An algebraic test forA
0-stability |
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Authors: | A Friedli R Jeltsch |
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Institution: | (1) Seminar für Angewandte Mathematik, Swiss Federal Institute of Technology, Clausiusstr. 55, CH-8006 Zürich, Switzerland;(2) Computer Science Department, Stanford University, 94305 Stanford, CA |
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Abstract: | The stability of a large class of numerical methods to solve initial value problems of ordinary differential equations is governed by a two-variable polynomial (,) when the method is applied toy'=qy. Here=hq, whereh is the stepsize. This class of methods includes Runge-Kutta methods, linear multistep methods, predictor-corrector methods, composite multistep methods and linear multistep-multiderivative methods. An algebraic test is given to determineA
0-stability of such methods in a finite number of operations (additions, subtractions, multiplications and divisions). It is shown that the number of multiplications and divisions is of order 1/82(4 +O(3)), where is the degree of (,) in the variable and the degree in the variable. The test has been implemented for multistep-multiderivative methods in a symbol manipulation language. For Enright's second derivativek-step methods it is proved that the methods areA
0-stable if and only ifk<8.Supported by the Swiss National Foundation Grant No. 82.524.077. On leave from Institute of Mathematics, Ruhr-University Bochum, D-463 Germany. |
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