ON THE ACCURACY OF INVARIANT NUMERICAL SCHEMES

被引：6

作者：

Chhay, Marx ^{[1
]}

Hamdouni, Aziz ^{[1
]}

机构：

[1] Univ La Rochelle, LEPTIAB, F-17000 La Rochelle, France

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2011年 / 10卷 / 02期

关键词：

Invariant methods; Lie symmetry; order of accuracy; moving frames; parametrized scheme; geometric integration; MULTISYMPLECTIC GEOMETRY; VARIATIONAL INTEGRATORS; MOVING COFRAMES; SYMMETRY;

D O I：

10.3934/cpaa.2011.10.761

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present a method of construction of invariant numerical schemes for partial differential equations. The resulting schemes preserve the Lie-symmetry group of the continuous equation and they are at least as accurate as the original scheme. The improvement of the numerical properties thanks to the Lie-symmetry preservation is illustrated on the example of the Burgers equation.

引用

页码：761 / 783

页数：23

共 49 条

[1] [Anonymous], P I MATH NAS UKRAINE
[2] [Anonymous], SOLVING ORDINARY DIF
[3] [Anonymous], AM MATH SOC TRANSL
[4] Symmetry-preserving difference schemes for some heat transfer equations
Bakirova, MI
Dorodnitsyn, VA
Kozlov, RV
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1997, 30 (23): : 8139 - 8155
[5] Multi-symplectic structures and wave propagation
Bridges, TJ
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1997, 121 : 147 - 190
[6] Symmetry-adapted moving mesh schemes for the nonlinear Schrodinger equation
Budd, C
Dorodnitsyn, V
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (48): : 10387 - 10400
[7] Budd C.J., 2000, HDB NUMERICAL ANAL V, VXI., P35
[8] Budd C.J., 1998, NUMERICAL ANAL 1997, P16
[9] ACCURATE LONG-TERM INTEGRATION OF DYNAMICAL-SYSTEMS
CALVO, MP
HAIRER, E
[J]. APPLIED NUMERICAL MATHEMATICS, 1995, 18 (1-3) : 95 - 105
[10] Cartan E., 1935, ESPACES GEN HERMANN, V5

← 1 2 3 4 5 →