volterra fredholm integral equation of the first kind and spectral relationships here the solution in one two and three dimensional for the volterra fredholm integral equation of the first kind is obtained in the space l 2 w xc 0 t t using a numerical method the integral equation of volterra fredholm becomes a linear system of fredholm integral equation when that the kernel of fredholm integral takes a logarithmic form carleman function generalized potential function and macdonald function are considered as special cases

fredholm integral equation with potential kernel and its structure resolvent the purpose of this paper is to establish and solve the fredholm integral equation of the second kind with potential kernel from the semi symmetric hertz problem for two different elastic materials in three dimensions the kernel of the problem is represented in the non homogeneous wave equation also the structure resolvent of the problem is obtained

goursat functions for an infinite plate with a generalized curvilinear hole in ζ plane we used a rational mapping function with complex constants to derive exact and close expressions of goursat functions for the first and second fundamental problems plane elasticity problems of an infinite plate weakened by a hole having arbitrary shape notable the area outside the hole is conformally mapped outside a unit circle by means of the rational mapping the complex variable method has been applied in the procedure and it transforms the fundamental problems to the integro differential equations that can be solved by using cauchy type integrals the hole takes different famous shapes which can be found throughout the nature like tunnels caves excavation in soil or rock etc many previous works have been considered as special cases of this work also many new cases can be derived from the problem

monte carlo algorithms performance analysis for some computer architectures abstract the paper deals with the performance analysis of three monte carlo algorithms for some models of computer architectures to estimate the performance and the speedup of these algorithms we introduce a special modification of the criterion for the time required to achieve a preset probable error and consider a serial von neumann architecture a pipeline architecture and two mimd multiple instruction stream multiple data stream parallel architectures an approach to constructing monte carlo vector algorithms to be efficiently run on pipeline computers has also been considered

toeplitz matrix method and nonlinear integral equation of hammerstein type the existence and uniqueness solution of the nonlinear integral equation of hammerstein type with discontinuous kernel are discussed the normality and continuity of the integral operator are proved toeplitz matrix method is used as a numerical method to obtain a nonlinear system of algebraic equations also many important theorems related to the existence and uniqueness of the produced algebraic system are derived finally numerical examples when the kernel takes a logarithmic and carleman forms are discussed and the estimate error in each case is calculated

the perturbed galerkin method for cauchy singular integral equations with constant coefficients we have considered the numerical solution of cauchy singular integral equations with constant coefficients via a polynomial based galerkin method l 2 and uniform convergence results are proved under holder continuity conditions on the kernel and right hand side and taking into account the quadrature errors produced when inner products are replaced by numerical quadratures these results generalize those of miel who considered only the case of equations of the first kind with index 0

parallel monte carlo computations for solving slae with minimum communications in this paper we introduce new development of parallel monte carlo methods for solving system of linear algebraic equations we discuss compressing the data and we consider a suitable statistical distribution to generate the non zero elements of the coefficient matrix in the system given by x ax f in this way we eliminate sending all elements of the matrix even the compressed partitioned matrix in parallel implementation we obtain only the parameters of the distribution of non zero elements of the coefficient matrix and we just send these parameters therefore we minimize the amount of data sent during the computation

a new iterative monte carlo approach for inverse matrix problem a new approach of iterative monte carlo algorithms for the well known inverse matrix problem is presented and studied the algorithms are based on a special techniques of iteration parameter choice which allows to control the convergence of the algorithm for any column row of the matrix using different relaxation parameters the choice of these parameters is controlled by a posteriori criteria for every monte carlo iteration the presented monte carlo algorithms are implemented on a sun sparkstation numerical tests are performed for matrices of moderate in order to show how work the algorithms the algorithms under consideration are well parallelized

taylor collocation method and convergence analysis for the volterra fredholm integral equations in this paper the taylor collocation method is presented for numerically solving the volterra fredholm integral equations in terms of taylor polynomials this method transforms the integral equation to a matrix equation via the collocation points the convergence analysis of the collocation solution on the integral equation is given the method is computationally attractive and applications are demonstrated through illustrative examples

