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
收藏
页码：346 / 357
页数：12
相关论文
共 50 条
  • [31] On the generation of P-stable exponentially fitted Runge-Kutta-Nystrom methods by exponentially fitted Runge-Kutta methods (vol 200, pg 778, 2007)
    Van de Vyver, Hans
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 200 (02) : 778 - 779
  • [32] Embedded Exponentially-Fitted Explicit Runge-Kutta-Nystrom Methods for Solving Periodic Problems
    Demba, Musa Ahmed
    Kumam, Poom
    Watthayu, Wiboonsak
    Phairatchatniyom, Pawicha
    COMPUTATION, 2020, 8 (02)
  • [33] Conditions for Trigonometrically Fitted Runge-Kutta Methods
    Kalogiratou, Z.
    Monovasilis, Th.
    Simos, T. E.
    NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS 1 AND 2, 2009, 1168 : 1600 - +
  • [34] An embedded exponentially-fitted Runge-Kutta method for the numerical solution of the Schrodinger equation and related periodic initial-value problems
    Avdelas, G
    Simos, TE
    Vigo-Aguiar, J
    COMPUTER PHYSICS COMMUNICATIONS, 2000, 131 (1-2) : 52 - 67
  • [35] PRECONDITIONING OF IMPLICIT RUNGE-KUTTA METHODS
    Jay, Laurent O.
    SCALABLE COMPUTING-PRACTICE AND EXPERIENCE, 2009, 10 (04): : 363 - 372
  • [36] A family of trigonometrically fitted partitioned Runge-Kutta symplectic methods
    Monovasilis, Th.
    Kalogiratou, Z.
    Simos, T. E.
    APPLIED MATHEMATICS AND COMPUTATION, 2009, 209 (01) : 91 - 96
  • [37] Sixth-order symmetric and symplectic exponentially fitted Runge-Kutta methods of the Gauss type
    Calvo, M.
    Franco, J. M.
    Montijano, J. I.
    Randez, L.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 223 (01) : 387 - 398
  • [38] Embedded Pairs of Exponentially Fitted Explicit Runge-Kutta Methods for the Numerical Integration of Oscillatory Problems
    Paris, A.
    Randez, L.
    NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, 2008, 1048 : 1008 - 1010
  • [39] Exponentially-fitted Runge-Kutta-Nystrom method for the numerical solution of initial-value problems with oscillating solutions
    Simos, TE
    APPLIED MATHEMATICS LETTERS, 2002, 15 (02) : 217 - 225
  • [40] Exponentially fitted explicit Runge-Kutta-Nystrom methods
    Franco, JM
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 167 (01) : 1 - 19
12345