Abstract
We consider the basic propositions of the theory of multistep fractional-rational numerical methods with a variable step of integration. We establish general regularities in determining the coefficients of the methods. We prove the A-stability of these methods of arbitrary order, and also the absence of extraneous roots of the characteristic equations of the methods.
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Literature Cited
R. V. Slonevskii, “Fractional-rational approximations of systems of differential equations,” Ukrainian Academy of Sciences Mathematical Institute Preprint No. 154, L'vov, (1988).
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Additional information
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 148–152.
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Slon'ovs'kii, R.V., Stolyarchuk, R.R. Stable multistep methods of numerical integration of rigid systems of differential equations. J Math Sci 90, 2450–2453 (1998). https://doi.org/10.1007/BF02433983
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DOI: https://doi.org/10.1007/BF02433983