numerical solution of volterra fredholm integral equations using the collocation method based on a special form of the muntz legendre polynomials abstract this paper presents a computational technique based on a special family of the muntz legendre polynomials to solve a class of volterra fredholm integral equations the relationship between the jacobi polynomials and muntz legendre polynomials in a particular state are expressed the proposed method reduces the integral equation into algebraic equations via the chebyshev gauss lobatto points so that the system matrix coefficients are obtained by the least squares approximation method the useful properties of the jacobi polynomials are exploited to analyze the approximation error the performance and accuracy of our method are examined with some illustrative examples

integral equation with macdonald kernel and its application to a system of contact problem a generalized potential theory method is used to construct a closed form solution of the axi symmetric contact problem for a finite system of impressing stamps of angular form in a plane into a half space occupying the domain

on the solution of a mixed nonlinear integral equation in this paper we consider a mixed nonlinear integral equation of the second kind in position and time the existence of a unique solution of this equation is discussed and proved a numerical method is used to obtain a system of harmmerstein integral equations of the second kind in position then the modified toeplitz matrix method as a numerical method is used to obtain a nonlinear algebraic system many important theorems related to the existence and uniqueness solution to the produced nonlinear algebraic system are derived the rate of convergence of the total error is discussed finally numerical examples when the kernel of position takes a logarithmic and carleman forms are presented and the error estimate in each case is calculated

four properties for complex potentials in power series form based on the basic equations of plane and anti plane problems and the feature of stress fields four important properties for complex potentials expressed in power series expansion in the plane and anti plane elastic fields are obtained first the complex potentials in the plane or anti plane elastic fields are both even functions when the stress states are symmetrical with regard to the origin next it is found that the coefficients of complex potentials in the plane elastic field must be real quantity when the stress states are symmetrical with regard to the x axis the last conclusion is that the complex potentials in the anti plane elastic field only have imaginary coefficients when the stress states are anti symmetric with regard to the x axis then based on the above conclusions some classic solutions are rearrived at which indicates the results derived in the paper are right and may simplify the process of constructing and solving the complex potential functions the present conclusions provide an efficient tool to discover the complex potentials in the sophisticated state

a new numerical approximation for volterra integral equations combining two quadrature rules abstract this paper describes a numerical approximation to the solution of volterra integral equations of the second kind this algorithm combines trapezoidal and simpson rules we prove the convergence of the method numerical examples are provided to illustrate the accuracy of the method

on the solution of linear and nonlinear integral equation the purpose of this paper is to establish the solution of fredholm volterra integral equation of the second kind in the space l 2 w xc 0 t considering the following when fredholm integral term in li 2 w and volterra integral term in 0 t are linear also each of fredholm or volterra integral term is linear while the other term is nonlinear here w is defined as the domain of integration with respect to position while t is consider as the time email protected 0 t t also the fredholm volterra integral equation of the first kind is established as special case of these work many special in one two and three dimensional problems of integral equation are considered representing the kernel of fredholm integral term in the form of logarithmic function carleman function potential and generalized potential function and macdonald function are considered

a solution of a nonlinear integral equation in this work we will prove the existence of integrable solution of nonlinear integral equation of type hammerstein volterra of the second kind by using the technique of measure of weak noncompactness and schauder fixed point theorem also the solution of the integral equation is obtained and studied

least squares approximation method for the solution of hammerstein volterra delay integral equations in this paper an efficient numerical method is developed for solving the hammerstein volterra delay integral equations by least squares ls approximation method which is based on a polynomial of degree n to compute an approximation to the solution of hammerstein volterra delay integral equations the convergence analysis of the approximation solution relative to the exact solution of the integral equation is proved and its accuracy is illustrated on two numerical examples the study of this integral equation is important because it has as a particular case the variant of a mathematical model from epidemiology

new approach to the statistical properties of energy levels the joint distribution of energy eigenvalues of a hamiltonian is derived by means of the usual statistical laws of classical many body systems it makes a transition from the poisson type to the gaussian type depending on the value of a single parameter characteristic of the hamiltonian

biological applications and numerical solution based on monte carlo method for a two dimensional parabolic inverse problem a numerical algorithm involving the combined use of the finite difference method and monte carlo method is proposed as a solution algorithm for a two dimensional parabolic inverse problem with an unknown boundary condition the algorithm is based on the discretize governing equations by finite difference method owing to the application of the finite difference method some large sparse systems of linear algebraic equations are obtained an approach of monte carlo method is employed to solve the linear systems the least squares scheme is proposed to modify unknown boundary condition furthermore two applications of the present problem in biological systems are provided numerical test is performed in order to show the efficiency and accuracy of the present work

