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

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.

delay Fredholm integro-differential equations
pseudospectral method
nonlinear programming
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