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

共 50 条

[1] An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems
Fernandes, Ryan I.
Fairweather, Graeme
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (19) : 6248 - 6267
[2] Convergence of the Crank-Nicolson Method for a Singularly Perturbed Parabolic Reaction-Diffusion System
Victor, Franklin
Miller, John J. H.
Sigamani, Valarmathi
[J]. DIFFERENTIAL EQUATIONS AND NUMERICAL ANALYSIS, 2016, 172 : 77 - 97
[3] An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems on evolving domains
Fernandes, Ryan I.
Bialecki, Bernard
Fairweather, Graeme
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 299 : 561 - 580
[4] IN DEFENSE OF CRANK-NICOLSON METHOD
WILKES, JO
[J]. AICHE JOURNAL, 1970, 16 (03) : 501 - &
[5] A CRANK-NICOLSON ADI SPECTRAL METHOD FOR A TWO-DIMENSIONAL RIESZ SPACE FRACTIONAL NONLINEAR REACTION-DIFFUSION EQUATION
Zeng, Fanhai
Liu, Fawang
Li, Changpin
Burrage, Kevin
Turner, Ian
Anh, V.
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2014, 52 (06) : 2599 - 2622
[6] Local Crank-Nicolson Method for Solving the Nonlinear Diffusion Equation
Abduwali, Abdurishit
Kohno, Toshiyuki
Niki, Hiroshi
[J]. INFORMATION-AN INTERNATIONAL INTERDISCIPLINARY JOURNAL, 2008, 11 (02): : 165 - 169
[7] ALTERNATING BAND CRANK-NICOLSON METHOD FOR
陈劲
张宝琳
[J]. Applied Mathematics:A Journal of Chinese Universities, 1993, (02) : 150 - 162
[8] An analysis of the Crank-Nicolson method for subdiffusion
Jin, Bangti
Li, Buyang
Zhou, Zhi
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2018, 38 (01) : 518 - 541
[9] Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
Celik, Cem
Duman, Melda
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (04) : 1743 - 1750
[10] Invariantization of the Crank-Nicolson method for Burgers' equation
Kim, Pilwon
[J]. PHYSICA D-NONLINEAR PHENOMENA, 2008, 237 (02) : 243 - 254

← 1 2 3 4 5 →