invariant formulation for the minimum induced drag conditions of nonplanar wing systems under the hypotheses of linear potential flow and rigid wake aligned with the freestream a configuration invariant analytical formulation for the induced drag minimization of single wing nonplanar systems is presented following a variational approach the resulting euler lagrange integral equation in the unknown circulation distribution is obtained the kernel presents a singularity of the first order and an efficient computational method ideal for the early conceptual phases of the design is proposed munk s theorem on the normalwash and its relation with the geometry of the wing under optimal conditions is naturally obtained with the present method moreover munk s constant of proportionality not provided in his original work is demonstrated to be the ratio between the freestream velocity and the optimal aerodynamic efficiency the augmented munk s minimum induced drag theorem is then formulated additional induced drag theorems are demonstrated following the derivations of this invariant proced

numerical solution of the neural field equation in the two dimensional case we are concerned with the numerical solution of a class of integro differential equations known as neural field equations which describe the large scale dynamics of spatially structured networks of neurons these equations have many applications in neuroscience and robotics we describe a numerical method for the approximation of solutions in the two dimensional case including a space dependent delay in the integrand function compared with known algorithms for this type of equation we propose a scheme with higher accuracy in the time discretization since computational efficiency is a key issue in this type of calculation we use a new method for reducing the complexity of the algorithm the convergence issues are discussed in detail and a number of numerical examples are presented which illustrate the performance of the method

an efficient method for the numerical solution of hammerstein mixed vf integral equations on 2d irregular domains abstract in this work we adapt the implicity linear collocation method for solving nonlinear two dimensional mixed volterra fredholm integral equations of hammerstein type by using imq rbfs on a non rectangular domain the proposed method is mesh free and it is independent of the geometry of domain convergence analysis of the proposed method together with some benchmark examples is provided which support its reliability and numerical stability

iterative method and convergence analysis for a kind of mixed nonlinear volterra fredholm integral equation in this paper the iterative method is presented for numerically solving the nonlinear volterra fredholm integral equation first considering some conditions on k i and l i i 1 2 of the integral equation then we define the equidistance collocation points and the integral part of equation is discretized by newton cotes integration formula finally the approximate solutions of integral equation are obtain by iterative method the convergence analysis of the integral equation is given some numerical examples are given to illustrate the accuracy and dependability of the method

a highly parallel algorithm for computing the action of a matrix exponential on a vector based on a multilevel monte carlo method abstract a novel algorithm for computing the action of a matrix exponential over a vector is proposed the algorithm is based on a multilevel monte carlo method and the vector solution is computed probabilistically generating suitable random paths which evolve through the indices of the matrix according to a suitable probability law the computational complexity is proved in this paper to be significantly better than the classical monte carlo method which allows the computation of much more accurate solutions furthermore the positive features of the algorithm in terms of parallelism were exploited in practice to develop a highly scalable implementation capable of solving some test problems very efficiently using high performance supercomputers equipped with a large number of cores for the specific case of shared memory architectures the performance of the algorithm was compared with the results obtained using an available krylov based algorithm outperforming the latter in all benchmarks analyzed so far

first passage times of two dimensional correlated processes given a two dimensional correlated diffusion process we determine the joint density of the first passage times of the process to some constant boundaries this quantity depends on the joint density of the first passage time of the first crossing component and of the position of the second crossing component before its crossing time first we show that these densities are solutions of a system of volterra fredholm first kind integral equations then we propose a numerical algorithm to solve it and we describe how to use the algorithm to approximate the joint density of the first passage times the convergence of the method is theoretically proved for bivariate diffusion processes we derive explicit expressions for these and other quantities of interest in the case of a bivariate wiener process correcting previous misprints appearing in the literature finally we illustrate the application of the method through a set of examples

