Accurate continuous numerical solutions of time dependent mixed partial differential problems

In this paper, a separation of variables method for the solution of time dependent problems of the type utt = c(t)uxx, 0 < x < p, t > 0, subject to u(0, t) = u(p, t) = 0 and u(x, 0) = ƒ(x}, ut(x, 0) = g(x) is developed. First, an exact series solution of the problem is given. Given an admissible error ε > 0, and a bounded domain D(T) = {(x, t); 0 ≤ x ≤ p, 0 ≤ t ≤ T, a continuous numerical solution is constructed so that the approximation error is uniformly upper bounded by ε in D(T)