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A Method for Solving Fredholm Integral Equations of the First Kind Based on Chebyshev Wavelets 被引量:2
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作者 M. Bahmanpour M. A.Fariborzi Araghi 《Analysis in Theory and Applications》 2013年第3期197-207,共11页
In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] a... In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other. 展开更多
关键词 first kind fredholm integral equation Galerkin and Modified Galerkin method Legendre wavelets Chebyshev wavelets.
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ON THE REGULARIZATION METHOD OF THE FIRST KIND OFFREDHOLM INTEGRAL EQUATION WITH A COMPLEX KERNEL AND ITS APPLICATION
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作者 尤云祥 缪国平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第1期75-83,共9页
The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate reg... The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate regularized solutions is discussed. As an application of the method, an inverse problem in the two-dimensional wave-making problem of a flat plate is solved numerically, and a practical approach of choosing optimal regularization parameter is given. 展开更多
关键词 inverse problem fredholm integral equation of the first kind complex kernel regularization method
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AUTOMATIC AUGMENTED GALERKIN ALGORITHMS FOR FREDHOLM INTEGRAL EQUATIONS OF THE FIRST KIND
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作者 S.Abbasbandy E.Babolian 《Acta Mathematica Scientia》 SCIE CSCD 1997年第1期69-84,共16页
In recent papers, Babolian & Delves [2] and Belward[3] described a Chebyshev series method for the solution of first kind integral equations. The expansion coefficients of the solution are determined as the soluti... In recent papers, Babolian & Delves [2] and Belward[3] described a Chebyshev series method for the solution of first kind integral equations. The expansion coefficients of the solution are determined as the solution of a mathematical programming problem.The method involves two regularization parameters, Cf and r, but values assigned to these parameters are heuristic in nature. Essah & Delves[7] described an algorithm for setting these parameters automatically, but it has some difficulties. In this paper we describe three iterative algorithms for computing these parameters for singular and non-singular first kind integral equations. We give also error estimates which are cheap to compute. Finally, we give a number of numerical examples showing that these algorithms work well in practice. 展开更多
关键词 fredholm integral equations Galerkin method Regularization parameters Error estimation Ill-Posed problems Product of chebyshev series
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Function-valued partial Padé-type approximation method for estimating eigenvalues of Fredholm integral equation of the second kind
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作者 顾传青 沈进东 《Journal of Shanghai University(English Edition)》 CAS 2007年第6期531-535,共5页
Abstract A new function-valued partial Padé-type approximation was introduced in the polynomial space, and an explicit determinant formula was derived by means of some orthogonal polynomials. This method can be a... Abstract A new function-valued partial Padé-type approximation was introduced in the polynomial space, and an explicit determinant formula was derived by means of some orthogonal polynomials. This method can be applied to estimating surplus eigenvalues of the Fredholm integral equation of the second kind when its partial eigenvalues have been known, and at the same time, it can be applied to solving the approximating solution of the given equation. 展开更多
关键词 linear functional function-valued partial Padé approximation DETERMINANT fredholm integral equation of thesecond kind eigenvalue.
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USING FREDHOLM INTEGRAL EQUATION OF THE SECOND KINDTO SOLVE THE VERTICAL VIBRATION OF ELASTICPLATE ON AN ELASTIC HALF SPACE
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作者 金波 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第2期157-162,共6页
The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By a... The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By applying Abel transformation the dual integral equations are reduced to Fredholm integral equation of the second kind which is solved numerically. 展开更多
关键词 elastic half space elastic plate dynamic response fredholm integral equation of the second kind
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The Successive Approximation Method for Solving Nonlinear Fredholm Integral Equation of the Second Kind Using Maple
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作者 Dalal Adnan Maturi 《Advances in Pure Mathematics》 2019年第10期832-843,共12页
In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the... In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the non-linear Fredholm integral equation of the second kind. Finally, several examples are presented to illustrate the application of the algorithm and results appear that this method is very effective and convenient to solve these equations. 展开更多
关键词 NONLINEAR fredholm integral equation of the SECOND kind Successive Approximation Method Maple18
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Numerical Solutions for Nonlinear Fredholm Integral Equations of the Second Kind and Their Superconvergence
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作者 徐定华 《Advances in Manufacturing》 SCIE CAS 1997年第2期98-104,共7页
This paper discusses the numerical solutions for the nonlinear Fredholm integral equations of thesecond kind. On the basis of the Galerkin method, the author establishes a Galerkin algorithm, a Wavelet-Galerkinalgorit... This paper discusses the numerical solutions for the nonlinear Fredholm integral equations of thesecond kind. On the basis of the Galerkin method, the author establishes a Galerkin algorithm, a Wavelet-Galerkinalgorithm and their corresponding iterated correction schemes for this kind of equations.The superconvergemceof the numerical solutions of these two algorithms is proved. Not only are the results concerning the Hammersteinintegral equations generalized to nonlinear Fredilolm equations of the second kind, but also more precise resultsare obtained by tising the wavelet method. 展开更多
关键词 nonlinear fredholm integral equations Galerkin Inethod ofthonormal multiresoltltion analysis superconvergence.