a way to obtain monte carlo matrix inversion with minimal error abstract in this paper we present a novel monte carlo algorithm for obtaining the inverse of a given nonsingular matrix a with high accuracy the method is performed by splitting the given matrix a d b where d is a strictly diagonally dominant matrix and it can be easily constructed based on matrix a and b k a such that k can be selected as an arbitrary number greater than or equal to 1 the accuracy of presented algorithm is compatible with any numerical method the theory of the method and its numerical results are also presented

stochastic inverse matrix computation with minimum variance of errors this paper presents the most suitable probability transition matrix using monte carlo method for obtaining inverse matrix in theory and numerical also we find the minimum length of markov chains and the minimum number of trajectories as parameters to make optimum the cost of computations we will show that the selected probability transition has the minimum variance too

integral equation of mixed type and integrals of orthogonal polynomials a method is used to obtain the general solution of the fredholm volterra integral equation of the first kind fviefk in the space l2 0 a c 0 t 0 x a 0 t t the kernel of the fredholm integal term is considered in a generalized discontinuous form which belongs to c 0 a 0 a while the kernel of volterra integral term is a positive continuous function in the class c 0 t many interesting cases of integrals of orthogonal polynomials and spectral relationships are obtained and established from this work

convergence results for continuous time waveform methods for volterra integral equations in this paper the waveform methods for solving systems of second kind volterra integral equations are introduced the convergence properties of continuous time waveform methods on finite length and infinite length time intervals are investigated with particular regard to parallel waveform relaxation methods

integral equation and contact problem for a system of impressing stamps a method is used to construct a closed form solution of the axi symmetric contact problem for a finite system of impressing stamps of angular form in a plane into a half space the problem reduces to a complex mixed problem of the theory of elasticity in cylindrical coordinates

a modified homotopy perturbation method for solving the nonlinear mixed volterra fredholm integral equation the purpose of this paper is to obtain the approximation solution of the strongly nonlinear mixed volterra fredholm integral equation vfie for some strongly nonlinear problems the traditional homotopy perturbation method is divergent so we propose a modified homotopy perturbation method which is still convergent when solving the strongly nonlinear mixed vfie by means of this method an algorithm is successfully established for solving the strongly nonlinear mixed vfie and the convergence of the algorithm is proved strictly finally several examples are presented to illustrate the application of the algorithm

monte carlo method via a numerical algorithm to solve a parabolic problem this paper is intended to provide a numerical algorithm consisted of the combined use of the finite difference method and monte carlo method to solve a one dimensional parabolic partial differential equation the numerical algorithm is based on the discretize governing equations by finite difference method due to the application of the finite difference method a large sparse system of linear algebraic equations is obtained an approach of monte carlo method is employed to solve the linear system numerical tests are performed in order to show the efficiency and accuracy of the present work

random walk on distant mesh points monte carlo methods a new technique for obtaining monte carlo algorithms based on the markov chains with a finite number of states is suggested instead of the classical random walk on neighboring mesh points a general way of constructing monte carlo algorithms that could be called random walk on distant mesh points is considered it is applied to solve boundary value problems the numerical examples indicate that the new methods are less laborious and therefore more efficient

numerical solution of a class of mixed two dimensional nonlinear volterra fredholm integral equations using multiquadric radial basis functions an efficient numerical method is proposed for solving the mixed nonlinear volterra fredholm two dimensional integral equations ies using two dimensional radial basis functions rbfs this method is based on interpolation by radial basis functions including multiquadrics mqs using legendre gauss lobatto nodes and weights also a theorem is proved for convergence analysis some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method

continuous time collocation methods for volterra fredholm integral equations integral equations of mixed volterra fredholm type arise in various physical and biological problems in the present paper we study continuous time collocation time discretization and their global and discrete convergence properties

on the weighted galerkin method of numerical solution of cauchy type singular integral equations the well known weighted galerkin method for the direct numerical solution of cauchy type singular integral equations of the first and the second kind based on the approximation of the unknown function by a finite series of appropriate orthogonal polynomials is shown to be identical to the corresponding method based on the reduction of the cauchy type singular integral equation to an equivalent fredholm integral equation of the second kind and the application to the latter of the weighted galerkin method this result permits the direct transfer of the whole set of convergence and rate of convergence results for the weighted galerkin method of numerical solution of fredholm integral equations with regular kernels to the case of cauchy type singular integral equations an application to the case where chebyshev polynomials are used is also made and the available convergence results for the direct weighted galerkin method are rederived with essentially no analysis

