Abstract
We investigate some classes of general linear methods withs internal andr external approximations, with stage orderq and orderp, adjacent to the class withs=r=q=p considered by Butcher. We demonstrate that interesting methods exist also ifs+1=r=q, p=q orq+1,s=r+1=q, p=q orq+1, ands=r=q, p=q+1. Examples of such methods are constructed with stability function matching theA-acceptable generalized Padé approximations to the exponential function.
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The work of Z. Jackiewicz was partially supported by the National Science Foundation under grant NSF DMS-9208048.
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Butcher, J.C., Jackiewicz, Z. Diagonally implicit general linear methods for ordinary differential equations. BIT 33, 452–472 (1993). https://doi.org/10.1007/BF01990528
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DOI: https://doi.org/10.1007/BF01990528