Analytic numerical approximation with a priori error bound for the wave equation with time dependent coefficient

This paper deals with the problem utt = c(t) uxx, u(0,t) = u(p,t) = 0, t > 0, u(x,0) = f(x), ut(x,0) = g(x), 0 ≤ x < p, where c(t) is a positive continuously differentiable function. First, an exact series solution is given using separation of variables. Then, after truncation, using Frobenius method and Bernstein polynomials for solving the underlying differential equations, an analytic approximated solution is constructed whose error with respect to the exact solution is less than a prefixed error in a bounded subdomain D(T) = {(x, t); 0 ≤ x ≤ p, 0 < t < T}.