Diagonally implicit general linear methods for ordinary differential equations |
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Authors: | J C Butcher Z Jackiewicz |
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Institution: | (1) Department of Mathematics and Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand;(2) Department of Mathematics, Arizona State University, 85287-1804 Tempe, AZ, USA |
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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.The work of Z. Jackiewicz was partially supported by the National Science Foundation under grant NSF DMS-9208048. |
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Keywords: | AMS(MOS) 65L05 65L07 |
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