A splitting approach for the Kadomtsev-Petviashvili equation

被引：15

作者：

Einkemmer, Lukas ^{[1
]}

Ostermann, Alexander ^{[1
]}

机构：

[1] Univ Innsbruck, Dept Math, A-6020 Innsbruck, Austria

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2015年 / 299卷

基金：

奥地利科学基金会;

关键词：

Kadomtsev-Petviashvili equation; Splitting methods; Dispersive equation; MASS CONSTRAINT;

D O I：

10.1016/j.jcp.2015.07.024

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We consider a splitting approach for the Kadomtsev-Petviashvili equation with periodic boundary conditions and show that the necessary interpolation procedure can be efficiently implemented. The error made by this numerical scheme is compared to exponential integrators which have been shown in Klein and Roidot (2011) [2] to perform best for stiff solutions of the Kadomtsev-Petviashvili equation. Since many classic high order splitting methods do not perform well, we propose a stable extrapolation method in order to construct an efficient numerical scheme of order four. In addition, the conservation properties and the possibility of order reduction for certain initial values for the numerical schemes under consideration are investigated. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：716 / 730

页数：15

共 20 条

[1] On the necessity of negative coefficients for operator splitting schemes of order higher than two [J].

Blanes, S ;

Casas, F .

APPLIED NUMERICAL MATHEMATICS, 2005, 54 (01) :23-37

[2] Exponential time differencing for stiff systems [J].

Cox, SM ;

Matthews, PC .

JOURNAL OF COMPUTATIONAL PHYSICS, 2002, 176 (02) :430-455

[3] Comparison of Eulerian Vlasov solvers [J].

Filbet, F ;

Sonnendrücker, E .

COMPUTER PHYSICS COMMUNICATIONS, 2003, 150 (03) :247-266

[4] The Cauchy problem for the Kadomtsev-Petviashvili-I equation without the zero mass constraint [J].

Fokas, AS ;

Sung, LY .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1999, 125 :113-138

[5] A fast Fourier transform compiler [J].

Frigo, M .

ACM SIGPLAN NOTICES, 1999, 34 (05) :169-180

[6]

Galassi M., 2009, GNU Scientific Library Reference Manual.

[7]

Hairer E., 2006, GEOMETRIC NUMERICAL

[8] High order splitting methods for analytic semigroups exist [J].

Hansen, Eskil ;

Ostermann, Alexander .

BIT NUMERICAL MATHEMATICS, 2009, 49 (03) :527-542

[9]

Hochbruck M, 2010, ACTA NUMER, V19, P209, DOI 10.1017/S0962492910000048

[10]

Holden H, 2013, MATH COMPUT, V82, P173

← 1 2 →