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.
