on existence of positive solutions of sturm liouville boundary value problems for a nonlinear singular differential system abstract by employing the fixed point theorem of cone expansion and compression of norm type we investigate the existence of positive solutions of sturm liouville boundary value problems for a nonlinear singular differential system some well known results in the literature are generalized and improved an example is presented to illustrate the application of our main result

a non hybrid method for the pdf equations of turbulent flows on unstructured grids in probability density function pdf methods of turbulent flows the joint pdf of several flow variables is computed by numerically integrating a system of stochastic differential equations for lagrangian particles a set of parallel algorithms is proposed to provide an efficient solution of the pdf transport equation modeling the joint pdf of turbulent velocity frequency and concentration of a passive scalar in geometrically complex configurations in the vicinity of walls the flow is resolved by an elliptic relaxation technique down to the viscous sublayer explicitly modeling the high anisotropy and inhomogeneity of the low reynolds number wall region without damping or wall functions an unstructured eulerian grid is employed to extract eulerian statistics to solve for quantities represented at fixed locations of the domain i e the mean pressure and the elliptic relaxation tensor and to track particles all three aspects regarding the grid make use of the finite element method employing the simplest linear shapefunctions to model the small scale mixing of the transported scalar the interaction by exchange with the conditional mean iecm model is adopted an adaptive algorithm to compute the velocity conditioned scalar mean is proposed that homogenizes the statistical error over the sample space with no assumption on the shape of the underlying velocity pdf compared to other hybrid particle in cell approaches for the pdf equations the current methodology is consistent without the need for consistency conditions the algorithm is tested by computing the dispersion of passive scalars released from concentrated sources in two different turbulent flows the fully developed turbulent channel flow and a street canyon or cavity flow algorithmic details on estimating conditional and unconditional statistics particle tracking and particle number control are presented in detail relevant aspects of performance and parallelism on cache based shared memory machines are discussed

the hybrid method for the pdf equations of turbulent reactive flows consistency conditions and correction algorithms the hybrid method solves the modeled transport equation for the joint pdf of velocity turbulence frequency and compositions for turbulent reactive flows a finitevolume fv method is used to solve the mean conservation equations for mass momentum and energy and the mean equation of state and a particle method is used to solve the modeled pdf equation the method is completely consistent at the level of the governing equations solved by the fv and particle algorithms in this work the conditions to be fulfilled for full consistency at the numerical solution level are examined and the independent consistency conditions are identified then correction algorithms are developed to enforce these independent consistency conditions to achieve full consistency at the numerical solution level in addition a new formulation of the energy equation and the equation of state is developed which is both general and simple the hybrid method is applied to a non premixed piloted jet flame the numerical results show that the correction algorithms are completely successful in achieving consistency the convergence of the method is demonstrated and in particular it is shown that the bias error is dramatically reduced compared to that in previous pdf calculations in addition the results are shown to be in a good agreement with some earlier pdf calculations and also with the available experimental data because of the substantially reduced numerical error for given grid size and number of particles the present hybrid method represents a significant advance in the computational efficiency of particle mesh method for the solution of pdf equations c 2001 academic press

positive solutions for three point boundary value problems with dependence on the first order derivative abstract a new fixed point theorem in a cone is applied to obtain the existence of at least one positive solution for the second order three point boundary value problem x f t x x 0 0 x 0 0 x 1 x where f is a nonnegative continuous function 0 0 1

iterative multiscale finite volume method the multiscale finite volume msfv method for the solution of elliptic problems is extended to an efficient iterative algorithm that converges to the fine scale numerical solution the localization errors in the msfv method are systematically reduced by updating the local boundary conditions with global information this iterative multiscale finite volume i msfv method allows the conservative reconstruction of the velocity field after any iteration and the msfv method is recovered if the velocity field is reconstructed after the first iteration both the i msfv and the msfv methods lead to substantial computational savings where an approximate but locally conservative solution of an elliptic problem is required in contrast to the msfv method the i msfv method allows a systematic reduction of the error in the multiscale approximation line relaxation in each direction is used as an efficient smoother at each iteration this smoother is essential to obtain convergence in complex highly anisotropic heterogeneous domains numerical convergence of the method is verified for different test cases ranging from a standard poisson equation to highly heterogeneous anisotropic elliptic problems finally to demonstrate the efficiency of the method for multiphase transport in porous media it is shown that it is sufficient to apply the iterative smoothing procedure for the improvement of the localization assumptions only infrequently i e not every time step this result is crucial since it shows that the overall efficiency of the i msfv algorithm is comparable with the original msfv method at the same time the solutions are significantly improved especially for very challenging cases

