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

• Autores: Joachim Rang
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 262, Nº 1, 2014, págs. 105-114
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.09.062
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• Resumen

  • 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.