The number of conditions for a Runge-Kutta method to have effective order p

被引：20

作者：

Butcher, JC ^{[1
]}

SanzSerna, JM ^{[1
]}

机构：

[1] UNIV VALLADOLID, FAC CIENCIAS, DEPT MATEMAT APLICADA & COMPUTAC, VALLADOLID, SPAIN

来源：

APPLIED NUMERICAL MATHEMATICS | 1996年 / 22卷 / 1-3期

关键词：

Runge-Kutta method; B-series method; order conditions; effective order; pre-processor; post-processor;

D O I：

10.1016/S0168-9274(96)00028-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We count the number of conditions that a one-step numerical integrator has to satisfy to achieve a given effective order of accuracy p. Effective order refers to the order of the numerical method after the numerical solution has been enhanced by suitable pre- and post-processors, The methods considered include not only Runge-Kutta methods, but also all methods that can be represented by B-series, such as multiderivative generalizations of Runge-Kutta methods.

引用

页码：103 / 111

页数：9

共 17 条

[1]

ARAUJO AL, IN PRESS SIAM J NUME

[2]

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

[3]

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

[4]

BUTCHER JC, 1972, MATH COMPUT, V26, P79, DOI 10.1090/S0025-5718-1972-0305608-0

[5] CANONICAL B-SERIES [J].

CALVO, MP ;

SANZSERNA, JM .

NUMERISCHE MATHEMATIK, 1994, 67 (02) :161-175

[6]

Hairer E., 2008, Solving Ordinary Differential Equations I Nonstiff problems

[7]

LITTELL TR, 1995, ERROR ANAL SYMPLECTI

[8]

LOPEZMARCOS MA, 1996, NUMERICAL ANAL 1995, P107

[9]

LOPEZMARCOS MA, IN PRESS SIAM J SCI

[10]

LOPEZMARCOS MA, 1996, MITCHELL 75 BIRTHDAY, P163

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