positive solutions to differential inclusions with nonlocal nonlinear boundary conditions we demonstrate the existence of at least one positive solution to the differential inclusion u t f t u t email protected 0 1 equipped with the boundary conditions u 0 h f u and u 1 0 here f is linear functional realized as a lebesgue stieltjes integral and h is a nonlinear function consequently the boundary condition at t 0 can be both nonlocal and nonlinear by imposing an asymptotic condition on h we provide conditions under which the problem will have at least one positive solution

a smart nonstandard finite difference scheme for second order nonlinear boundary value problems a new kind of finite difference scheme is presented for special second order nonlinear two point boundary value problems an artificial parameter is introduced in the scheme symbolic computation is proposed for the construction of the scheme local truncation error of the method is discussed numerical examples are illustrated numerical results show that the method is very effective

a solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion in this paper a stochastic model is presented to simulate the flow of gases which are not in thermodynamic equilibrium like in rarefied or micro situations for the interaction of a particle with others statistical moments of the local ensemble have to be evaluated but unlike in molecular dynamics simulations or dsmc no collisions between computational particles are considered in addition a novel integration technique allows for time steps independent of the stochastic time scale the stochastic model represents a fokker planck equation in the kinetic description which can be viewed as an approximation to the boltzmann equation this allows for a rigorous investigation of the relation between the new model and classical fluid and kinetic equations the fluid dynamic equations of navier stokes and fourier are fully recovered for small relaxation times while for larger values the new model extents into the kinetic regime numerical studies demonstrate that the stochastic model is consistent with navier stokes in that limit but also that the results become significantly different if the conditions for equilibrium are invalid the application to the knudsen paradox demonstrates the correctness and relevance of this development and comparisons with existing kinetic equations and standard solution algorithms reveal its advantages moreover results of a test case with geometrically complex boundaries are presented

sixth order symmetric and symplectic exponentially fitted runge kutta methods of the gauss type the construction of exponentially fitted runge kutta efrk methods for the numerical integration of hamiltonian systems with oscillatory solutions is considered based on the symplecticness symmetry and exponential fitting properties two new three stage rk integrators of the gauss type with fixed or variable nodes are obtained the new exponentially fitted rk gauss type methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions exp lt exp email protected email protected c and in particular sin wt cos wt when email protected email protected r the algebraic order of the new integrators is also analyzed obtaining that they are of sixth order like the classical three stage rk gauss method some numerical experiments show that the new methods are more efficient than the symplectic rk gauss methods either standard or else exponentially fitted proposed in the scientific literature

nonlinear fourth order elliptic equations with nonlocal boundary conditions this paper is concerned with a class of fourth order nonlinear elliptic equations with nonlocal boundary conditions including a multi point boundary condition in a bounded domain of rn also considered is a second order elliptic equation with nonlocal boundary condition and the usual multi point boundary problem in ordinary differential equations the aim of the paper is to show the existence of maximal and minimal solutions the uniqueness of a positive solution and the method of construction for these solutions our approach to the above problems is by the method of upper and lower solutions and its associated monotone iterations the monotone iterative schemes can be developed into computational algorithms for numerical solutions of the problem by either the finite difference method or the finite element method

on a generalization of the miranda theorem and its application to boundary value problems abstract in this paper we have proved a multi valued version of the miranda theorem involving an admissible map in the sense of gorniewicz examples of its application to boundary value problems have been given

