Stability domains of explicit multistep methods
I.V. Kireev1,2, A.E. Novikov2, E.A. Novikov1,2
1Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia
2Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russia
Keywords: Ams-Bashforth method, locus, stability domain, Bernoulli method, ndelin-Lobachevsky-Graeffe method
Abstract
A new algorithm is proposed for obtaining stability domains of multistep numerical schemes. The algorithm is based on Bernoulli's algorithm for computing the greatest in magnitude root of a polynomial with complex coefficients and the ndelin-Lobachevsky-Graeffe method for squaring the roots. Numerical results on the construction of stability domains of Ams-Bashforth methods of order 3-11 are given.
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