Exact and analytic numerical solution of coupled diffusion problems in a semi-infinite medium

In this paper, we consider coupled semi-infinite diffusion problems of the form ut(x, t) = A2uxx(x, t), x> 0, t> 0, subject to u(0, t) = B and u(x, 0) = 0, where A is a matrix in , and u(x, t) and B are vectors in r. Given an admissible error ε and a bounded domain D(x0, x1, t0) = {(x, t); 0 < x0 ≤ x ≤ x1, 0 ≤ t ≤ t0, t0 > 0}, an analytic numerical solution is constructed so that the error, with respect to the exact solution, is uniformly upper bounded by ε in D(x0, x1, t0).