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

Authors:
Joachim Rang
Affiliations:
-
Venue:
Journal of Computational and Applied Mathematics
Year:
2014

Citing 10
Cited 0

A PI stepsize control for the numerical solution of ordinary differential equations

BIT
Order barriers for the B-convergence of ROW methods

Computing
Rosenbrock methods for partial differential equations and fractional orders of convergence

SIAM Journal on Numerical Analysis
A class of low order DIRK methods for a class of DAEs

Applied Numerical Mathematics
A four-stage index 2 diagonally implicit Runge-Kutta method

Applied Numerical Mathematics
Quasi stage order conditions for SDIRK methods

Applied Numerical Mathematics
Additive Runge-Kutta schemes for convection-diffusion-reaction equations

Applied Numerical Mathematics
A column pre-ordering strategy for the unsymmetric-pattern multifrontal method

ACM Transactions on Mathematical Software (TOMS)
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method

ACM Transactions on Mathematical Software (TOMS)
MooNMD – a program package based on mapped finite element methods

Computing and Visualization in Science

Quantified Score

Hi-index	7.29

Visualization

Abstract

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.