Approximate solution of partial integro-differential equation using pseudo-spectral method

Abstract

The subject of this dissertation is to apply a pseudo-spectral method based on Chebyshev cardinal functions to solve parabolic partial integro-differential equations (PIDEs). Since these equations play an essential role in mathematics, physics, and engineering. Finding an approximate solution of the equation is important. The numerical technique is based on the combination between the approximation of the solution by the Chebyshev cardinal functions and using Gauss quadrature to approximate the integral appeared in the equation. The problem is reduced to a nonlinear system of algebraic equations. The convergence analysis is investigated and some numerical examples are given to guaranted the efficiency of the proposed algorithm.