fredholm volterra integral equation and generalized potential kernel a method is used to solve the fredholm volterra integral equation of the first kind in the space l 2 w xc 0 t w x y email protected x 2 y 2

the galerkin method for singular integral equations revisited abstract in an earlier work the author has obtained error bounds for the galerkin method for solving cauchy singular integral equations discovering that the usually neglected constants contain the riemann zeta function when evaluated in the supremum norm the aim of this investigation is twofold to show that the occurrence of the riemann zeta function in the error bound for the chebyshev norm is sharp and secondly to use this result to obtain a class of forcing functions for which the method does not yield an approximate solution differing from the analytical one by at most a prescribed error tolerance these counterexamples indicate that in practical situations for functions exhibiting a behavior similar to the one presented here galerkin s method might not lead to an acceptable solution

on a method for solving an integral equation in the displacement contact problem in this paper the solution in a series form of the integral equation of the mixed type in the space l w xc 0 t is obtained where w x y z

solution of a class of two dimensional integral equations the two dimensional integral equation 1 d r r ds f r0 0 defined on a circular disk d r0 a 0 0 2 is considered in the present paper here r in the kernel denotes the distance between two points p r and p0 r0 0 in d and 0 2 or 2 4 based on some known results of bessel functions integral representations of the kernel are established for 0 2 and 2 4 respectively and employed to solve the corresponding two dimensional integral equation the solutions of the weakly singular integral equation for 0 2 and of the hypersingular integral equation for 2 4 are obtained respectively

global exponential convergence and stability of gradient based neural network for online matrix inversion wang proposed a gradient based neural network gnn to solve online matrix inverses global asymptotical convergence was shown for such a neural network when applied to inverting nonsingular matrices as compared to the previously presented asymptotical convergence this paper investigates more desirable properties of the gradient based neural network e g global exponential convergence for nonsingular matrix inversion and global stability even for the singular matrix case illustrative simulation results further demonstrate the theoretical analysis of gradient based neural network for online matrix inversion

on the numerical solutions of fredholm volterra integral equation toeplitz matrix method and the product nystrom method are described for mixed fredholm volterra singular integral equation of the second kind the results are compared with the exact solution of the integral equation the error of each method is calculated

fredholm volterra integral equation in contact problem in this work the solution of the integral equation of the mixed type in the domain w x y z email protected

integral equations and potential theortic type integrals of orthogonal polynomials abel s theorem is used to solve the fredholm integral equations of the first kind with gauss s hypergeometric kernel the case that the kernel takes general form is discussed in detail and the solution is given here the works of some authors are considered as special cases the discussion focuses on the three dimensional contact problems in the theory of elasticity with general kernel

hybrid legendre polynomials and block pulse functions approach for nonlinear volterra fredholm integro differential equations this paper introduces an approach for obtaining the numerical solution of the nonlinear volterra fredholm integro differential nvfid equations using hybrid legendre polynomials and block pulse functions these hybrid functions and their operational matrices are used for representing matrix form of these equations the main characteristic of this approach is that it reduces nvfid equations to a system of algebraic equations which greatly simplifying the problem numerical examples illustrate the validity and applicability of the proposed method

on the numerical treatment of the singular integral equation of the second kind here a numerical treatment for solving the integral equation of the second kind with cauchy kernel is presented the singular term has been removed and the solution in the legendre polynomial form has been used to obtain a system of linear algebraic equation this system is solved numerically

representation of exact solution for the nonlinear volterra fredholm integral equations abstract in this paper the representation of the exact solution for the nonlinear volterra fredholm integral equations will be obtained in the reproducing kernel space the exact solution is given by the form of series its approximate solution is obtained by truncating the series and a new numerical approximate method is obtained the error of the approximate solution is monotone deceasing in the sense of w 2 1 a b the intrinsic merit of the method given in the paper lies in its speedy convergence in addition it must be pointed out that additional conditions as linearization or unjustified assumptions are not required for nonlinear cases

