Numerical Simulation of a Model for Transport and Reaction of Radionuclides
LSSC '01 Proceedings of the Third International Conference on Large-Scale Scientific Computing-Revised Papers
Weighted iterative operator-splitting methods: stability-theory
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
Splitting methods and their application to the abstract cauchy problems
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
A domain decomposition method based on the iterative operator splitting method
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
A second order self-consistent IMEX method for radiation hydrodynamics
Journal of Computational Physics
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In this paper we design higher-order time integrators for systems of stiff ordinary differential equations. We combine implicit Runge-Kutta and BDF methods with iterative operator-splitting methods to obtain higher-order methods. The idea of decoupling each complicated operator in simpler operators with an adapted time scale allows to solve the problems more efficiently. We compare our new methods with the higher-order fractional-stepping Runge-Kutta methods, developed for stiff ordinary differential equations. The benefit is the individual handling of each operator with adapted standard higher-order time integrators. The methods are applied to equations for convection-diffusion reactions and we obtain higher-order results. Finally we discuss the applications of the iterative operator-splitting methods to multi-dimensional and multi-physical problems.