an:06317726
Zbl 1302.65179
Rang, Joachim
An analysis of the Prothero-Robinson example for constructing new DIRK and ROW methods
EN
J. Comput. Appl. Math. 262, 105-114 (2014).
0377-0427
2014
j
65L80 65L06
Rosenbrock-type methods; differential-algebraic equations; order reduction; diagonally implicit Runge-Kutta methods; Rosenbrock-Wanner methods; Prothero-Robinson example; Navier-Stokes equations; numerical examples
Summary: 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 [\textit{A. Prothero} and \textit{A. Robinson}, Math. Comput. 28, 45--162 (1974; Zbl 0309.65034)]. 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.
0309.65034