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

existence and multiplicity of positive solutions for multi parameter three point differential equations system abstract in this paper we study the existence and multiplicity of positive solutions for the differential equations system x a 1 t f 1 x t y t 0 0 t 1 y a 2 t f 2 x t y t 0 0 t 1 x 0 0 x 1 1 x 1 y 0 0 y 1 2 y 2 where 0 are parameters 0 2 1 1 1 2 0 1 a 1 c 0 1 0 and f 2 c 0 0 0 the system is a semi positone problem since the nonlinear term f 1 is allowed to take negative values and a 2 t may change sign on 0 1 the results are established via fixed point index theory

on a class of modified newton cotes quadrature formulae based upon mixed type interpolation abstract we present quadrature rules which integrate exactly not only polynomials up to a certain degree but also the functions sin kx and cos kx where k is a free parameter the formulae we obtain are modified newton cotes formulae they are derived by replacing the integrand by an interpolation function of the form a cos kx b sin kx n 2j 0cjxj based on equally spaced nodes the total truncation error of the modified quadrature formulae is discussed and a rigorous proof of the error term is given for the modified simpson s 3 8 rule numerical examples show the efficiency of the modified rules and the importance of the error term

a three point formula for numerical quadrature of oscillatory integrals with variable frequency abstract a simple three point formula is constructed for the evaluation of general oscillatory integrals a rigorous derivation of the local error term is presented and the implications to high frequency oscillations are discussed simple examples given include integrals with variable frequency for which the usual filon formula would be inappropriate for cases where filon s formula is appropriate the new formula appears to be computationally more efficient the main application of the formula is to an example chosen from a class of integrals arising in the theory of water waves on a sloping beach comparison with exact results is possible from the work of stoker 16 for a case which whilst special in the physical sense does not simplify the integral involved in all cases the implementation of the formula is as straightforward as the implementation of the ordinary simpson rule

on a new type of mixed interpolation abstract we approximate every function f by a function f n x of the form a cos kx b sin kx n 2 i 0 c i x i so that f jh f n jh for the n 1 equidistant points jh j 0 n that interpolation function f n x is proved to be unique and can be written as the sum of the n th degree interpolation polynomial based on the same points and two correction terms the error term is also discussed the results for this mixed type of interpolation reduce to the known results of the polynomial case as the parameter k is tending to 0 this new interpolation theory will be used in the future for the construction of quadrature rules and multistep methods for ordinary differential equations

trigonometric polynomial or exponential fitting approach the application of a trigonometric polynomial and an exponential fitting approach is compared for a three point formula for second order derivatives for simpson s quadrature rule and for numerov s scheme for second order differential equations the expressions for the occurring parameters are constructed in both the approaches and the behaviour of these parameters with respect to the introduced frequency is studied the errors for specific problems obtained in both the approaches as a function of the frequency are compared

consistent inflow and outflow boundary conditions for transported probability density function methods in transported probability density function pdf methods the pdf transport equations are most often solved with realization based techniques using particles in this paper a consistent treatment of particle in and outflow boundary conditions for transported pdf methods is devised it is shown that the presented approach is simple and most important consistent with the underlying eulerian pdf transport equation this is not the case for other boundary condition implementations discussed in the literature especially if the fluctuating particle velocities are high compared with the averaged ones

singular boundary value problems on a half line singular boundary value problems of nonlinear second order differential equations on a half line are considered the main methods used are modified upper and lower solution techniques necessary and sufficient conditions for the existence of solutions to a class of sublinear singular boundary value problems are obtained

stochastic modeling of evaporating sprays within a consistent hybrid joint pdf framework in the present study a framework for modeling two phase evaporating flow is presented which employs an eulerian lagrangian lagrangian approach for the continuous phase a joint velocity composition probability density function pdf method is used opposed to other approaches such pdf methods require no modeling for turbulent convection and chemical source terms for the dispersed phase the pdf of velocity diameter temperature seen gas velocity and seen gas composition is calculated this provides a unified formulation which allows to consistently address the different modeling issues associated with such a system because of the high dimensionality particle methods are employed to solve the pdf transport equations to further enhance computational efficiency a local particle time stepping algorithm is implemented and a particle time averaging technique is employed to reduce statistical and bias errors in comparison to previous studies a significantly smaller number of droplet particles per grid cell can be employed for the computations which rely on two way coupling between the droplet and gas phases the framework was validated using established experimental data and a good overall agreement can be observed

