Abstract
In this paper, a separation of variables method for the solution of time dependent problems of the type u tt = c(t)u xx , 0 < x < p, t > 0, subject to u(0, t) = u(p, t) = 0 and u( x, 0) = ƒ( x}, u t ( 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)
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