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

被引：14

作者：

de la Cruz, H. ^{[1
,2
]}

Biscay, R. J. ^{[3
,4
]}

Jimenez, J. C. ^{[4
]}

Carbonell, F. ^{[5
]}

机构：

[1] IMPA, Rio De Janeiro, Brazil

[2] FGV, Escola Matemat Aplicada, Rio De Janeiro, Brazil

[3] Univ Valparaiso, CIMFAV, Valparaiso, Chile

[4] Inst Cibernet Matemat & Fis, Havana, Cuba

[5] McGill Univ, Montreal Neurol Inst, Montreal, PQ, Canada

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2013年 / 57卷 / 3-4期

关键词：

Numerical integrators; A-stability; Local linearization; Runge-Kutta methods; Variation of constants formula; Hyperbolic stationary points; DIFFERENTIAL-EQUATIONS; NUMERICAL-INTEGRATION; STIFF SYSTEMS; APPROXIMATION; SCHEMES; CONVERGENCE;

D O I：

10.1016/j.mcm.2012.08.011

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

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.

引用

页码：720 / 740

页数：21

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