A Fourth-order Compact Algorithm for Nonlinear Reaction-diffusion Equations with Neumann Boundary Conditions
Document Type
Article
Publication Date
7-26-2005
Publication Title
Numerical Methods for Partial Differential Equations
Abstract
In this article, we discuss a scheme for dealing with Neumann and mixed boundary conditions using a compact stencil. The resulting compact algorithm for solving systems of nonlinear reaction-diffusion equations is fourth-order accurate in both the temporal and spatial dimensions. We also prove that the standard second-order approximation to zero Neumann boundary conditions provides fourth-order accuracy when the nonlinear reaction term is independent of the spatial variables. Numerical examples, including an application of this algorithm to a mathematical model describing frontal polymerization process, are presented in the article to demonstrate the accuracy and efficiency of the scheme.
Repository Citation
Liao, W., Zhu, J., and Khaliq, A. Q. M. (2006). A Fourth-order Compact Algorithm for Nonlinear Reaction-diffusion Equations with Neumann Boundary Conditions. Numerical Methods for Partial Differential Equations, 22(3), 600 - 616, doi: 10.1002/num.20111.
Original Citation
Liao, W., Zhu, J., and Khaliq, A. Q. M. (2006). A Fourth-order Compact Algorithm for Nonlinear Reaction-diffusion Equations with Neumann Boundary Conditions. Numerical Methods for Partial Differential Equations, 22(3), 600 - 616, doi: 10.1002/num.20111.
DOI
10.1002/num.20111
Publisher's Statement
The definitive version is available at www3.interscience.wiley.com
Volume
22
Issue
3
Comments
Contract grant sponsor: National Science Foundation; contract grant number: 0082979