positive solutions of four point singular boundary value problems abstract existence of c 1 positive solutions for a class of second order nonlinear singular equations of the type x t x t f t x t t 0 1 subjectto four point boundary conditions of the type x 0 ax x 1 bx 0 1 is established existence of c 1 positive solution is proved with the upper and lower solutions method examples are included to show the validity of our results finally the method of quasilinearization is developed to approximate the solution we show that under suitable conditions on f there exists a sequence of solutions of linear problems that converges monotonically and quadratically to the solution of the original nonlinear problem

families of backward differentiation methods based on a new type of mixed interpolation abstract backward differentiation methods based on a new type of mixed interpolation for the first order initial value problems whose solutions are known to be periodic are constructed the angular frequency k is calculated by minimizing the local truncation error within each integration interval the resulting methods depend on a parameter hk h the step length and reduce to classical backward methods if k 0 numerical examples are provided to illustrate the algorithms

necessary and sufficient conditions for the existence of positive solutions of fourth order multi point boundary value problems abstract this paper investigates the existence of positive solutions of singular multi point boundary value problems of fourth order ordinary differential equation with p laplacian a necessary and sufficient condition for the existence of c 2 0 1 positive solution as well as pseudo c 3 0 1 positive solution is given by means of the fixed point theorems on cones

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

positive solution of singular dirichlet boundary value problems for second order differential equation system this paper investigates the existence of positive solutions of singular dirichlet boundary value problems for second order differential system a necessary and sufficient condition for the existence of c 0 1 c 0 1 positive solutions as well as c1 0 1 c1 0 1 positive solutions is given by means of the method of lower and upper solutions and the fixed point theorems our nonlinearity fi t x1 x2 may be singular at x1 0 x2 0 t 0 and or t 1 i 1 2

exponentially fitted numerov methods the error in the estimate of the kth eigenvalue of a regular sturm liouville problem obtained by numerov s method with mesh length h is o k 6h 4 it is shown that the error can be reduced to o k 3h 4 by using one of the three versions of the exponentially fitted numerov method numerical examples demonstrate the usefulness of this approach even for low values of k

twin solutions to singular dirichlet problems the existence of two nonnegative solutions to dirichlet second order boundary value problems is established in this paper our nonlinearity may be singular at y 0 t 0 and or t 1

positive solutions of singular sublinear emden fowler boundary value problems abstract this paper is about the dirichlet boundary value problem of singular sublinear emden fowler equations a necessary and sufficient condition for the existence of positive solutions to this problem has been obtained by using the method of lower and upper solutions the uniqueness of positive solutions has also been discussed

positive solutions of second order systems of boundary value problems abstract the existence of nonnegative solutions of boundary value problems of the form x t a t x t y t 0 y t b t g x t y t 0 x 0 x 1 y 0 y 1 0 is investigated where and g are functions from r p r q into r p and r q respectively and a b are functions defined on 0 1 with values in the spaces of diagonal matrices of order p and q respectively all functions are assumed to be continuous and nonnegativity as well as monotonicity and growth conditions are imposed on and g the existence results hold for a bounded interval of values of if and g are assumed to grow fast and have only nonzero values while if 0 0 0 g 0 0 0 it is shown that under reasonable conditions there exists a nontrivial nonnegative solution for every 0

existence and multiplicity for positive solutions of a multi point boundary value problem abstract in this paper we study the existence and multiplicity of positive solutions of multi point boundary value problems for systems of nonlinear second order ordinary differential equations

a lagrangian stochastic modeling framework for multi phase flow in porous media many of the complex physical processes relevant for compositional multi phase flow in porous media are well understood at the pore scale level in order to study co 2 storage in sub surface formations however it is not feasible to perform simulations at these small scales directly and effective models for multi phase flow description at darcy scale are needed unfortunately in many cases it is not clear how the micro scale knowledge can rigorously be translated into consistent macroscopic equations here we present a new methodology which provides a link between lagrangian statistics of phase particle evolution and darcy scale dynamics unlike in finite volume methods the evolution of lagrangian particles representing small fluid phase volumes is modeled each particle has a state vector consisting of its position velocity fluid phase information and possibly other properties like phase composition while the particles are transported through the computational domain according to their individual velocities the properties are modeled via stochastic processes honoring specified lagrangian statistics note that the conditional expectations of the particle velocities are different for different fluid phases the goal of this paper is to present the general framework for this alternative modeling approach various one and two dimensional numerical experiments demonstrate that with appropriate stochastic rules the particle solutions are consistent with a standard two phase darcy flow formulation in the end we demonstrate how to model non equilibrium phenomena within the stochastic particle framework which will be the main focus of the future work

