ISSN:
1572-9125
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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 Φ(ζ,μ) when the method is applied toy'=qy. Hereμ=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 1/8λ2(χ4 +O(χ3)), where λ is the degree of Φ(ζ,μ) in the μ variable and χ the degree in the ζ 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01932019
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