Analytic-numerical solutions with A priori error bounds for time-dependent mixed partial differential problems

The aim of this paper is double. First, we point out that the hypothesis D(t(1))D(t(2)) = D(t(2))D(t(1)) imposed in [1] can be removed. Second, a constructive method for obtaining analytic-numerical solutions with a prefixed accuracy in a bounded domain Omega(t(0),t(1)) = [0,p] x [t(0),t(1)], for mixed problems of the type u(t)(x,t)-D(t)u(xx)(x,t) = 0, 0 < x < p,t > 0, subject to u(0,t) = u(p,t) = 0 and u(x,0) = F(x) is proposed. Here, u(x,t) and F(x) are r-component vectors, D(t) is a C-rXr valued analytic function and there exists a positive number delta such that every eigenvalue z of (1/2) (D(t) + D(t)(H)) is bigger than delta. An illustrative example is included.