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

Contributed Talk

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Delay-dependent stability of high order time discretizations for delay partial differential equations

C. Huang and S. Vandewalle

Abstract
This talk is concerned with the stability of difference methods for partial differential equations (PDEs) with time-delay. By using a variant of the classical second-order central differences to discretize the spatial derivatives, we first obtain a semi-discrete system, which is a set of ordinary differential equations in the time variable. Then, the time discretizations based on Runge-Kutta methods with a non-constrained mesh are applied, where an equi-stage interpolation procedure is employed to approximate the delay argument. We establish a general stability criterion which can guarantee that the fully discrete system completely preserves the delay-dependent stability of the PDE test problem under consideration. Some high order methods with certain linear or parabolic interpolation are proved to satisfy this criterion. Finally, numerical experiments are presented to confirm the theoretical results.

Organized by         Universidad de Valladolid     IMUVA