Iterative operator-splitting methods with higher-order time integration methods and applications for parabolic partial differential equations

By Jürgen Geiser. 2008

69 citations recorded by the source corpus.

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.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/68700600df2625388a3cba00824dddd4c50d2583

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In Numerical Analysis

1. Jisheng Kou
2. Shuyu Sun

In Statistical and Nonlinear Physics

1. Jisheng Kou
2. Shuyu Sun

Citations in the corpus

• Fully mass-conservative IMPES schemes for incompressible two-phase flow in porous media (2019, unknown): “By this approach, one can further construct iterative operator-splitting schemes [24, 26, 31] which can be viewed as an iterative approach to solve the nonlinear system.”
• ON ITERATIVE IMPES FORMULATION FOR TWO-PHASE FLOW WITH CAPILLARITY IN HETEROGENEOUS POROUS MEDIA (2010, methodology): “By operator-splitting approach, we can construct iterative operatorsplitting methods [30, 32, 42], which may be used to solve the nonlinear system arisen after the fully implicit scheme.”