Analytic-numerical solution with a priori error bounds for coupled time-dependent telegraph equations:: Mixed problems

This paper deals with the construction of analytic-numerical approximations with A priori error bounds for coupled telegraph mixed systems of the form u(tt) + C(t)u(t) + B(t)u = A(t)u(xx), 0 < x < d, t > 0,u(0, t) = u(d,t) = 0, u(x, 0) = f(x),u(t)(x, 0) = g(x), 0 less than or equal to x less than or equal to d. After truncation of an exact series solution and the study of the growth of solutions of certain parametric matrix equations, the following question is addressed: given epsilon > 0 and b > 0, how do we construct an analytic-numerical approximation so that the error with respect to the exact series solution is less than epsilon uniformly in D(b) = ((x, t); 0 less than or equal to x less than or equal to d, 0 less than or equal to t less than or equal to b}. (C) 1999 Elsevier Science Ltd. All rights reserved.