Solutions of Linear and Nonlinear Volterra Integral Equations Using Hermite and Chebyshev Polynomials

Abstract

The purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on Galerkin weighted residual approximation. In this method Hermite and Chebyshev piecewise, continuous and differentiable polynomials are exploited as basis functions. A rigorous effective matrix formulation is proposed to solve the linear and nonlinear Volterra integral equations of the first and second kind with regular and singular kernels. The algorithm is simple and can be coded easily. The efficiency of the proposed method is tested on several numerical examples to get the desired and reliable good accuracy.