Continuous numerical solutions of coupled mixed partial differential systems using Fer's factorization

Abstract

In this paper continuous numerical solutions expressed in terms of matrix exponentials are constructed to approximate time-dependent systems of the type u t − A(t) u xx − 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 Fer's factorization. Given ε > 0 and t 0, t 1, with 0< t 0 < t 1 and D( t 0, t 1) = { s( x, t); 0⩽ x⩽ p, t 0⩽ t⩽ t 1} the error of the approximated solution with respect to the exact series solution is less than ε uniformly in D( t 0, t 1). An algorithm is also included.