on a singular nonlinear semilinear elliptic problem where k x c2 b v9 a p 0 1 and l is a real parameter such singular elliptic problems arise in the contexts of chemical heterogeneous catalysts nonnewtonian fluids and also the theory of heat conduction in electrically conducting materials see 3 5 8 9 for a detailed discussion obviously 1 1 cannot have a solution u c2 v9 if k x is not vanishing near v however under various appropriate assumptions on k x we will obtain classical solutions of 1 1 for l belonging to a certain range and we will also obtain some uniqueness criteria here a classical solution is a solution u of 1 1 which belongs to c2 v mc v9 with u 0 in v we also study the boundary behaviour of solutions of 1 1 and we will show that the solution u of 1 1 lies in a certain holder class the special case when k x is negative and l 0 has been studied by several authors the existence and uniqueness of the solution were established by crandall rabinowitz and tartar 6 del pino 7 gomes 10 and lazer and mckenna

on the error estimation for a mixed type of interpolation we analyse the error induced by the approximation of a function by an interpolation function which is a combination of algebraic and first order trigonometric polynomials we prove that under certain conditions this error can be expressed in a similar form as in the purely polynomial case as an application we establish in closed form the local truncation error for a class of extended linear multistep methods of the adams type

accurate computation of higher sturm liouville eigenvalues the computation of eigenvalues of regular sturm liouville problems is considered it is shown that a simple step dependent linear multistep method can be used to reduce the error of the orderk 4 h 2 of the centered finite difference estimate of thek th eigenvalue with uniform step lengthh to an error of orderkh 2 by an appropriate minimization of the local error term of the method one can obtain even more accurate results a comparison of the simple correction techniques of paine de hoog and anderssen and of andrew and paine is given numerical examples demonstrate the usefulness of this correction even for low values ofk

a hybrid algorithm for the joint pdf equation of turbulent reactive flows in this paper a new particle finite volume hybrid algorithm for the joint velocityfrequency composition pdf method for turbulent reactive flows is presented this method is a combination of a finite volume scheme and a particle method the finitevolume scheme is used to solve the reynolds averaged navier stokes equations and the particle method to solve the joint pdf transport equation the motivation is to reduce the bias and the statistical error and to have an algorithm which is more efficient than stand alone particle mesh methods therefore in the particle method we use the smoother mean densityh i and favre averaged velocity u fields computed

existence and uniqueness of positive solution for singular boundary value problem this paper presents two sufficient conditions which guarantee the existence and uniqueness of a positive solution for a class of singular boundary value problems

multiple solutions of singular boundary value problems for differential systems by constructing a special cone and using fixed point index theory in cone this paper investigates the existence of multiple solutions of singular boundary value problems for differential systems

analysis of trigonometric implicit runge kutta methods using generalized collocation techniques based on fitting functions that are trigonometric rather than algebraic as in classical integrators we develop a new class of multistage one step variable stepsize and variable coefficients implicit runge kutta methods to solve oscillatory ode problems the coefficients of the methods are functions of the frequency and the stepsize we refer to this class as trigonometric implicit runge kutta tirk methods they integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency we characterize the order and a stability of the methods and establish results similar to that of classical algebraic collocation rk methods

existence and estimates of solutions for singular nonlinear elliptic problems for both bounded and unbounded domain in r d 3 with smooth boundary the function 0 0 is measurable and satisfies some appropriate hypotheses detailed below the problem 1 has been studied extensively for the special nonlinearity x t p x t 0 indeed in 7 edelson proved the existence of a positive solution u c2 loc r decaying as x 2 n as x provided that p c loc r 0 0 for x 0 and satisfying the growth condition

