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(t1)D(t2) = D(t2)D(t1) imposed in [1] can be removed. Second, a constructive method for obtaining analytic-numerical solutions with a prefixed accuracy in a bounded domain Ω(t0,t1) = [0,p] × [t0,t1], for mixed problems of the type ut(x,t) − D(t)uxx(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 Cr × r valued analytic function and there exists a positive number δ such that every eigenvalue z of (1/2) (D(t) + D(t)H) is bigger than δ. An illustrative example is included.