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PRACTICAL RUNGE–KUTTA METHODS FOR SCIENTIFIC COMPUTATION

Part of: Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  03 November 2009

J. C. BUTCHER
J. C. BUTCHER*
Affiliation:
Department of Mathematics, University of Auckland, 38 Princes St, Science Centre, Building 303, Level 3, Auckland Central (email: butcher@math.auckland.ac.nz)
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Abstract

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Implicit Runge–Kutta methods have a special role in the numerical solution of stiff problems, such as those found by applying the method of lines to the partial differential equations arising in physical modelling. Of particular interest in this paper are the high-order methods based on Gaussian quadrature and the efficiently implementable singly implicit methods.

Keywords

implicit Runge–Kutta methodsimplicit Euler methodstiff problemsA-stabilityL-stabilitymethod of linesGauss–Legendre quadratureDIRK methodsSIRK methodsLaguerre polynomials

MSC classification

Secondary: 65L05: Initial value problems
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 3: This Special Issue is dedicated to Dr Stephen White , January 2009 , pp. 333 - 342
Copyright
Copyright © Australian Mathematical Society 2009

References

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