Abstract
This paper describes a numerical method for solving initial-boundary value problems of parabolic equations. Based on a representation of the Trotter product, we derive a new technique for tow-dimensional problems, which does not yield a large linear system, by using a splitting of th coefficient matrix. Furthermore, we prove that the proposed method, which is explicit, is unconditionally stable. Some numerical examples show that our method is superior to the Crank-Nicolson method.