structure preservation of exponentially fitted runge kutta methods the preservation of some structure properties of the flow of differential systems by numerical exponentially fitted runge kutta efrk methods is considered a complete characterisation of efrk methods that preserve linear or quadratic invariants is given and following the approach of bochev and scovel on quadratic invariants and symplectic structure bit 34 1994 337 345 the sufficient conditions on symplecticity of efrk methods derived by van de vyver a fourth order symplectic exponentially fitted integrator comput phys comm 174 2006 255 262 are obtained further a family of symplectic efrk two stage methods with order four has been derived it includes the symplectic efrk method proposed by van de vyver as well as a collocation method at variable nodes that can be considered as the natural collocation extension of the classical rk gauss method finally the results of some numerical experiments are presented to compare the relative merits of several fitted and nonfitted fourth order methods in the integration of oscillatory systems

a new quadrature rule based on a generalized mixed interpolation formula of exponential type abstract a new method of approximating a function f x uniquely by a function fn x of the form fn x elx au1 kx bu2 kx i 0n 2cixi so that fn x interpolates f x at n 1 equidistant points x0 x0 h x0 nh with h 0 is derived in a closed form various equivalent forms of the interpolation formula are also derived a closed form expression is derived for the error involved in such an approximation with the aid of the newly derived interpolation formula a set of newton cotes quadrature rules of the closed type are also derived the total truncation error involved in these quadrature rules are analysed and closed form expressions for error terms are proposed as conjectures in the two cases when n is odd and when n is even separately a more general exponential type interpolation formula and quadrature rules based upon the generalized mixed interpolation formula are also explained and discussed a few numerical examples are worked out as illustrations and the results are compared with the results of some of the earlier methods

sublinear singular elliptic problems with two parameters abstract we establish several existence and nonexistence results for the boundary value problem u k x g u f x u h x in u 0 on where is a smooth bounded domain in r n and are positive parameters h is a positive function while f has a sublinear growth the main feature of this paper is that the nonlinearity g is assumed to be unbounded around the origin our analysis shows the importance of the role played by the decay rate of g combined with the signs of the extremal values of the potential k x on the proofs are based on various techniques related to the maximum principle for elliptic equations

multiple solutions of some boundary value problems with parameters abstract in this paper we study the existence and multiplicity of nontrivial solutions for the following second order dirichlet nonlinear boundary value problem with odd order derivative u t a u t b u t f t u t for all t 0 1 with u 0 u 1 0 where a b r 1 f c 1 0 1 r 1 r 1 by using the morse theory we impose certain conditions on f which are able to guarantee that the problem has at least one nontrivial solution two nontrivial solutions and infinitely many solutions separately

a general mass consistency algorithm for hybrid particle finite volume pdf methods an algorithm is devised to maintain a correct spatial distribution of computational particles in hybrid particle finite volume fv probability density function pdf methods for chemically reacting turbulent flows the approach is by design compatible with existing fv computational fluid dynamics cfd codes that are used to model practical engineering flows in complex geometric configurations the algorithm is suitable for general three dimensional incompressible or compressible steady or time dependent flows using structured or unstructured stationary or deforming computational meshes it is compatible with a variety of element shapes commonly used in research and engineering cfd codes including hexahedra prisms and tetrahedra robustness accuracy and efficiency of the approach are demonstrated via computations for several two and three dimensional steady and unsteady flow configurations using computational meshes that vary in element type and in mesh quality both composition pdf and velocity pdf methods are employed this work broadens the accessibility of pdf methods for practical turbulent combustion systems

positive solutions for second order m point boundary value problems by using the schauder fixed point theorem and analysis method we establish the existence of solutions for the m point boundary value problem u t a t f u 0 u 0 0 u 1 i 1m 2kiu i b where b ki 0 i 1 2 m 2 0 b

positive solutions of a system of second order boundary value problems involving first order derivatives via r n monotone matrices abstract in this paper we study the existence and multiplicity of positive solutions for the system of second order boundary value problems for nonlinear ordinary differential equations depending on first order derivatives u i f i t u 1 u 1 u n u n u i 0 u i 1 0 i 1 n here n 2 f i c 0 1 r 2 n r r 0 based on a priori estimates achieved by using integral inequalities and r n monotone matrices we use fixed point index theory to establish our main results for the above problem

