Iterative Operator-Splitting Methods with higher order Time-Integration Methods and Applications for Parabolic Partial Differential Equations

Abstract

In this paper we design higher order time integrators for systems of stiff ordinary differential equations. We could combine implicit Runge-Kutta- and BDF-methods with iterative operator-splitting methods to obtain higher order methods. The motivation of decoupling each complicate operator in simpler operators with an adapted time-scale allow us to solve more efficiently our problems. We compare our new methods with the higher order Fractional-Stepping Runge-Kutta methods, developed for stiff ordinary differential equations. The benefit will be the individual handling of each operators with adapted standard higher order time-integrators. The methods are applied to convection-diffusion-reaction equations and we could obtain higher order results. Finally we discuss the iterative operator-splitting methods for the applications to multi-physical problems.