A parallel numerical algorithm for two point boundary value FIDEs using a projection method

摘要

In this paper, we develop a parallel algorithm for processing a nonlinear system which represents the discrete solution of a Fredholm integro-differential equation with two-point boundary conditions. The matrix on the left hand side of the system is a five-band near symmetric and Toeplitz system. With appropriate perturbations, it can be factored and solved by parallel implementation of the conjugate gradient method. Two numerical examples illustrate the results.