Continuous numerical solutions of coupled mixed partial differential systems using Ferʹs factorization

In this paper continuous numerical solutions expressed in terms of matrix exponentials are constructed to approximate time-dependent systems of the type ut − A(t)uxx − B(t)u = 0, 0 < x < p, t > 0, u(0,t) = u(p,t) = 0, u(x,0) = f(x), 0⩽x⩽p. After truncation of an exact series solution, the numerical solution is constructed using Ferʹs factorization. Given ε > 0 and t0,t1, with 0< t0 < t1 and D(t0,t1) = {s(x,t); 0⩽x⩽p, t0⩽t⩽t1} the error of the approximated solution with respect to the exact series solution is less than ε uniformly in D(t0,t1). An algorithm is also included.