Local Linearization-Runge-Kutta methodsa class of A-stable explicit integrators for dynamical systems

Resumo

A new approach for the construction of high order A-stable explicit integrators for ordinary differential equations (ODEs) is theoretically studied. Basically, the integrators are obtained by splitting, at each time step, the solution of the original equation in two parts: the solution of a linear ordinary differential equation plus the solution of an auxiliary ODE. The first one is solved by a Local Linearization scheme in such a way that A-stability is ensured, while the second one can be approximated by any extant scheme, preferably a high order explicit Runge-Kutta scheme. Results on the convergence and dynamical properties of this new class of schemes are given, as well as some hints for their efficient numerical implementation. An specific scheme of this new class is derived in detail, and its performance is compared with some Matlab codes in the integration of a variety of ODEs representing different types of dynamics. (C) 2012 Elsevier Ltd. All rights reserved.

Ficha do documento

Tipo

Artigo científico

Ano

2013

Instituição

Pergamon-Elsevier Science Ltd

Fonte

Repositório da FGV

Idioma

Inglês

Acesso

Acesso aberto

DOI

10.1016/j.mcm.2012.08.011

Identificador

oai:repositorio.fgv.br:10438/23296

Temas

Tecnologia

Palavras-chave

Numerical integratorsA-stabilityLocal linearizationRunge-Kutta methodsVariation of constants formulaHyperbolic stationary pointsOrdinary differential-equationsInitial-value problemsStiff systemsExponential integratorsNumerical-integrationMatrix exponentialsParabolic problemsApproximationSchemesConvergenceTecnologiaEquações diferenciaisRunge-Kutta, Fórmulas de