Galerkin Method for Nonlinear Volterra-Fredholm Integro-Differential Equations Based on Chebyshev Polynomials

Abstract

We aim in this paper to develop a new algorithm for approximating the analytic solution for the integrodifferential equations using the Galerkin method. The bases of the solution obtained by the proposed algorithm are Chebyshev polynomials. Meanwhile, some theorems are deducted to simplify the nonlinear algebraic set resulted from applying the Galerkin method, while Newton's method is used to solve the resulting nonlinear algebraic system. Examples are introduced to prove the effectiveness of this algorithm in comparison with some other methods.