Abstract
The special case of diagonally-implicit multistage integration methods is considered in which the order, the stage order, the number of values passed between steps and the number of stages in a step, all coincide. It is shown that a similarity transformation can be applied to the matrices characterizing the method so as to simplify the expression for the stability polynomial and thus aid in the search for methods with acceptable stability.
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References
J. C. Butcher,Diagonally implicit multi-stage integration methods, Appl. Numer. Math. 11 (1993), 347–363.
J. C. Butcher,Some general linear methods for the parallel solution of ordinary diferential equations, World Scientific Series in Applicable Analysis, 2 (1993), 99–111.
J. C. Butcher and Z. Jackiewicz,Diagonally implicit general linear methods for ordinary differential equations, BIT 33, (1993), 452–472.
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Dedicated to Carl-Erik Fröberg on the occasion of his 75th birthday
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Butcher, J.C. A transformation for the analysis of DIMSIMs. BIT 34, 25–32 (1994). https://doi.org/10.1007/BF01935014
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DOI: https://doi.org/10.1007/BF01935014