Szczegóły publikacji

Opis bibliograficzny

Autorzy (4)

• AGHBraś Michał
• Cardone Angelamaria
• AGHJackiewicz Zdzisław
• Welfert Bruno

Słowa kluczowe

Dane bibliometryczne

ID BaDAP	109435
Data dodania do BaDAP	2017-10-23
Tekst źródłowy	URL
DOI	10.1016/j.apnum.2017.04.001
Rok publikacji	2017
Typ publikacji	artykuł w czasopiśmie
Otwarty dostęp
Czasopismo/seria	Applied Numerical Mathematics

Abstract

The order reduction phenomenon for general linear methods (GLMs) for stiff differential equations is investigated. It turns out that, similarly as for standard Runge-Kutta methods, the effective order of convergence for a large class of GLMs applied to stiff differential systems, is equal to the stage order of the method. In particular, it is demonstrated that the global error vertical bar vertical bar e([n])vertical bar vertical bar of GLMs of order p and stage order q applied to the Prothero-Robinson test problem y'(t) = lambda(y(t) - phi(t) + phi'(t), t is an element of [t(0), T], y(to) = phi(t(0)), is O(h(q)) + O(h(p)) as h -> 0 and h lambda -> -infinity. Moreover, for GLMs with Runge-Kutta stability which are A(0)-stable and for which the stability function R(z) of the underlying Runge-Kutta methods, (i.e., the corresponding RK methods which have the same absolute stability properties as the GLMs), is such that R(infinity) not equal 1, the global error satisfies vertical bar vertical bar e([n])vertical bar vertical bar = 0(h(q+1)) + O(h(P)) as h -> 0 and h lambda -> -infinity. These results are confirmed by numerical experiments. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.

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