Solution of a System of Linear Fredholm Integral Equations of the Second Kind by Iteration Methods (original) (raw)

Comparison of Some Methods for the Solution of Linear Fredholm Integral Equations of the Second Kind

2019

This paper concern study of some solution technics for the explanation of linear Fredholm integral equations. In this research paper our aim is to compare some new and traditional method that are using for solution of linear Fredholm integral equations. Our essential goal in this paper is to investigate the advantage of each method for solution and solution process of a linear Fredholm integral equation. This research article will focus on Fredholm determinant method, Adomian decomposition method, Modified decomposition method, successive approximation method and direct computational method. Finally, we want to apply this method on a problem and compare the result of the research.

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 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.

A numerical scheme for a class of nonlinear Fredholm integral equations of the second kind

Journal of Computational and Applied Mathematics, 2009

In this paper an iterative approach for obtaining approximate solutions for a class of nonlinear Fredholm integral equations of the second kind is proposed. The approach contains two steps: at the first one, we define a discretized form of the integral equation and prove that by considering some conditions on the kernel of the integral equation, solution of the discretized form converges to the exact solution of the problem. Following that, in the next step, solution of the discretized form is approximated by an iterative approach. We finally on some examples show the efficiency of the proposed approach.

Using (Direct computation, Variation iteration, Successive approximation and Regularization) methods to solve linear Fredholm integral equation and comparison of these methods

International Journal of Research and Analytical Reviews (IJRAR), 2020

Integral equation is the equation in which the unknown function to be determined, appears under integral sign as it presented in introduction I discussed about linear Fredholm integral equation in which it is one kind of integral equation and solved this equation by different methods (Direct Computation, Variational Iteration, Successive approximation and the Regularization methods and comparison of these methods in order to solve linear Fredholm integral equation) This paper has three parts: First part: I introduced the Fredholm integral equation Second part is methods that is written above and on third part, I solved one example by these different method and compare the methods.