Application of Bernstein polynomials for solving Fredholm integro-differential-difference equations  

作　　者：Esmail Hesameddini Mehdi Shahbazi 

机构地区：[1]Department of Mathematics Sciences,Shiraz University of Technology,P.O.Box 71555-313,Shiraz,Iran

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2022年第4期475-493,共19页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the Shiraz University of Technology,Shiraz,Iran.

摘　　要：In this paper,the Bernstein polynomials method is proposed for the numerical solution of Fredholm integro-differential-difference equation with variable coefficients and mixed conditions.This method is using a simple computational manner to obtain a quite acceptable approximate solution.The main characteristic behind this method lies in the fact that,on the one hand,the problem will be reduced to a system of algebraic equations.On the other hand,the efficiency and accuracy of the Bernstein polynomials method for solving these equations are high.The existence and uniqueness of the solution have been proved.Moreover,an estimation of the error bound for this method will be shown by preparing some theorems.Finally,some numerical experiments are presented to show the excellent behavior and high accuracy of this algorithm in comparison with some other well-known methods.

关 键 词：Fredholm integro-differential-difference equation Bernstein polynomials existence and uniqueness error estimate 

分 类 号：O175[理学—数学]