An Efficient Numerical Method for a Class of Nonlinear Volterra Integro-Differential Equations

Abstract

We investigate an efficient numerical method for solving a class of nonlinear Volterra integro-differential equations, which is a combination of the parametric iteration method and the spectral collocation method. The implementation of the modified method is demonstrated by solving several nonlinear Volterra integro-differential equations. The results reveal that the developed method is easy to implement and avoids the additional computational work. Furthermore, the method is a promising approximate tool to solve this class of nonlinear equations and provides us with a convenient way to control and modify the convergence rate of the solution.