Volume 26, Issue 2
A Monotone Compact Implicit Scheme for Nonlinear Reaction-Diffusion Equations

Yuanming Wang & Benyu Guo

DOI:

J. Comp. Math., 26 (2008), pp. 123-148

Published online: 2008-04

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  • Abstract

A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate of the iteration.

  • Keywords

Nonlinear reaction-diffusion equation Monotone compact implicit scheme High accuracy Monotone iteration Rapid convergence rate

  • AMS Subject Headings

65M06 65M12.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-26-123, author = {}, title = {A Monotone Compact Implicit Scheme for Nonlinear Reaction-Diffusion Equations}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {2}, pages = {123--148}, abstract = { A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate of the iteration.}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8616.html} }
TY - JOUR T1 - A Monotone Compact Implicit Scheme for Nonlinear Reaction-Diffusion Equations JO - Journal of Computational Mathematics VL - 2 SP - 123 EP - 148 PY - 2008 DA - 2008/04 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8616.html KW - Nonlinear reaction-diffusion equation KW - Monotone compact implicit scheme KW - High accuracy KW - Monotone iteration KW - Rapid convergence rate AB - A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate of the iteration.
Yuanming Wang & Benyu Guo. (1970). A Monotone Compact Implicit Scheme for Nonlinear Reaction-Diffusion Equations. Journal of Computational Mathematics. 26 (2). 123-148. doi:
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