An analysis of the Prothero-Robinson example for constructing new DIRK and ROW methods

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:262

Article; Proceedings Paper

Rang, Joachim

关键词: Rosenbrock-type methods;    Differential-algebraic equations;    Order reduction;    DIRK methods;    ROW methods;   

DOI  :  10.1016/j.cam.2013.09.062

来源: Elsevier

【 摘 要 】

This note analyses the order reduction phenomenon of diagonally implicit Runge-Kutta methods (DIRK methods) and Rosenbrock-Wanner methods (ROW methods) applied on the Prothero-Robinson example. New order conditions to reduce order reduction are derived, and a new third-order DIRK and ROW method is created. The new schemes are applied to the Prothero-Robinson example and on the semi-discretised incompressible Navier-Stokes equations. Numerical examples show that the new methods have better convergence properties than comparable methods. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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