A generalization of singly-implicit Runge-Kutta methods

被引：19

作者：

Butcher, JC ^{[1
]}

Chartier, P ^{[1
]}

机构：

[1] INRIA,RENNES,FRANCE

来源：

APPLIED NUMERICAL MATHEMATICS | 1997年 / 24卷 / 2-3期

关键词：

effective order; Runge-Kutta methods; singly-implicit methods;

D O I：

10.1016/S0168-9274(97)00031-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The concept of effective order allows for the possibility that the result computed in a Runge-Kutta step is an approximation to some quantity more general than the actual solution at a step point. This generalization is applied here to singly-implicit methods. The limitation that requires severe and inconvenient restrictions on the abscissae in the method is removed and all that is now needed is that the abscissae be distinct. Finally, the construction of several low order methods will be detailed. (C) 1997 Elsevier Science B.V.

引用

页码：343 / 350

页数：8

共 14 条

[1]

[Anonymous], NUMERICAL METHODS ST

[2]

[Anonymous], 1973, ANAL DISCRETIZATION, DOI DOI 10.1007/978-3-642-65471-8

[3]

Burrage K., 1978, BIT (Nordisk Tidskrift for Informationsbehandling), V18, P22, DOI 10.1007/BF01947741

[4]

Burrage K., 1980, BIT (Nordisk Tidskrift for Informationsbehandling), V20, P326, DOI 10.1007/BF01932774

[5]

Butcher J. C., 1976, BIT (Nordisk Tidskrift for Informationsbehandling), V16, P237, DOI 10.1007/BF01932265

[6]

Butcher J. C., 1987, The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods

[7]

Butcher J C., 1969, Conference on the numerical solution of differential equations, P133

[8] TRANSFORMED IMPLICIT RUNGE-KUTTA METHOD [J].

BUTCHER, JC .

JOURNAL OF THE ACM, 1979, 26 (04) :731-738

[9] TOWARDS EFFICIENT IMPLEMENTATION OF SINGLY-IMPLICIT METHODS [J].

BUTCHER, JC .

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1988, 14 (01) :68-75

[10] TOWARDS EFFICIENT RUNGE-KUTTA METHODS FOR STIFF SYSTEMS [J].

BUTCHER, JC ;

CASH, JR .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1990, 27 (03) :753-761

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