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Numerical Solution of Two Dimensional Fredholm Integral Equations of the Second Kind by the Barycentric Lagrange Function
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作者 Hongyan Liu Jin Huang Yubin Pan 《Journal of Applied Mathematics and Physics》 2017年第2期259-266,共8页
This paper solves the two dimensional linear Fredholm integral equations of the second kind by combining the meshless barycentric Lagrange interpolation functions and the Gauss-Legendre quadrature formula. Inspired by... This paper solves the two dimensional linear Fredholm integral equations of the second kind by combining the meshless barycentric Lagrange interpolation functions and the Gauss-Legendre quadrature formula. Inspired by this thought, we convert the equations into the associated algebraic equations. The results of the numerical examples are given to illustrate that the approximated method is feasible and efficient. 展开更多
关键词 Two Dimensional fredholm integral equations Barycentric LAGRANGE Interpolation Functions Gauss-Legendre QUADRATURE FORMULA
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Numerical Simulation for Fredholm Integral Equation of the Second Kind
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作者 Peng Guo 《Journal of Applied Mathematics and Physics》 2020年第11期2438-2446,共9页
This work mainly focuses on the numerical simulation of the Fredholm integral equation of the second kind. Applying the idea of Gauss-Lobatto quadrature formula, a numerical method is developed. For the integral item,... This work mainly focuses on the numerical simulation of the Fredholm integral equation of the second kind. Applying the idea of Gauss-Lobatto quadrature formula, a numerical method is developed. For the integral item, we give an approximation with high precision. The existence condition of the solution for the Fredholm equation is given. Furthermore, the error analyses are presented. Finally, the numerical examples verify the theoretical analysis, and show the efficiency of the algorithm we discussed. 展开更多
关键词 integral equation fredholm Gauss-Lobatto Numerical Method
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Integral Operator Solving Process of the Boundary Value Problem of Abstract Kinetic Equation with the First Kind of Critical Parameter and Generalized Periodic Boundary Conditions
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作者 YU De-jian 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第1期110-117,共8页
In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space whic... In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process. 展开更多
关键词 abstract kinetic equation with the first kind of critical parameter boundary value problem of abstract kinetic equation generalized periodic boundary conditions abstract linear integral operator of Volterra type integral operator solving process
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EXTRAPOLATION FOR COLLOCATION METHOD OF THE FIRST KIND VOLTERRA INTEGRAL EQUATIONS
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作者 周爱辉 《Acta Mathematica Scientia》 SCIE CSCD 1991年第4期471-476,共6页
1. Introduction It is known that the following Cauchy problem for a parabolic partial differential equation (where the values at the right boundary, u.(1, t)=v(t) are unknown and sought for) is ill-posed: the solution... 1. Introduction It is known that the following Cauchy problem for a parabolic partial differential equation (where the values at the right boundary, u.(1, t)=v(t) are unknown and sought for) is ill-posed: the solution (v) does not depend continuously on the data (g). In order to treat the ill-posedness and develop the numerical method, one reformulates the problem as a Volterra integral equation of the first kind wish a convolution type kernel (see Sneddon [1], Carslaw and Jaeger [2]) 展开更多
关键词 EXTRAPOLATION FOR COLLOCATION METHOD of THE first kind VOLTERRA integral equationS
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Uniqueness of the Fredholm-Stiltjes Linear Integral Equations Solutions of the Third Kind
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作者 Aizat Toigonbaeva Avyt Asanov +5 位作者 Aisalkyn Kambarova Gumushai Obodoeva Ularbek Moldoyarov Aibek Toktorbaev Aichurok Abdukadyr Kyzy Zhypargul Abdullaeva 《Advances in Linear Algebra & Matrix Theory》 2021年第4期109-116,共8页
