An efficient high-order algorithm for solving systems of 3-D reaction-diffusion equations

被引：30

作者：

Gu, YX

Liao, WY

Zhu, JP ^{[1
]}

机构：

[1] Univ Akron, Dept Theoret & Appl Mech, Akron, OH 44325 USA

[2] Dalian Univ Technol, State Key Lab Struct Anal Ind Equip, Dalian 116023, Peoples R China

[3] Mississippi State Univ, Dept Math & Stat, Mississippi State, MS 39762 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2003年 / 155卷 / 01期

关键词：

high-order algorithms; approximate factorization; reaction-diffusion equations; finite difference algorithm;

D O I：

10.1016/S0377-0427(02)00889-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss an efficient higher order finite difference algorithm for solving systems of 3-D reaction-diffusion equations with nonlinear reaction terms. The algorithm is fourth-order accurate in both the temporal and spatial dimensions. It requires only a regular seven-point difference stencil similar to that used in the standard second-order algorithms, such as the Crank-Nicolson algorithm. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm. (C) 2003 Elsevier Science B.V. All rights reserved.

引用

页码：1 / 17

页数：17

共 10 条

[1] HIGHLY ACCURATE COMPACT IMPLICIT METHODS AND BOUNDARY-CONDITIONS [J].

ADAM, Y .

JOURNAL OF COMPUTATIONAL PHYSICS, 1977, 24 (01) :10-22

[2] ON THE NUMERICAL INTEGRATION OF D2U-DX2+D2U-DY2=DU-D+ IMPLICIT METHODS [J].

DOUGLAS, J .

JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 1955, 3 (01) :42-65

[3]

Gustafson B, 1995, TIME DEPENDENT PROBL

[4] HIGHER-ORDER ACCURATE DIFFERENCE SOLUTIONS OF FLUID MECHANICS PROBLEMS BY A COMPACT DIFFERENCING TECHNIQUE [J].

HIRSH, RS .

JOURNAL OF COMPUTATIONAL PHYSICS, 1975, 19 (01) :90-109

[5] COMPACT FINITE-DIFFERENCE SCHEMES WITH SPECTRAL-LIKE RESOLUTION [J].

LELE, SK .

JOURNAL OF COMPUTATIONAL PHYSICS, 1992, 103 (01) :16-42

[6] An efficient high-order algorithm for solving systems of reaction-diffusion equations [J].

Liao, WY ;

Zhu, JP ;

Khaliq, AQM .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2002, 18 (03) :340-354

[7]

MITCHELL A, 1980, FINITE DIFFERENCE ME

[8] THE NUMERICAL SOLUTION OF PARABOLIC AND ELLIPTIC DIFFERENTIAL EQUATIONS [J].

PEACEMAN, DW ;

RACHFORD, HH .

JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 1955, 3 (01) :28-41

[9] Implicit, compact, linearized θ-methods with factorization for multidimensional reaction-diffusion equations [J].

Ramos, JI .

APPLIED MATHEMATICS AND COMPUTATION, 1998, 94 (01) :17-43

[10]

WILSON RV, 1998, 9813 ICASE

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