Legendre-Galerkin method for the nonlinear Volterra-Fredholm integro-differential equations

Abstract

Abstract The study of solving nonlinear integro-differential equations in Volterra-Fredholm type presents in this paper. The proposed method tends to use Legendre polynomials as a basis in the Galekin method to obtain the numerical solution. We use the Newton method to get the numerical solution of the nonlinear equations resulted from applying the Galerkin method. The comparison of the present study with the existing results in the literature shows an excellent agreement. Numerical examples explain the convergence, applicability, and efficiency of algorithm.