Integral equations theoretical parts and applications have been studied and investigated in previous works. In this work, results on investigations of the uniqueness of the Fredholm-Stiltjes linear integral equations ... Integral equations theoretical parts and applications have been studied and investigated in previous works. In this work, results on investigations of the uniqueness of the Fredholm-Stiltjes linear integral equations solutions of the third kind were considered. Volterra integral equations of the first and third kind with smooth kernels were studied, and proof of the existence of a multiparameter family of solutions is described. Additionally, linear Fredholm integral equations of the first kind were investigated, for which Lavrent’ev regularizing operators were constructed. 展开更多
关键词 Solution integral equations UNIQUENESS fredholm-Stiltjes Linear integral equations Third kind
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FAST DENSE MATRIX METHOD FOR THE SOLUTION OF INTEGRAL EQUATIONS OF THE SECOND KIND 被引量:2
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作者 陈汉夫 林福荣 吴荣辉 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1998年第1期105-120,共16页
We present a fast algorithm based on polynomial interpolation to approximate matrices arising from the discretization of second-kind integral equations where the kernel function is either smooth, non-oscillatory and p... We present a fast algorithm based on polynomial interpolation to approximate matrices arising from the discretization of second-kind integral equations where the kernel function is either smooth, non-oscillatory and possessing only a finite number of singularities or a product of such function with a highly oscillatory coefficient function. Contrast to wavelet-like approximations, ourapproximation matrix is not sparse. However, the approximation can be construced in O(n) operations and requires O(n) storage, where n is the number of quadrature points used in the discretization. Moreover, the matrix-vector multiplication cost is of order O(nlogn). Thus our scheme is well suitable for conjugate gradient type methods. Our numerical results indicate that the algorithm is very accurate and stable for high degree polynomial interpolation. 展开更多
关键词 fredholm integral equation POLYNOMIAL interpolation.
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Regularization and Choice of the Parameter for the Third Kind Nonlinear Volterra-Stieltjes Integral Equation Solutions 被引量:1
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作者 Nurgul Bedelova Avyt Asanov +1 位作者 Zhypar Orozmamatova Zhypargul Abdullaeva 《International Journal of Modern Nonlinear Theory and Application》 2021年第2期81-90,共10页
The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was c... The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind. 展开更多
关键词 REGULARIZATION SOLUTIONS Nonlinear Volterra-Stieltjes integral equations Third kind Choice of Regularization Parameter
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Convergence of Discrete Adomian Method for Solving a Class of Nonlinear Fredholm Integral Equations
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作者 Ibrahim Lotfy Hassan Alkalla Reda Abdo Abd-Elmonem Ayman Mohamed Ali Ahmed Gomaa 《Applied Mathematics》 2013年第1期217-222,共6页
In recent papers the solution of nonlinear Fredholm integral equations was discussed using Adomian decomposition method (ADM). For case in which the integrals are analytically impossible, ADM can not be applied. In th... In recent papers the solution of nonlinear Fredholm integral equations was discussed using Adomian decomposition method (ADM). For case in which the integrals are analytically impossible, ADM can not be applied. In this paper a discretized version of the ADM is introduced and the proposed version will be called discrete Adomian decomposition method (DADM). An accelerated formula of Adomian polynomials is used in calculations. Based on this formula, a new convergence approach of ADM is introduced. Convergence approach is reliable enough to obtain an explicit formula for the maximum absolute truncated error of the Adomian’s series solution. Also, we prove that the solution of nonlinear Fredholm integral equation by DADM converges to ADM solution. Finally, some numerical examples were introduced. 展开更多
关键词 NONLINEAR fredholm integral equationS CONTRACTION Mapping Adomian Decomposition Method QUADRATURES Techniques
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A Wavelet Based Method for the Solution of Fredholm Integral Equations
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作者 En-Bing Lin Yousef Al-Jarrah 《American Journal of Computational Mathematics》 2012年第2期114-117,共4页
