Design and Implementation of Predictors for Additive Semi-Implicit Runge--Kutta Methods

Abstract. Space discretization of some time-dependent partial differential equations gives rise to stiff systems of ordinary differential equations. In this case, implicit methods should be used and therefore, in general, nonlinear systems must be solved. The solutions to these systems are approximated by iterative schemes and, in order to obtain an efficient code, good initializers should be used. Recently, a parallel code based on some Runge-Kutta and additive Runge-Kutta methods has been constructed, focusing especially on additive semi-implicit Runge-Kutta (ASIRK) methods. The aim of the present paper is to develop efficient initializers for these methods.