Collocation Approximation Methods for the Numerical Solutions of General nth Order Nonlinear Integro-Differential Equations by Canonical Polynomial

Abstract

In this Paper, a method based on the Tau method by canonical polynomials as the basis function is developed to find the numerical solutions of general nth order nonlinear integro-differential equations. The differential parts appearing in the equation are used to construct the canonical polynomials and the nonlinear cases are linearized by the Newton’s linearization scheme of order n and hence resulted to the use of iteration. Numerical examples are given to illustrate the effectiveness, convergence and the computational cost of the methods.