numerical solution of integral equations 1 a survey of boundary integral equation methods for the numerical solution of laplace s equation in three dimensions 2 superconvergence 3 perturbed projection methods for various classes of operator and integral equations 4 numerical solution of parallel processors of two point boundary value problems of astrodynamics 5 introduction to the numerical solution of cauchy singular integral equations 6 convergence theorems for singular integral equations 7 planing surfaces 8 abel integral equations

on dynamic problem and integral equation in this work the fredholm integral equation of the second kind with logarithmic kernel is established from dynamic elastic problem such problem appears for example when a stamp of length 2a is impressed into the boundary of a strip y h by a variable force p t with time t 0 t t also the strip without fraction lies on a rigid elastic layer of thickness h the solution of the integral equation is obtained using chebyshev polynomial a numerical result is obtained for the problem

iterated collocation methods and their discretizations for volterra integral equations it is known that the numerical solution of volterra integral equations of the second kind by polynomial spline collocation at the gauss legendre points does not lead to local superconvergence at the knots of the approximating function in the present paper we show that iterated collocation approximation restores optimal local superconvergence at the knots but does not yield global superconvergence on the entire interval of integration in contrast to fredholm integral equations with smooth kernels we also analyze the discretized versions obtained by suitable numerical quadrature of the collocation and iterated collocation methods

fredholm volterra integral equation of the first kind and contact problem regular and singular asymptotic methods are applied to one and two dimensional fredholm volterra integral equation f vie of the first kind that arise in the treatment of various two dimensional axisymmetric and three dimensional problems with mixed boundary conditions in the mechanics of continuous media the solution of the integral equation is obtained in the space l 2 w xc 0 t 0

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

fredholm integral equation of the second kind with potential kernel a method is used to solve the fredholm integral equation of the second kind which is investigated from the semi symmetric hertz problem for two different elastic materials in three dimensions also the kernel is represented in the nonhomogeneous wave equation form

numerical methods of singular integral equation for solving some problem in fluid dynamic consider a contact problem of two different layers under certain conditions the aim of this work is obtaining the stress potential function between the two layers and obtaining the solution numerically using two different method toeplitz matrix method and product nystrom method numerical results are considered and the error in each case is computed

further convergence results for the weighted galerkin method of numerical solution of cauchy type singular integral equations the convergence of the weighted lalerkin method based on chcbvshen or jacobi polvnoinials for the direct numerical solution of one dimensional real cauchv tvpe singular integral equations of the first and of the second kind on a finite interval is proved under sufficientlv weak continuitv assumptions for the kernels and the right side functions of thc integral equations

numerical solution of volterra fredholm integral equations based on e svr method in this paper we try to study the numerical methods for solving integral equations from a new perspective machine learning method by means of the idea of kernel e support vector regression machine e svr we construct an optimization modeling for a class of volterra fredholm integral equations and propose a novel numerical method for solving them the proposed method has a certain versatility and can be used to solve some other kinds of integral equations in order to verify the effectiveness of the proposed method we perform a series of comparative experiments with six specific volterra fredholm integral equations and a method proposed in wang et al 2014 experimental results show that the proposed method has a good approximation property

solving system of volterra fredholm integral equations with bernstein polynomials and hybrid bernstein block pulse functions this work approximates the unknown functions based on the bernstein polynomials and hybrid bernstein block pulse functions in conjunction with the collocation method for the numerical solution of system of fredholm volterra integral equations in both methods the system of integral equations is approximated by the gauss quadrature formula with respect to the legendre weight function the proposed methods reduce the system of integral equations to a system of algebraic equations that can be easily solved by any usual numerical methods moreover the convergence analysis of these algorithms will be shown by preparing some theorems numerical experiments are presented to show the superiority and efficiency of proposed methods in comparison with some other well known methods

new advantages to obtain accurate matrix inversion this paper presents a refinement algorithm for improving the inverse of a given nonsingular matrix here we also improve the previously presented results by setting an efficient refinement algorithm we finally presents the performances of the algorithm supporting by the introduced refitment

he s variational iteration method for solving nonlinear mixed volterra fredholm integral equations in this paper he s variational iteration method is used to give the approximate solution of nonlinear mixed volterra fredholm integral equations the method constructs a convergent sequence of functions which approximates the exact solution with few iterations numerical results and a comparison with the exact solution are given which reveal its efficiency

