Stability of collocation-based Runge-Kutta-Nyström methods |
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Authors: | P J van der Houwen B P Sommeijer Nguyen Huu Cong |
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Institution: | (1) Centre for Mathematics and Computer Science, Box 4079, 1009 AB Amsterdam, The Netherlands;(2) Faculty of Mathematics, Mechanics and Informatics, University of Hanoi, Thuong dinh, Dong Da, Hanoi, Vietnam |
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Abstract: | We analyse the attainable order and the stability of Runge-Kutta-Nyström (RKN) methods for special second-order initial-value problems derived by collocation techniques. Like collocation methods for first-order equations the step point order ofs-stage methods can be raised to 2s for alls. The attainable stage order is one higher and equalss+1. However, the stability results derived in this paper show that we have to pay a high price for the increased stage order.These investigations were supported by the University of Amsterdam who provided the third author with a research grant for spending a total of two years in Amsterdam. |
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Keywords: | 65M10 65M20 |
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