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 utt + C(t)ut + B(t)u = A(t)uxx, 0 < x < d, t > 0, u(0, t) = u(d, t) = 0, u(x, 0) = f(x), ut(x, 0) = g(x), 0 ≤ x ≤ 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 ϵ > 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 ϵ uniformly in D(b) = {(x, t); 0 ≤ x ≤ d, 0 ≤ t ≤ b}.