An ETD Crank-Nicolson method for reaction-diffusion systems

被引：36

作者：

Kleefeld, B. ^{[2
]}

Khaliq, A. Q. M. ^{[3
,4
]}

Wade, B. A. ^{[1
]}

机构：

[1] Univ Wisconsin, Dept Math Sci, Milwaukee, WI 53201 USA

[2] Brandenburg Tech Univ Cottbus, Inst Math, D-03013 Cottbus, Germany

[3] Middle Tennessee State Univ, Dept Math Sci, Murfreesboro, TN 37132 USA

[4] Middle Tennessee State Univ, Computat Sci Program, Murfreesboro, TN 37132 USA

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2012年 / 28卷 / 04期

关键词：

chemotaxis; exotic options; exponential time differencing; nonlinear Black-Scholes equation; transaction cost; RUNGE-KUTTA METHODS; PARABOLIC PROBLEMS; NONSMOOTH DATA; STIFF SYSTEMS; SCHEMES; INTEGRATION; OPTIONS;

D O I：

10.1002/num.20682

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A novel Exponential Time Differencing Crank-Nicolson method is developed which is stable, second-order convergent, and highly efficient. We prove stability and convergence for semilinear parabolic problems with smooth data. In the nonsmooth data case, we employ a positivity-preserving initial damping scheme to recover the full rate of convergence. Numerical experiments are presented for a wide variety of examples, including chemotaxis and exotic options with transaction cost. (c) 2011Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012

引用

页码：1309 / 1335

页数：27

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