Algebraically stable diagonally implicit general linear methods

Reference:

Hewitt, L. L. and Hill, A. T., 2010. Algebraically stable diagonally implicit general linear methods. Applied Numerical Mathematics, 60 (6), pp. 629-636.

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Official URL:

http://dx.doi.org/10.1016/j.apnum.2010.03.004

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.

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