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Volume 26, Issue 4
Energy Estimates for Delay Diffusion-Reaction Equations

J.A. Ferreira & P.M. da Silva

J. Comp. Math., 26 (2008), pp. 536-553.

Published online: 2008-08

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  • Abstract

In this paper we consider nonlinear delay diffusion-reaction equations with initial and Dirichlet boundary conditions. The behaviour and the stability of the solution of such initial boundary value problems (IBVPs) are studied using the energy method. Simple numerical methods are considered for the computation of numerical approximations to the solution of the nonlinear IBVPs. Using the discrete energy method we study the stability and convergence of the numerical approximations. Numerical experiments are carried out to illustrate our theoretical results.

  • Keywords

Delay diffusion reaction equation, Energy method, Stability, Convergence.

  • AMS Subject Headings

65M06, 65M20, 65M15.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-26-536, author = {J.A. Ferreira and P.M. da Silva}, title = {Energy Estimates for Delay Diffusion-Reaction Equations}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {4}, pages = {536--553}, abstract = {

In this paper we consider nonlinear delay diffusion-reaction equations with initial and Dirichlet boundary conditions. The behaviour and the stability of the solution of such initial boundary value problems (IBVPs) are studied using the energy method. Simple numerical methods are considered for the computation of numerical approximations to the solution of the nonlinear IBVPs. Using the discrete energy method we study the stability and convergence of the numerical approximations. Numerical experiments are carried out to illustrate our theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8641.html} }
TY - JOUR T1 - Energy Estimates for Delay Diffusion-Reaction Equations AU - J.A. Ferreira & P.M. da Silva JO - Journal of Computational Mathematics VL - 4 SP - 536 EP - 553 PY - 2008 DA - 2008/08 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8641.html KW - Delay diffusion reaction equation, Energy method, Stability, Convergence. AB -

In this paper we consider nonlinear delay diffusion-reaction equations with initial and Dirichlet boundary conditions. The behaviour and the stability of the solution of such initial boundary value problems (IBVPs) are studied using the energy method. Simple numerical methods are considered for the computation of numerical approximations to the solution of the nonlinear IBVPs. Using the discrete energy method we study the stability and convergence of the numerical approximations. Numerical experiments are carried out to illustrate our theoretical results.

J.A. Ferreira and P.M. da Silva. (2008). Energy Estimates for Delay Diffusion-Reaction Equations. Journal of Computational Mathematics. 26 (4). 536-553. doi:
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