a multiblock joint pdf finite volume hybrid algorithm for the computation of turbulent flows in complex geometries a new hybrid joint probability density function jpdf solution algorithm for turbulent flows in complex 3d geometries is presented the main focus is to demonstrate the applicability of jpdf methods for complex flows as observed in industrial applications all elements of the algorithm are explained in detail and extensive validation studies are presented a multiblock finite volume solver capable of handling globally unstructured locally structured grids was implemented together with a lagrangian particle method efficient and robust particle management and accurate schemes for estimation and interpolation of particle statistics have been developed for numerical efficiency particle sub time stepping and an implicit finite volume solver are applied a fast coupling strategy was developed together with a multigrid method that allows very fast convergence on refined grids comparison with an established jpdf code for a bluff body stabilized flow shows very good agreement furthermore robustness and consistency of the algorithm for turbulent flow simulations with complex geometry is demonstrated

frequency determination and step length control for exponentially fitted runge kutta methods an exponentially tted runge kutta efrk fth order method with six stages is constructed which exactly integrates rst order di8erential initial value problems whose solutions are linear combinations of functions of the form exp x exp x r or ir by combining this efrk method with an equivalent classical embedded 4 5 runge kutta method a technique is developed for the estimation of the occurring values error and step length control is carried out by using the richardson extrapolation procedure some numerical experiments show the e ciency of the introduced methods c 2001 elsevier science b v all rights reserved

positive solutions for 2p order and 2q order systems of singular boundary value problems with integral boundary conditions abstract in this paper we study the existence multiplicity and nonexistence of positive solutions for 2p order and 2q order systems of singular boundary value problems with integral boundary conditions the results are based upon the fixed point theorem of cone expansion and compression type due to krasnosel skill moreover it generalizes and includes some known results

assessment of numerical accuracy of pdf monte carlo methods for turbulent reacting flows this study is to explore the numerical features of a particle mesh algorithm developed for a stand alone joint velocity frequency composition pdf method for turbulent reactive flows numerical experiments are performed on a piloted jet nonpremixed turbulent flame of methane to characterize and quantify various numerical errors in terms of numerical parameters number of particles per cellnpc number of cells m2 and time step t first a stationary solution is obtained and is verified to be independent of the time step t then the total numerical error is identified as statistical error bias and discretization error it is revealed that the statistical error converges as npc 1 2 and the bias as npc 1 the statistical error can be reduced by time averaging or by performing multiple independent simulation e g with a parallelized program finally the scheme is shown to be second order accurate the spatial discretization error converging as m 2 a modified turbulence frequency model based on the turbulence production to dissipation ratio is shown to improve the numerical behavior of the turbulence model these results demonstrate that the particle mesh method is convergent also the optimal numerical parameters minimizing computational cost subject to a specified error tolerance are estimated an error reduction scheme similar to richardson extrapolation is proposed and shown to be quite effective in reducing the deterministic error

positive solutions for a system of second order multi point boundary value problems abstract in this paper we present some results for positive solutions of a system of nonlinear second order ordinary differential equations subject to multi point boundary conditions

on nonlinear boundary conditions satisfying certain asymptotic behavior abstract in this paper we consider a second order boundary value problem of the form y t a t g y t y 0 y y 1 0 we demonstrate that if the nonlinear functional y satisfies certain asymptotic behavior then the problem will possess at least one positive solution these results generalize and improve on some recent results in the literature on boundary value problems with nonlocal nonlinear boundary conditions and we provide some examples which illustrate these generalizations and improvements

a simple framework for the derivation and analysis of effective one step methods for odes in this paper we provide a simple framework to derive and analyse a class of one step methods that may be conceived as a generalization of the class of gauss methods the framework consists in coupling two simple tools firstly a local fourier expansion of the continuous problem is truncated after a finite number of terms and secondly the coefficients of the expansion are computed by a suitable quadrature formula different choices of the basis lead to different classes of methods even though we shall here consider only the case of an orthonormal polynomial basis from which a large subclass of runge kutta methods can be derived the obtained results are then applied to prove in a simplified way the order and stability properties of hamiltonian bvms hbvms a recently introduced class of energy preserving methods for canonical hamiltonian systems see 2 and references therein a few numerical tests are also included in order to confirm the effectiveness of the methods resulting from our analysis

