Solving a class of nonlinear delay Fredholm integro-differential equations with convergence analysis

Abstract

The main idea proposed in this article is an efficient shifted Legendre pseudospectral method for solving a class of nonlinear delay Fredholm integro-differential equations. In this method, first we transform the problem into an equivalent continuous-time optimization problem and then utilize a shifted pseudospectral method to discrete the problem. By this method, we obtained a nonlinear programming problem. Having solved the last problem, we can obtain an approximate solution for the original delay Fredholm integro-differential equation. Here, the convergence of the method is presented under some mild conditions. Illustrative examples are included to demonstrate the efficiency and applicability of the presented technique.