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