In this article, we use scaling function interpolation method to solve linear Fredholm integral equations, and we prove a convergence theorem for the solution of Fredholm integral equations. We present two examples wh... In this article, we use scaling function interpolation method to solve linear Fredholm integral equations, and we prove a convergence theorem for the solution of Fredholm integral equations. We present two examples which have better results than others. 展开更多
关键词 Coiflet SCALING Function INTERPOLATION WAVELET fredholm integral equation MULTIRESOLUTION Analysis
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Numerical Solution of the Fredholme-Volterra Integral Equation by the Sinc Function
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作者 Ali Salimi Shamloo Sanam Shahkar Alieh Madadi 《American Journal of Computational Mathematics》 2012年第2期136-142,共7页
In this paper, we use the Sinc Function to solve the Fredholme-Volterra Integral Equations. By using collocation method we estimate a solution for Fredholme-Volterra Integral Equations. Finally convergence of this met... In this paper, we use the Sinc Function to solve the Fredholme-Volterra Integral Equations. By using collocation method we estimate a solution for Fredholme-Volterra Integral Equations. Finally convergence of this method will be discussed and efficiency of this method is shown by some examples. Numerical examples show that the approximate solutions have a good degree of accuracy. 展开更多
关键词 fredholme-Volterra integral equation Sinc FUNCTION COLLOCATION Method
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ORTHOGONAL POLYNOMIALS AND DETERMINANT FORMULAS OF FUNCTION-VALUED PADE-TYPE APPROXIMATION USING FOR SOLUTION OF INTEGRAL EQUATIONS 被引量:2
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作者 顾传青 潘宝珍 吴蓓蓓 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第6期853-860,共8页
To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the s... To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given. 展开更多
关键词 generalized linear functional function-valued Padé-type approximation fredholm integral equation orthogonal polynomial determinant formula
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The Adomian Decomposition Method for Solving Volterra-Fredholm Integral Equation Using Maple 被引量:1
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作者 Hunida M. Malaikah 《Applied Mathematics》 2020年第8期779-787,共9页
In this paper, Adomian decomposition method (ADM) is used to solve the Volterra-Fredholm integral equation. A number of examples have been presented to explain the numerical results, which is the comparison between th... In this paper, Adomian decomposition method (ADM) is used to solve the Volterra-Fredholm integral equation. A number of examples have been presented to explain the numerical results, which is the comparison between the exact solution and the numerical solution, and it is found through the tables and the amount of error between the exact solution and the numerical solution, it is very small and almost non-existent and is also illustrated through the graph how the exact solution of completely applies to the numerical solution This proves the accuracy of the method, which is the Adomian decomposition method (ADM) for solving the Volterra Fredholm integral equation using Maple 18. And that this method is characterized by ease, speed and great accuracy in obtaining numerical results. 展开更多
关键词 Volterra-fredholm integral equation Adomian Decomposition Method Maple18
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Computation of the Eigenvalues of 3<i>D</i>“Charged” Integral Equations 被引量:1
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作者 Diego Caratelli Pierpaolo Natalini Paolo E. Ricci 《Journal of Applied Mathematics and Physics》 2017年第10期2051-2071,共21页
The Rayleigh-Ritz and the inverse iteration methods are used in order to compute the eigenvalues of 3D Fredholm-Stieltjes integral equations, i.e. 3D Fredholm equations with respect to suitable Stieltjes-type measures... The Rayleigh-Ritz and the inverse iteration methods are used in order to compute the eigenvalues of 3D Fredholm-Stieltjes integral equations, i.e. 3D Fredholm equations with respect to suitable Stieltjes-type measures. Some applications are shown, relevant to the problem of computing the eigenvalues of a body charged by a finite number of masses concentrated on points, curves or surfaces lying in. 展开更多
关键词 3D fredholm-Stieltjes integral equations EIGENVALUES Rayleigh-Ritz METHOD Inverse Iteration METHOD
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