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Article
A Fourth-order Compact Algorithm for Nonlinear Reaction-diffusion Equations with Neumann Boundary Conditions
Numerical Methods for Partial Differential Equations
  • Wenyuan Liao, University of Calgary
  • Jianping Zhu, Cleveland State University
  • Abdul Q.M. Khaliq, Middle Tennessee State University
Document Type
Article
Publication Date
7-26-2005
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.

Comments

Contract grant sponsor: National Science Foundation; contract grant number: 0082979

DOI
10.1002/num.20111
Citation Information
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.