a reliable treatment for mixed volterra fredholm integral equations the main goal of this paper is to demonstrate the use of the modified decomposition method for mixed nonlinear volterra fredholm integral equations the modified method combined with the noise terms phenomena may provide the exact solution by using two iterations only two numerical illustrations are given to show the pertinent features of the technique

taylor polynomial method and error estimation for a kind of mixed volterra fredholm integral equations in this paper an efficient numerical method of taylor polynomial method is developed to solve the volterra fredholm integral equations this method is based on first taking truncated taylor series of the functions in equation and then substituting them into the given equation thereby the equation reduces to a matrix equation finally we can solve the unknown taylor coefficients and obtained the approximation of solution error estimation and illustrative examples are included to demonstrate the validity and applicability of the method

on a symptotic methods for fredholm volterra integral equation of the second kind in contact problems a method is used to obtain the general solution of fredholm volterra integral equation of the second kind in the space l2 c 0 t 0 t t is the domain of integrations the kernel of the fredholm integral term belong to c and has a singular term and a smooth term the kernel of volterra integral term is a positive continuous in the class c 0 t while is the domain of integration with respect to the fredholm integral term besides the separation method the method of orthogonal polynomials has been used to obtain the solution of the fredholm integral equation the principal singular part of the kernel which corresponds to the selected domain of parameter variation is isolated the unknown and known functions are expanded in a chebyshev polynomial and an infinite algebraic system is obtained

galerkin s method for operator equations with nonnegative index with application to cauchy singular integral equations abstract we consider solving operator equation 1 hu ku f where h and k are bounded linear operators between two real hilbert spaces h1 and h2 operator h is assumed to have a finite dimensional nullspace n h and a bounded right inverse h1 h2 h1 and k is compact it follows that dim n h k dim n h so that to obtain uniqueness the m additional conditions 2 u k 1 bk k 1 2 h dim n h m are imposed where the k k 1m are an orthonormal basis for n h to solve 1 and 2 these equations are converted to an equivalent equation of the second kind to which galerkin s method is applied using the basis 1 2 m m 1 n it was shown that this method is equivalent to the method of weighted residuals when h 1 h the adjoint of h the results are applied to obtain convergence proofs of some numerical methods for solving several classes of cauchy singular integral equations whose kernels are only square integrable

different stochastic algorithms to obtain matrix inversion in this paper we present different monte carlo algorithms to obtain inverse matrix here we first determine two algorithms and describe their restrictions to be applicable for computing the inversion of a nonsingular matrix then we establish an efficient algorithm to obtain approximate inversion of an arbitrary nonsingular matrix this algorithm obtain an accurate inversion when the other two algorithm are broken down finally we compare the performances of third algorithm with two previous algorithms

lagrange collocation method for solving volterra fredholm integral equations in this paper the lagrange collocation method is used to solve the volterra fredholm integral equations this method transforms the system of the linear integral equations into matrix equations via lagrange collocation points the lagrange collocation solution of the three kinds of volterra fredholm integral equations and the error estimate of these equations are given some numerical examples are presented to illustrate the accuracy of the method

galerkin solution of a singular integral equation with constant coefficients galerkin methods are used to approximate the singular integral equation email protected x email protected 1 email protected t email protected 1 1k t x f t dt f x 10 are constants in this case f is decomposed as f x 1 x a 1 x bu x where email protected 0 0 is a small enough constant

numerical solution of volterra fredholm integral equations using legendre collocation method a numerical method for solving the volterra fredholm integral equations is presented the method is based upon shifted legendre polynomials approximation the properties of shifted legendre polynomials are first presented these properties together with the shifted gauss legendre nodes are then utilized to reduce the volterra fredholm integral equations to the solution of a matrix equation an estimation of the error is given illustrative examples are included to demonstrate the validity and applicability of the technique

