The Construction of Practical General Linear Methods

Authors: Butcher J.C.¹; Wright W.M.²

Source: Bit Numerical Mathematics, Volume 43, Number 4, December 2003 , pp. 695-721(27)

Publisher: Springer

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Abstract:

Using the property of ‘inherent Runge–Kutta stability’, it is possible to construct diagonally implicit general linear methods with stability regions exactly the same as for Runge–Kutta methods. In addition to A-stable methods found in this way, it is also possible to construct explicit methods with stability regions identical to those of explicit Runge–Kutta methods. The use of doubly companion matrices makes it possible to find all explicit and diagonally-implicit methods possessing the inherent Runge–Kutta stability property.

Keywords: general linear methods; inherent Runge–Kutta stability

Document Type: Research article

DOI: http://dx.doi.org/10.1023/B:BITN.0000009952.71388.23

Affiliations: 1: Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand., Email: butcher@imath.auckland.ac.nz 2: Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand., Email: will@math.auckland.ac.nz

Publication date: 2003-12-01