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Volume 16, Issue 3
The Global Dufort-Frankel Difference Approximation for Nonlinear Reaction-Diffusion Equations

Bainian Lu, Guohua Wan & Bolin Guo

J. Comp. Math., 16 (1998), pp. 275-288.

Published online: 1998-06

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  • Abstract

In this paper, the initial value problem of nonlinear reaction-diffusion equation is considered. The Dufort-Frankel finite difference approximation for the long time scheme is given for the $d$-dimensional reaction-diffusion equation with the two different cases. The global solution and global attractor are discussed for the Dufort-Frankel scheme. Moreover, properties of the solution are studied. The error estimate is presented in a finite time region and in the global time region for some special cases. Finally the numerical results for the equation are investigated for Allen-Cahn equation and some other equations and the homoclinic orbit is simulated numerically.

  • Keywords

Globel Dufort-Frankel method, reaction-diffusion equation, global attractor, error estimate, numerical experiments.

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COPYRIGHT: © Global Science Press

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@Article{JCM-16-275, author = {Lu , BainianWan , Guohua and Guo , Bolin}, title = {The Global Dufort-Frankel Difference Approximation for Nonlinear Reaction-Diffusion Equations}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {3}, pages = {275--288}, abstract = {

In this paper, the initial value problem of nonlinear reaction-diffusion equation is considered. The Dufort-Frankel finite difference approximation for the long time scheme is given for the $d$-dimensional reaction-diffusion equation with the two different cases. The global solution and global attractor are discussed for the Dufort-Frankel scheme. Moreover, properties of the solution are studied. The error estimate is presented in a finite time region and in the global time region for some special cases. Finally the numerical results for the equation are investigated for Allen-Cahn equation and some other equations and the homoclinic orbit is simulated numerically.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9159.html} }
TY - JOUR T1 - The Global Dufort-Frankel Difference Approximation for Nonlinear Reaction-Diffusion Equations AU - Lu , Bainian AU - Wan , Guohua AU - Guo , Bolin JO - Journal of Computational Mathematics VL - 3 SP - 275 EP - 288 PY - 1998 DA - 1998/06 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9159.html KW - Globel Dufort-Frankel method, reaction-diffusion equation, global attractor, error estimate, numerical experiments. AB -

In this paper, the initial value problem of nonlinear reaction-diffusion equation is considered. The Dufort-Frankel finite difference approximation for the long time scheme is given for the $d$-dimensional reaction-diffusion equation with the two different cases. The global solution and global attractor are discussed for the Dufort-Frankel scheme. Moreover, properties of the solution are studied. The error estimate is presented in a finite time region and in the global time region for some special cases. Finally the numerical results for the equation are investigated for Allen-Cahn equation and some other equations and the homoclinic orbit is simulated numerically.

Lu , BainianWan , Guohua and Guo , Bolin. (1998). The Global Dufort-Frankel Difference Approximation for Nonlinear Reaction-Diffusion Equations. Journal of Computational Mathematics. 16 (3). 275-288. doi:
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