An Efficient High-Order Algorithm for Solving Systems of Reaction-Diffusion Equations

Wenyuan Liao; Jianping Zhu; Abdul Q.M. Khaliq

doi:10.1002/num.10012

An Efficient High-Order Algorithm for Solving Systems of Reaction-Diffusion Equations

Wenyuan Liao, Jianping Zhu, Abdul Q.M. Khaliq

Research output: Contribution to journal › Article › peer-review

Abstract

An efficient higher-order finite difference algorithm is presented in this article for solving systems of two-dimensional reaction-diffusion equations with nonlinear reaction terms. The method is fourth-order accurate in both the temporal and spatial dimensions. It requires only a regular five-point difference stencil similar to that used in the standard second-order algorithm, such as the Crank-Nicolson algorithm. The Padé approximation and Richardson extrapolation are used to achieve high-order accuracy in the spatial and temporal dimensions, respectively. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm.

Original language	American English
Journal	Numerical Methods for Partial Differential Equations
Volume	18
DOIs	https://doi.org/10.1002/num.10012
State	Published - Jan 1 2002

Keywords

High order algorithms
Reaction-diffusion equations
Extrapolation and interpolations

Disciplines

Partial Differential Equations

Access to Document

10.1002/num.10012License: CC BY

http://onlinelibrary.wiley.com/doi/10.1002/num.10012/abstract

Cite this

@article{4996fcd2c5074309aef5699bbead4c95,

title = "An Efficient High-Order Algorithm for Solving Systems of Reaction-Diffusion Equations",

abstract = " An efficient higher-order finite difference algorithm is presented in this article for solving systems of two-dimensional reaction-diffusion equations with nonlinear reaction terms. The method is fourth-order accurate in both the temporal and spatial dimensions. It requires only a regular five-point difference stencil similar to that used in the standard second-order algorithm, such as the Crank-Nicolson algorithm. The Pad{\'e} approximation and Richardson extrapolation are used to achieve high-order accuracy in the spatial and temporal dimensions, respectively. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm.",

keywords = "High order algorithms, Reaction-diffusion equations, Extrapolation and interpolations",

author = "Wenyuan Liao and Jianping Zhu and Khaliq, \{Abdul Q.M.\}",

note = "Liao, W., Zhu, J., and Khaliq, A. Q. M. (2002). An Efficient High-order Algorithm for Solving Systems of Reaction-diffusion Equations. Journal of Numerical Methods for Partial Differential Equations, 18(3), 340 - 354, doi: 10.1002/num.10012.",

year = "2002",

month = jan,

day = "1",

doi = "10.1002/num.10012",

language = "American English",

volume = "18",

journal = "Numerical Methods for Partial Differential Equations",

}

TY - JOUR

T1 - An Efficient High-Order Algorithm for Solving Systems of Reaction-Diffusion Equations

AU - Liao, Wenyuan

AU - Zhu, Jianping

AU - Khaliq, Abdul Q.M.

N1 - Liao, W., Zhu, J., and Khaliq, A. Q. M. (2002). An Efficient High-order Algorithm for Solving Systems of Reaction-diffusion Equations. Journal of Numerical Methods for Partial Differential Equations, 18(3), 340 - 354, doi: 10.1002/num.10012.

PY - 2002/1/1

Y1 - 2002/1/1

N2 - An efficient higher-order finite difference algorithm is presented in this article for solving systems of two-dimensional reaction-diffusion equations with nonlinear reaction terms. The method is fourth-order accurate in both the temporal and spatial dimensions. It requires only a regular five-point difference stencil similar to that used in the standard second-order algorithm, such as the Crank-Nicolson algorithm. The Padé approximation and Richardson extrapolation are used to achieve high-order accuracy in the spatial and temporal dimensions, respectively. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm.

AB - An efficient higher-order finite difference algorithm is presented in this article for solving systems of two-dimensional reaction-diffusion equations with nonlinear reaction terms. The method is fourth-order accurate in both the temporal and spatial dimensions. It requires only a regular five-point difference stencil similar to that used in the standard second-order algorithm, such as the Crank-Nicolson algorithm. The Padé approximation and Richardson extrapolation are used to achieve high-order accuracy in the spatial and temporal dimensions, respectively. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm.

KW - High order algorithms

KW - Reaction-diffusion equations

KW - Extrapolation and interpolations

UR - https://engagedscholarship.csuohio.edu/scimath_facpub/62

UR - http://onlinelibrary.wiley.com/doi/10.1002/num.10012/abstract

U2 - 10.1002/num.10012

DO - 10.1002/num.10012

M3 - Article

VL - 18

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

ER -

An Efficient High-Order Algorithm for Solving Systems of Reaction-Diffusion Equations

Abstract

Keywords

Disciplines

Access to Document

Other files and links

Cite this