the existence of solutions to second order singular boundary value problems abstract this article analyzes qualitative properties of solutions to two point boundary value problems for singular ordinary differential equations in particular we form new approaches that ensure that all possible solutions satisfy certain a priori bounds the methods involve differential inequalities the ideas are then applied to generate new existence results for solutions to the boundary value problems under consideration many of the results are novel for both the singular and the nonsingular cases the main concepts are further illustrated via applications to various equations arising in modeling such as the poisson boltzmann equation and the thomas fermi equation with an ionized atom

three positive solutions for second order m point boundary value problems for the second order m point boundary value problemu t f t u 0 0 0 i 1 2 m 2 0 x 1 x 2 x m 2 1 growth conditions are imposed on f which yield the existence of at least three positive solutions by using the leggett williams fixed point theorem the associated green s function for the m point boundary value problem is also given

the asymptotic behaviour of the unique solution for the singular lane emden fowler equation abstract by karamata regular variation theory and constructing comparison functions we show the exact asymptotic behaviour of the unique classical solution u c 2 c near the boundary to a singular dirichlet problem u k x g u u 0 x u 0 where is a bounded domain with smooth boundary in r n g c 1 0 0 lim t 0 g t g t for each 0 for some 0 and k c loc for some 0 1 is nonnegative on which is also singular near the boundary

three positive solutions of singular nonlocal boundary value problems for systems of nonlinear second order ordinary differential equations abstract in this paper we consider the existence of at least three positive solutions of singular nonlocal boundary value problems for systems of nonlinear second order ordinary differential equations the associated green s function for the boundary value problems is first given the proofs of our main results are based upon the leggett williams fixed point theorem finally we give an example to demonstrate our result

frequency evaluation in exponential fitting multistep algorithms for odes we consider the linear multistep algorithms for first order odes and examine the problem of how the frequencies should be tuned in order to obtain the maximal benefit from the exponential fitting versions of such algorithms we find out that the key of the answer consists in analysing the behaviour of the error on further investigating the simple case of two step bdf algorithms we produce formulae for the optimal s and show that if the optimal s are used the order of the method is increased by one unit the reported numerical illustrations suggest that further investigations along these lines deserve a real attention

nonnegative solutions to nonlocal boundary value problems for systems of second order differential equations dependent on the first order derivatives abstract in this paper we consider nonlocal boundary value problems for systems of second order differential equations with dependence on the first order derivatives and deviating arguments by using a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three nonnegative solutions to such problems we investigate our problem both for delayed and advanced arguments i i and also for the case when i t i t t t 0 1 in all cases arguments i i can change the character on 0 1 so in some subinterval i of 0 1 they can be delayed in i and advanced in 0 1 i some remarks concern also the case when differential equations do not depend on the first order derivatives examples illustrate some results

nonlinear superlinear singular and nonsingular second order boundary value problems abstract many new existence theorems are presented for singular and nonsingular second order boundary value problems singularities at y 0 t 0 and t 1 will be discussed

regular article a consistent hybrid finite volume particle method for the pdf equations of turbulent reactive flows the paper describes a new hybrid finite volume fv particle method developed for the solution of the pdf equations for statistically stationary turbulent reactive flows in this approach the conservation equations for mean mass momentum and energy conservation are solved by a fv method while a particle algorithm is employed to solve the fluctuating velocity turbulence frequency compositions joint pdf transport equation the mean velocity and pressure are supplied to the particle code by the fv code which in turn obtains all the reynolds stresses the scalar fluxes and the reaction terms needed in the fv code an important feature of the method is the complete consistency between the set of equations solved by the fv and particle methods the algorithmic and numerical issues arising in the development of the hybrid method are studied in the simple setting of the stochastic ideal flow equations numerical results are obtained for 1d reactive stochastic ideal flow to demonstrate numerical properties of the method the total numerical error is identified as statistical error bias spatial truncation error and temporal truncation error in contrast to the self contained particle method the bias is found to be negligibly small it is shown that all the numerical errors converge at the expected rates finally the global convergence of the hybrid method is demonstrated and the optimal strategy for time averaging that gives the best global convergence rate is investigated