The SBP-SAT technique for initial value problems

被引：40

作者：

Lundquist, Tomas ^{[1
]}

Nordstrom, Jan ^{[1
]}

机构：

[1] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2014年 / 270卷

关键词：

Time integration; Initial value problems; High order accuracy; Initial boundary value problems; Boundary conditions; Global methods; Stability; Convergence; Summation-by-parts operators; Stiff problems; SUMMATION-BY-PARTS; ORDINARY DIFFERENTIAL-EQUATIONS; RUNGE-KUTTA SCHEMES; BOUNDARY-CONDITIONS; TIME; ACCURACY; ORDER; DISCRETIZATIONS; STABILITY; OPERATORS;

D O I：

10.1016/j.jcp.2014.03.048

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

A detailed account of the stability and accuracy properties of the SBP-SAT technique for numerical time integration is presented. We show how the technique can be used to formulate both global and multi-stage methods with high order of accuracy for both stiff and non-stiff problems. Linear and non-linear stability results, including A-stability, L-stability and B-stability are proven using the energy method for general initial value problems. Numerical experiments corroborate the theoretical properties. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：86 / 104

页数：19

共 25 条

[1]

AxELSSON O., 1964, BIT, V4, P69

[2] On the impact of boundary conditions on dual consistent finite difference discretizations [J].

Berg, Jens ;

Nordstrom, Jan .

JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 236 :41-55

[3] Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form [J].

Berg, Jens ;

Nordstrom, Jan .

JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (20) :6846-6860

[4] General linear methods for stiff differential equations [J].

Butcher, JC .

BIT, 2001, 41 (02) :240-264

[5] INITIAL-VALUE PROBLEMS - NUMERICAL-METHODS AND MATHEMATICS [J].

BUTCHER, JC .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1994, 28 (10-12) :1-16

[6] Fourth-order Runge-Kutta schemes for fluid mechanics applications [J].

Carpenter, MH ;

Kennedy, CA ;

Bijl, H ;

Viken, SA ;

Vatsa, VN .

JOURNAL OF SCIENTIFIC COMPUTING, 2005, 25 (01) :157-194

[7] TIME-STABLE BOUNDARY-CONDITIONS FOR FINITE-DIFFERENCE SCHEMES SOLVING HYPERBOLIC SYSTEMS - METHODOLOGY AND APPLICATION TO HIGH-ORDER COMPACT SCHEMES [J].

CARPENTER, MH ;

GOTTLIEB, D ;

ABARBANEL, S .

JOURNAL OF COMPUTATIONAL PHYSICS, 1994, 111 (02) :220-236

[8] A stable and conservative interface treatment of arbitrary spatial accuracy [J].

Carpenter, MH ;

Nordström, J ;

Gottlieb, D .

JOURNAL OF COMPUTATIONAL PHYSICS, 1999, 148 (02) :341-365

[9] A method for global approximation of the initial value problem [J].

Costabile, F ;

Napoli, A .

NUMERICAL ALGORITHMS, 2001, 27 (02) :119-130

[10] Analysis of the order of accuracy for node-centered finite volume schemes [J].

Eriksson, Sofia ;

Nordstrom, Jan .

APPLIED NUMERICAL MATHEMATICS, 2009, 59 (10) :2659-2676

← 1 2 3 →