CONTINUOUS NUMERICAL-SOLUTIONS AND ERROR-BOUNDS FOR TIME-DEPENDENT SYSTEMS OF PARTIAL-DIFFERENTIAL EQUATIONS - MIXED PROBLEMS

The aim of this paper is to construct continuous numerical solutions w ith 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). Here, u(x, t) and F(x) are r-component vectors and D(t) is a C-rXr valued two-times continuously differentiable function, so that D(t(1))D(t(2)) = D(t(2))D(t(1)) for t(w) greater than or equal to t(1) > 0 and there exists a positive number delta such that every eigenval ue z of (D(t) + D-H(t))/2 with t > 0 is bigger than delta.