Some remarks on a new DQ-based method for solving a class of Volterra integro-differential equations

Abstract

In this paper a numerical Picard-like method, which combines successive approximations with integral and differential quadrature, is considered to solve some Volterra integro-differential equations where rational functions are involved. Under certain conditions, the method provides solutions in explicit form, without any recursive computation, and for some cases it is possible to give a formula to compute the related error. Several numerical examples are proposed to illustrate the behaviour of the method, by comparing it, where possible, with some existing methods.