Algebraically stable diagonally implicit general linear methods

Authors:
L. L. Hewitt;A. T. Hill
Affiliations:
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK;Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK
Venue:
Applied Numerical Mathematics
Year:
2010

Citing 4
Cited 3

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Abstract

This paper concerns algebraically stable diagonally implicit general linear methods, intended for stiff differential equations. The first step in the construction of such methods is to apply the order theory from the series of papers by Butcher and Jackiewicz. The order theory and structural assumptions leave a number of free parameters, which may be chosen to make the method both simple and algebraically stable. Here, this choice is made by applying new sufficient conditions for algebraic stability. Methods of 2 steps and 2 stages are constructed with stage order 2, and total order up to 4.