Solving a Class of Two-Dimensional Volterra Integral Equations.

Abstract

In this dissertation , Taylor collocation method is applied to obtain the approximate solution for two-dimensional linear Volterra integral equations of the first and second kind, and two-dimensional partial differential equations of the second order. The method is based on the use of Taylor polynomials in two dimensional. The pproximate solution is given by using explicit schemes and the method is proved to be convergent with respect to the aximum norm. Some numerical examples are included to prove the validity of the presented convergent method.