SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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A class of implicit-explicit general linear methods

A. Sandu and H. Zhang

Implicit-explicit (IMEX) time stepping methods can efficiently solve differential equations with both stiff and nonstiff components. IMEX Runge-Kutta methods and IMEX linear multistep methods have been studied in the literature. In this talk we discuss new implicit-explicit methods of general linear type (IMEX-GLMs). We develop an order conditions theory for high stage order partitioned GLMs that share the same abscissae, and show that no additional coupling order conditions are needed. Consequently, GLMs offer an excellent framework for the construction of multi-method integration algorithms. Next, we propose a family of IMEX schemes based on diagonally-implicit multi-stage integration methods and construct practical schemes of order three. Numerical results confirm the theoretical findings.

[1] Hong Zhang and Adrian Sandu, Partitioned and implicit-explicit general linear methods for ordinary differential equations,

Organized by         Universidad de Valladolid     IMUVA