Optimal implicit exponentially-fitted Runge-Kutta methods

被引：38

作者：

Vanden Berghe, G

Ixaru, LG

Van Daele, M

机构：

[1] Univ Ghent, Vakgrp Toegepaste Wiskunde & Informat, B-9000 Ghent, Belgium

[2] Dept Theoret Phys, Inst Phys & Nucl Engn, R-76900 Bucharest, Romania

来源：

COMPUTER PHYSICS COMMUNICATIONS | 2001年 / 140卷 / 03期

关键词：

implicit Runge-Kutta methods; initial-value problems; oscillating solutions; exponential fitting; stiff equations;

D O I：

10.1016/S0010-4655(01)00279-X

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Implicit Runge-Kutta methods for first-order ODEs are considered and the problem of how frequencies should be tuned in order to obtain the maximal benefit from the exponential fitted versions of such algorithms is examined. The key to the answer lies in the analysis of the behaviour of the error. A two-stage implicit Runge-Kutta method is particularly investigated. Formulae for optimal frequencies are produced; in that case the order of the method is increased by one unit. A numerical experiment illustrates the properties of the developed algorithms. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：346 / 357

页数：12

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