low cost numerical solution for three dimensional linear and nonlinear integral equations via three dimensional jacobi polynomials in recent years numerical methods have been introduced to solve two dimensional volterra and fredholm integral equations in this study a numerical scheme is constructed to solve classes of linear and nonlinear three dimensional integral equations volterra fredholm and mixed volterrafredholm this operational approach is proposed to easily and directly solve these equations at low computational costs the scheme is based on the jacobi polynomials on the interval 0 1 where three variable jacobi polynomials are introduced and their operational matrices of integration and product are derived compared to other existing methods for multidimensional problems the jacobi operational method eliminates the time consuming computations and solely employs the one dimensional operational matrix to construct corresponding multidimensional operational matrices the absolute error of the proposed method is almost constant on the studied interval even at higher dimensions confirming the stability of the proposed operational jacobi method required theorems on the convergence of the method are proved in jacobi weighted sobolev space it is established that the error function vanishes as n increases the method is evaluated using several illustrative examples which indicate the proposed method with lesser computational size compared to the blockpulse functions differential transform and degenerate kernel methods

numerical solution of fredholm volterra integral equation in one dimension with time dependent in this paper we consider fredholm volterra integral equation in one dimension with time dependent the kernel of the fredholm term is assumed to be singular while the kernel of volterra term is continuous the existence of the solution is proved and a numerical method is presented to get an approximate to such solution

a new algorithm with maximal rate convergence to obtain inverse matrix this paper introduces a new efficient algorithm to obtain the accurate inverse of a given nonsingular matrix with maximal rate of convergence the method is performed efficiently based on accurate inversion of the diagonally dominant matrix which is made from the given matrix where it should be inverted the presented algorithm can be employed in any numerical method

taylor polynomial solution of high order nonlinear volterra fredholm integro differential equations in this paper a taylor method is developed to find an approximate solution for high order nonlinear volterra fredholm integro differential equation numerical examples presented to illustrate the accuracy of the method

posteriori error estimates for the nonlinear volterra fredholm integral equations abstract we study the numerical approximation of the nonlinear volterra fredholm integral equations by combining the discrete time collocation method 1 and the new formulation of kumar and sloan 2 which converts an integral equation of the conventional hammerstein form into a conductive form for approximation by a collocation method the intrinsic merit of this alternative formulation lies in its computational savings posteriori error estimates of the method for two typical nonlinearities i e algebraic and exponential nonlinearity are obtained some remarks on the generalization of the method to higher dimensional cases are offered and finally some numerical examples are given

a generalisation of the calogero moser system abstract a generalised calogero moser many body system in which the particles possess extra internal degrees of freedom is introduced and solved by the method of olshanetsky and perelomov further the hierarchy of flows commuting with this system is obtained from a hierarchy of linear systems possessing sl n symmetry by the usual method of reduction thus they are shown to be integrable

least squares approximation method for the solution of volterra fredholm integral equations in this paper an efficient numerical method is developed for solving the volterra fredholm integral equations by least squares approximation method which is based on a polynomial of degree n to compute an approximation to the solution of volterra fredholm integral equations the convergence analysis of the approximation solution relative to the exact solution of the integral equation is proved the reliability and efficiency of the proposed method are demonstrated by some numerical experiments

energy level motion and a supersymmetric hamiltonian from the eigenvalue equation hlambda mod psi n lambda en lambda mod psi n lambda where hlambda identical to h0 lambda v one can derive an autonomous system of first order differential equations for the eigenvalues en lambda and the matrix elements vmn lambda psi m lambda mod v mod psi n lambda where lambda is the independent variable to solve the dynamical system the authors need the initial values en lambda 0 and mod psi n lambda 0 thus one finds the motion of the energy levels en lambda they derive the equations of motion for the extended case hlambda h0 lambda v1 lambda 2v2 and give an application to a supersymmetric hamiltonian

convergence analysis of markov chain monte carlo linear solvers using ulam von neumann algorithm the convergence of markov chain based monte carlo linear solvers using the ulam von neumann algorithm for a linear system of the form x hx b is investigated in this paper we analyze the convergence of the monte carlo solver based on the original ulam von neumann algorithm under the conditions that h 1 as well as rho h 1 where rho h is the spectral radius of h we find that although the monte carlo solver is based on sampling the neumann series the convergence of neumann series is not a sufficient condition for the convergence of the monte carlo solver actually properties of h are not the only factors determining the convergence of the monte carlo solver the underlying transition probability matrix plays an important role an improper selection of the transition matrix may result in divergence even though the condition h 1 holds however if the condition h 1 is satisfied we show that there always exist certain transition matrices that guarantee convergence of