An Application of the Weighted Mean Value Method to Fredholm integral equations with Toeplitz plus Hankel kernels (original) (raw)

Multistage Integral Mean Value Method for the Fredholm Integral Equations of the Second Kind

2020

In this paper, a modified multistage integral mean value method, for handling the Fredholm integral equations of the second kind, to improve the accuracy of the solutions, is applied. The application of the proposed algorithm is based on the applying the multistage schema to the modified integral mean value method. Also, the equivalency of integral mean value method and degenerate kernel method (DKM) is established. The efficiency of the approach will be shown by applying the procedure on some prototype examples. The Mathematica programs based on the procedures in this paper are designed. MSC: 45Fxx; 45G10; 35C10

An algorithm based on the regularization and integral mean value methods for the Fredholm integral equations of the first kind

Applied Mathematical Modelling, 2013

In this paper, an algorithm based on the regularization and integral mean value methods, to handle the ill-posed multi-dimensional Fredholm equations, is introduced. The application of this algorithm is based on the transforming the first kind equation to a second kind equation by the regularization method. Then, by converting the first kind to a second kind, the integral mean value method is employed to handle the resulting Fredholm integral equations of the second kind. The efficiency of the approach will be shown by applying the procedure on some examples.

Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem

Applied Mathematical Modelling, 2011

In this paper, we present a new semi-analytical method for solving linear and nonlinear Fredholm integral and integro-differential equations of the second kind and the systems including them. The main idea in this method is applying the mean value theorem for integrals. Some examples are presented to show the ability of the model. The results confirm that the method is very effective and simple.

Algebraic Kernel Method for Solving Fredholm Integral Equations

International Frontier Science Letters, 2016

In this paper, we study the exact solution of linear Fredholm integral equations using some classical methods including degenerate kernel method and Fredholm determinants method. We propose an analytical method for solving such integral equations. This work has some goals related to suggested technique for solving Fredholm integral equations. The primary goal gives analytical solutions of such equations with minimum steps. Another goal is to compare the suggested method used in this study with classical methods. The final goal is that the propose method is an explicit formula that can be studied in detail for non-algebraic function kernels by using Taylor series expansion and for system of Fredholm integral equations.

A comparison of Numerical Solutions for Linear Fredholm Integral Equation of the Second Kind

Journal of Physics: Conference Series

The aim of this paper,we offereda new numerical methodwhich is Touchard Polynomials (T-Ps) for solving Linear Fredholm Integral Equation of the Second Kind (LFIE2-K), to find approximating Numerical Solution (N-S). At the beginning, we demonstrate (T-Ps) andconstruct the operational matrix which is a matrix representation for solution. The algorithm and someexamples are given; comparing the numerical results of proposed method with the numerical results of the other numerical method which is Bernstein Polynomials (B-Ps).Wewill show the high resolution of results by proposed method.The comparison between the Exact Solution(E-S) and the results of two methods are given by calculating absolute value of error and the Least Square Error (L.S.E).The results are calculated in Matlabcode.

Numerical Solution of the Linear Fredholm Integral Equations of the Second Kind

2010

The theory of integral equation is one of the major topics of applied mathematics. The main purpose of this paper is to introduce a numerical method based on the interpolation for approximating the solution of the second kind linear Fredholm integral equation. In this case, the divided difierences method is applied. At last, two numerical examples are presented to show the accuracy of the proposed method.

A Modified Degenerate Kernel Method for the System of Fredholm Integral Equations of the Second Kind

Iranian Journal of Mathematical Sciences and Informatics, 2019

In this paper, the system of Fredholm integral equations of the second kind is investigated by using a modified degenerate kernel method (MDKM). To construct a MDKM the source function is approximated by the same way of producing degenerate kernel. The interpolation is used to make the needed approximations. Lagrange polynomials are adopted for the interpolation. The equivalency of proposed method and Lagrange-collocation method is shown. The error and convergence analysis of the algorithm are given strictly. The efficiency of the approach will be shown by applying the procedure on some prototype examples.

Computational Methods for Solving Fredholm Integral Equation of the Second Kind

2013

The main purpose of this paper is the numerical solution of the one-dimensional linear Fredholm integral equation of the second kind by the collocation and the Nystrom methods, using the Lagrange basis functions for piecewise linear interpolation. Some effective algorithms implementing these methods using the Matlab software have been constructed. The numerical results of test examples are also included to verify the performance of the proposed algorithms.