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An analysis of the Prothero-Robinson example for constructing new DIRK and ROW methods. (English) Zbl 1302.65179
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 [A. Prothero and 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.

MSC:
65L80 Numerical methods for differential-algebraic equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
Software:
ROS3P; UMFPACK; RODAS; MooNMD
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References:
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