reproducing kernel method the final numerical experiments illustrate the method is efficient

numerical solution for system of cauchy type singular integral equations with its error analysis in complex plane abstract in this paper the problem of finding numerical solution for a system of cauchy type singular integral equations of first kind with index zero is considered the analytic solution of such system is known but it is of limited use as it is a nontrivial task to use it practically due to the presence of singularity in the known solution itself therefore a residual based galerkin method is proposed with legendre polynomials as basis functions to find its numerical solution the proposed method converts the system of cauchy type singular integral equations into a system of linear algebraic equations which can be solved easily further hadamard conditions of well posedness are established for system of cauchy singular integral equations as well as for system of linear algebraic equations which is obtained as a result of approximation of system of singular integral equations with cauchy kernel the theoretical error bound is derived which can be used to obtain any desired accuracy in the approximate solution of system of cauchy singular integral equations the derived theoretical error bound is also validated with the help of numerical examples

on the quadratic integral equations and their applications the class of quadratic integral equations contains as a special case numerous integral equations encountered in the theory of radiative transfer the queuing theory the kinetic theory of gases and the theory of neutron transport as a pursuit of this in the following pages sufficient conditions are given for the existence of positive continuous solutions to some possibly singular quadratic integral equations meanwhile we prove the existence of maximal and minimal solutions of our problems the method used here depends on both schauder and schauder tychonoff fixed point principles unlike all previous contributions of the same type no assumptions in terms of the measure of noncompactness were imposed on the nonlinearity of the given functions as far as we know the approach presented in this paper in particular the discussion of the existence of maximal and minimal solutions to the quadratic integral equations was never applied in the field of the quadratic integral equations and so is new

application of jacobi polynomials to approximate solution of a singular integral equation with cauchy kernel abstract in this paper exact solution of the characteristic equation with cauchy kernel on the interval 1 1 is presented next jacobi polynomials are used to derive approximate solutions of the characteristic and general cauchy type singular integral equations moreover estimations of errors of the approximated solutions are presented and proved

nystrom method for cauchy singular integral equations with negative index in this paper the authors propose a nystrom method to approximate the solutions of cauchy singular integral equations with constant coefficients having a negative index they consider the equations in spaces of continuous functions with weighted uniform norm they prove the stability and the convergence of the method and show some numerical tests that confirm the error estimates

a predictive view of the detection and characterization of influential observations in regression analysis abstract assuming a set of observations is available from the general linear model and assuming prior information about parameters we propose a method of assessing the influence of specified subsets of the data when the goal is to predict future observations

a bayesian approach to outlier detection and residual analysis summary an approach to detecting outliers in a linear model is developed an outlier is defined to be an observation with a large random error generated by the linear model under consideration outliers are detected by examining the posterior distribution of the random errors an augmented residual plot is also suggested as a graphical aid in finding outliers we propose a precise definition of an outlier in a linear model which appears to lead to simple ways of exploring data for the possibility of outliers the definition is such that if the parameters of the model are known then it is also known which observations are outliers alternatively if the parameters are unknown the posterior distribution can be used to calculate the posterior probability that any observation is an outlier in a linear model with normally distributed random errors ei with mean zero and variance a 2we declare the ith observation to be an outlier if iei i ko for some choice of k the value of k can be chosen so that the prior probability of an outlier is small and thus outliers are observations which are more extreme than is usually expected realizations of normally distributed errors of more than about three standard deviations from the mean are certainly surprising and worth further investigation such outlying observations can occur under the assumed model however and this should be taken into account when deciding what to do with outliers and in choosing k note that ei is the actual realization of the random error not the usual estimated residual i the problem of outliers is studied and thoroughly reviewed by barnett lewis 1984 hawkins 1980 beckman cook 1983 and pettit smith 1985 the usual bayesian approach to outlier detection uses the definition given by freeman 1980 freeman defines an outlier to be any observation that has not been generated by the mechanism that generated the majority of observations in the data set freeman s definition therefore requires that a model for the generation of outliers be specified and is implemented by for example box tiao 1968 guttman dutter freeman 1978 and abraham box 1978 our method differs in that we define outliers as arising from the model under consideration rather than arising from a separate expanded model our approach is similar to that described by zellner moulton 1985 and is an extension of the philosophy

an embedded pair of exponentially fitted explicit runge kutta methods an embedded pair of exponentially fitted explicit runge kutta rk methods for the numerical integration of ivps with oscillatory solutions is derived this pair is based on the exponentially fitted explicit rk method constructed in vanden berghe et al and we confirm that the methods which constitute the pair have algebraic order 4 and 3 some numerical experiments show the efficiency of our pair when it is compared with the variable step code proposed by vanden berghe et al j comput appl math 125 2000 107

numerical treatment of solving singular integral equations by using sinc approximations abstract in this paper we propose numerical treatment for singular integral equations the methods are developed by means of the sinc approximation with smoothing transformations such approximation is an effective technique against the singularities of the equations and achieves exponential convergence therefore the methods improve conventional results where only polynomial convergence have been reported the resulting algebraic system is solved by least squares approximation and leap frog algorithm estimation of errors of the approximate solution is presented some experimental tests are presented to show the efficient of the proposed methods

numerical solution of various cases of cauchy type singular integral equation abstract in this paper a robust but very simple numerical method is developed to solve various cases of cauchy type singular integral equation for this first bernstein polynomials are defined which are used for approximation of solution of the given singular integral equation then numerical method is introduced by using bernstein polynomials this ultimately leads to solution of a system of linear algebraic equations examples are illustrated to demonstrate simplicity of proposed method results are also compared with those present in literature to claim better efficiency of the method introduced

an unbiased nitsche s formulation of large deformation frictional contact and self contact in this paper we propose an extension of nitsche s method for frictional contact in large elastic deformations in fact we develop an unbiased strategy in which no asymmetry is considered between contact surfaces conversely to the master slave strategy this enables to take into account within the same formalism contact of two elastic bodies as well as self contact we provide a numerical study of the performance and robustness of the method

optimal quadrature formulas for cauchy type singular integrals in sobolev space in the present paper in l 2 m 1 1 space the optimal quadrature formula is constructed for approximate calculation of the cauchy type singular integral explicit formulas for the optimal coefficients are obtained

polygonal finite element methods for contact impact problems on non conformal meshes in this paper a polygonal finite element method is presented for large deformation frictionless dynamic contact impact problems with non conformal meshes the geometry and interfaces of the problem are modeled independent of the background mesh based on the level set method to produce polygonal elements at the intersection of the interface with the regular fe mesh various polygonal shape functions are employed to investigate the capability of polygonal fem technique in modeling frictionless contact impact problems the contact constraints are imposed between polygonal elements produced along the contact surface through the node to surface contact algorithm several contact impact problems are modeled using various polygonal interpolation functions including the wachspress interpolation functions the metric coordinate shape functions the natural neighbor based functions and the mean value coordinate functions to demonstrate the efficiency of proposed technique in modeling contact impact problems

exponentially fitted explicit runge kutta nystrom methods exponentially fitted runge kutta nystrom efrkn methods for the numerical integration of second order ivps with oscillatory solutions are derived these methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions exp t exp t c or equivalently sin t cos t when i r explicit efrkn methods with two and three stages and algebraic orders 3 and 4 are constructed in addition a 4 3 embedded pair of explicit efrkn methods based on the fsal technique is obtained which permits to introduce an error and step length control with a small cost added some numerical experiments show the efficiency of our explicit efrkn methods when they are compared with other exponential fitting type codes proposed in the scientific literature