Design and implementation of DIRK integrators for stiff systems

Authors:
Roger Alexander
Affiliations:
Department of Mathematics, 400 Carver Hall, Iowa State University, Ames, IA
Venue:
Applied Numerical Mathematics
Year:
2003

Citing 7
Cited 2

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Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations

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Evaluation of a Test Set for Stiff ODE Solvers

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Essentials of Numerical Analysis with Pocket Calculator Demonstrations

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Variable step-size fractional step Runge-Kutta methods for time-dependent partial differential equations

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Abstract

This paper presents new four-stage diagonally implicit Runge-Kutta integration formulas for stiff initial value problems, designed to be L-stable and have optimal order of accuracy. The design makes estimation of local error and interpolation of the solution possible without additional stages. It also enables improved prediction of stage values in a software implementation. Correctly monitoring the convergence rate of simplified Newton iterations improves the implementation too, by providing a sound basis for deciding on Jacobian updates.