ANALYTIC NUMERICAL-SOLUTION OF COUPLED SEMIINFINITE DIFFUSION-PROBLEMS

In this paper, we consider coupled semi-infinite diffusion problems of the form u(t)(x, t)-A(2) u(xx), (x, t) = 0, x > 0, t > 0, subject to u(0, t) = B and u(x, 0) = 0, where A is a matrix in C-tau X tau, and u (x, t), and B are vectors in C-r. Using the Fourier sine transform, an explicit exact solution of the problem is proposed. Given an admissib le error epsilon and a domain D(x(0), t(0)) = {(x, t); 0 less than or equal to x less than or equal to x(0), t greater than or equal to t(0) > 0}, an analytic approximate solution is constructed so that the err or with respect to the exact solution is uniformly upper bounded by ep silon in D(x(0), t(0)).