The single term alternating group explicit (stage) methods for solving periodic parabolic problems

Abstract

In 1983. Evans and Abdullah presented a new method, i.e. group explicit for the finite difference solution of a parabolic partial differential equation with Dirichlet boundary conditions. In this paper, we extend this group explicit strategy to a similar problem with periodic boundary conditions The stability of the method is discussed and the results of numerical experiments compared. Finally, a modified form of the group explicit method is presented. The new method is shown to possess similar convergence and stability properties with a reduced computational effort for the same problem.