NUMERICAL METHODS FOR SOLVING LINEAR FREDHOLM- VOLTERRA INTEGRAL EQUATIONS (original) (raw)

An Appropriate Numerical Method for Solving Nonlinear Volterra-Fredholm Integral Equations

International Journal of Mathematics and Systems Science, 2018

This paper is concerned with the numerical solution of the mixed Volterra-Fredholm integral equations by using a version of the block by block method. This method efficient for linear and nonlinear equations and it avoids the need for spacial starting values. The convergence is proved and finally performance of the method is illustrated by means of some significative examples.

Numerically Solving Volterra and Fredholm Integral Equations 1

2013

Abstract: Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM) is known to be two powerful tools for solving many functional equations such as ordinary and partial differential and integral equations. In this paper (HAM) is applied to solve linear Fredholm and Volterra first and second kind integral equations, the deformation equations are solved analytically by using MATLAB integration functions. Numerical techniques for solving deformation equation are also applied using interpolation methods and Gaussian integration. Auxiliary parameter h is also used experimentally to control convergence of partial sum of series solution. Several examples are tested by these methods and numerical results are compared with exact solution or existing numerical results to demonstrate the efficiency of the methods. These methods can be generalized to non-linear Volterra and Fredholm integral equation. The analytical and numerical results show the performance and reliability of prese...

A STUDY OF SOME EFFECTIVE TECHNIQUES FOR SOLVING VOLTERRA-FREDHOLM INTEGRAL EQUATIONS

Watam Press, 2019

In this paper, based on a strictly convex fuzzy number space and the Riemann integral of fuzzy-number-valued function which is taken value in the space, we propose iterative procedures based on Adomian Decomposition Method (ADM), Modified Adomian Decomposition Method (MADM) and Modified Variational Iteration Method (MVIM) to solve fuzzy Volterra-Fredholm integral equations of the second kind. That, a fuzzy Volterra-Fredholm integral equation has been converted to a system of Volterra-Fredholm integral equations in crisp case. The approximated methods using to find the approximate solution of this system and hence obtain an approximation for the fuzzy solution of the fuzzy Volterra-Fredholm integral equation. Moreover, we will prove the uniqueness of the solution and convergence of the proposed methods. Also, some numerical examples are included to demonstrate the validity and applicability of the proposed techniques.

Numerically Solving Volterra and Fredholm Integral Equations

2012

Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM) is known to be two powerful tools for solving many functional equations such as ordinary and partial differential and integral equations. In this paper (HAM) is applied to solve linear Fredholm and Volterra first and second kind integral equations, the deformation equations are solved analytically by using MATLAB integration functions. Numerical techniques for solving deformation equation are also applied using interpolation methods and Gaussian integration. Auxiliary parameter h is also used experimentally to control convergence of partial sum of series solution. Several examples are tested by these methods and numerical results are compared with exact solution or existing numerical results to demonstrate the efficiency of the methods. These methods can be generalized to non-linear Volterra and Fredholm integral equation. The analytical and numerical results show the perfo rmance and reliability of presented method.

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.

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.

A new computational method for Volterra-Fredholm integral equations

Computers & Mathematics with Applications, 1999

The main purpose of this article is to demonstrate the use of the Adomian decomposition method for mixed nonlinear Volterra-Fredholm integral equations. A bound is also given for the Adomian decomposition series. Finally, numerical examples are presented to illustrate the implementation and accuracy of the decomposition 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.

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.