A numerical study of stiffness effects on some high order splitting methods

Abstract

In this paper we compare operator splitting methods of first, second, third and fourth orders that are applied to problems with stiff matrices. In order to efficiently solve the resultant subproblems is necessary to use implicit Runge-Kutta methods. It is known that, in this context, the precision order of operator splitting schemes is reduced. Furthermore, we propose a fifth order operator splitting method that is obtained by applying Richardson extrapolation to a fourth order method. All methods are tested with a model problem with matrices such that its condition number is taken up to 20,000. Our conclusion is that order reduction is more severe for low order operator splitting methods.