ON EXACT FINITE DIFFERENCE SCHEME FOR THE COMPUTATION OF SECOND-ORDER FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS (original) (raw)

On solving linear Fredholm integro-differential equations via finite difference-Simpson's approach

Malaya Journal of Matematik

In this paper, a combination of Finite difference-Simpson's approach were applied to solve Linear Fredholm integro-differential equations of second kind by discritising the unknown function, which leads in generating a system of linear algebraic equations. The numerical results obtained from the proposed method were compared with exact solutions of the tested problems which show that the method derived is effective and promising when compared with some existing method in the literature and error estimation of the scheme was derived.

Improved Jacobi matrix method for the numerical solution of Fredholm integro-differential-difference equations

Mathematical Sciences, 2016

This study is aimed to develop a new matrix method, which is used an alternative numerical method to the other method for the high-order linear Fredholm integro-differential-difference equation with variable coefficients. This matrix method is based on orthogonal Jacobi polynomials and using collocation points. The improved Jacobi polynomial solution is obtained by summing up the basic Jacobi polynomial solution and the error estimation function. By comparing the results, it is shown that the improved Jacobi polynomial solution gives better results than the direct Jacobi polynomial solution, and also, than some other known methods. The advantage of this method is that Jacobi polynomials comprise all of the Legendre, Chebyshev, and Gegenbauer polynomials and, therefore, is the comprehensive polynomial solution technique Keywords Orthogonal Jacobi polynomials Á Fredholm integro-differential-difference equation Á Residual error technique Á Matrix method

An Efficient Hybrid Algorithm for the Computation of Second-Order Fredholm Integro-Differential Equations

Pacific Journal of Science and Technology, 2019

In this paper, an efficient hybrid algorithm shall be formulated for the computation of second-order Fredholm integro-differential equations. In developing the algorithm using the method of interpolation and collocation, power series was adopted as the basis function with the integration carried out within a one-step interval. The algorithm derived was then applied on some modeled second-order Fredholm integro-differential equations and from the results obtained; it is obvious that the algorithm is computationally reliable. The basic properties of the algorithm derived were also analyzed.

A method for the numerical solution of the integro-differential equations

Applied Mathematics and Computation, 2007

In this note, the differential transformation is applied to solve the linear first order ordinary Fredholm integro-differential equations. We will give an applicable relation between the one and two-dimensional differential transformation, in order to solve integro-differential equations. Also, we extend this method for searching the numerical solutions of linear higher-order ordinary Fredholm integro-differential equations. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method.

A Taylor polynomial approach for solving the most general linear Fredholm integro‐differential‐difference equations

Mathematical Methods in the Applied Sciences, 2012

In this study, a matrix method is developed to solve approximately the most general higher order linear Fredholm integro‐differential‐difference equations with variable coefficients under the mixed conditions in terms of Taylor polynomials. This technique reduces the problem into the linear algebraic system. The method is valid for any combination of differential, difference and integral equations. An initial value problem and a boundary value problem are also presented to illustrate the accuracy and efficiency of the method. Copyright © 2012 John Wiley & Sons, Ltd.

Application Of The Central-Difference With Half- Sweep Gauss-Seidel Method For Solving First Order Linear Fredholm Integro-Differential Equations

2012

The objective of this paper is to analyse the application of the Half-Sweep Gauss-Seidel (HSGS) method by using the Half-sweep approximation equation based on central difference (CD) and repeated trapezoidal (RT) formulas to solve linear fredholm integro-differential equations of first order. The formulation and implementation of the Full-Sweep Gauss-Seidel (FSGS) and Half- Sweep Gauss-Seidel (HSGS) methods are also presented. The HSGS method has been shown to rapid compared to the FSGS methods. Some numerical tests were illustrated to show that the HSGS method is superior to the FSGS method.

SOLVING FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS BY USING NUMERICAL TECHNIQUES

Kyungnam University Press, 2019

This paper mainly focuses on numerical techniques based on the Adomian Decomposition Method (ADM) and Direct Homotopy Analysis Method (DHAM) for solving Fredholm integro-differential equations of the second kind. The reliability of the methods and reduction in the size of the computational work give this methods wider applicability. Convergence analysis of the exact solution of the proposed methods will be established. Moreover, we proved the uniqueness of the solution. To illustrate the methods, an example is presented.

Numerical method for the solution of high order Fredholm integro-differential difference equations using Legendre polynomials

Ferdowsi University of Mashhad, 2024

This research paper deals with the numerical method for the solution of high-order Fredholm integro-differential difference equations using Legendre polynomials. We obtain the integral form of the problem, which is transformed into a system of algebraic equations using the collocation method. We then solve the algebraic equation using Newton's method. We establish the uniqueness and convergence of the solution. Numerical problems are considered to test the efficiency of the method, which shows that the method competes favorably with the existing methods and, in some cases, approximates the exact solution.

THE EFFECTIVE MODIFICATION OF SOME ANALYTICAL TECHNIQUES FOR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE, 2019

This paper mainly focuses on the recent advances in the homotopy approximated methods for solving Fredholm integro-differential equations of the second kind. This study shows the Homotopy Perturbation Method (HPM) and Direct Homotopy Analysis Method (DHAM), the reliability of the methods and reduction in the size of the computational work give this methods wider applicability. Convergence analysis of the exact solution of the proposed methods will be established. Moreover, we proved the existence and uniqueness of the solution. To illustrate the methods, some examples are presented.