Galerkin method for nonlinear volterra-fredholm integro-differential equations based on Chebyshev polynomials

الملخص EN

We aim in this paper to develop a new algorithm for approximating the analytic solution for the integrodifferentialequations using the Galerkin method.

The bases of the solution obtained by the proposed algorithmare Chebyshev polynomials.

Meanwhile, some theorems are deducted to simplify the nonlinear algebraic setresulted from applying the Galerkin method, while Newton's method is used to solve the resulting nonlinearalgebraic system.

Examples are introduced to prove the effectiveness of this algorithm in comparison with someother methods.