Analytical-numerical solution of coupled singular mixed diffusion type problems

The aim of this paper is to construct analytical approximate solutions for systems of partial differentiable equations of the form Eu-t(x, t) - Au-xx(x, t) = 0 for x is an element of [0, 1] and t > 0, subject to u(0, t) = 0 and Bu(1, t) + Cu-x(1, t) = 0 for t > 0 and u(x, 0) = f(x), x is an element of [0, 1]. Here, u(x, t), f(x) are m-component vectors and E, A, B, C are m(th)-order complex matrices where B and C are not simultaneously singular and E is singular. Scalar regular Sturm-Liouville problems are used to find exact series solution; the series is truncated, then its matrix exponential terms replaced by Taylor series approximation. With appropriate selections, the resulting approximate solution will be arbitrarily close (uniformly) on a domain [0, 1] x [t(0), t(1)] where t(o) > 0. (C) 1999 Elsevier Science Ltd. All rights reserved.