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Volume 7, Issue 3
Interior Layers in a Reaction-Diffusion Equation with a Discontinuous Diffusion Coefficient

C. de Falco & E. O'Riordan

Int. J. Numer. Anal. Mod., 7 (2010), pp. 444-461.

Published online: 2010-07

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  • Abstract

In this paper a problem arising in the modelling of semiconductor devices motivates the study of singularly perturbed differential equations of reaction-diffusion type with discontinuous data. The solutions of such problems typically contain interior layers where the gradient of the solution changes rapidly. Parameter-uniform methods based on piecewise-uniform Shishkin meshes are constructed and analysed for such problems. Numerical results are presented to support the theoretical results and to illustrate the benefits of using a piecewise-uniform Shishkin mesh over the use of uniform meshes in the simulation of a simple semiconductor device.

  • Keywords

Diffusion Reaction Equations, Singularly Perturbed Differential Equations, Finite Difference Methods on Fitted Meshes.

  • AMS Subject Headings

65N06, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-444, author = {C. de Falco and E. O'Riordan}, title = {Interior Layers in a Reaction-Diffusion Equation with a Discontinuous Diffusion Coefficient}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {3}, pages = {444--461}, abstract = {

In this paper a problem arising in the modelling of semiconductor devices motivates the study of singularly perturbed differential equations of reaction-diffusion type with discontinuous data. The solutions of such problems typically contain interior layers where the gradient of the solution changes rapidly. Parameter-uniform methods based on piecewise-uniform Shishkin meshes are constructed and analysed for such problems. Numerical results are presented to support the theoretical results and to illustrate the benefits of using a piecewise-uniform Shishkin mesh over the use of uniform meshes in the simulation of a simple semiconductor device.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/730.html} }
TY - JOUR T1 - Interior Layers in a Reaction-Diffusion Equation with a Discontinuous Diffusion Coefficient AU - C. de Falco & E. O'Riordan JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 444 EP - 461 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/730.html KW - Diffusion Reaction Equations, Singularly Perturbed Differential Equations, Finite Difference Methods on Fitted Meshes. AB -

In this paper a problem arising in the modelling of semiconductor devices motivates the study of singularly perturbed differential equations of reaction-diffusion type with discontinuous data. The solutions of such problems typically contain interior layers where the gradient of the solution changes rapidly. Parameter-uniform methods based on piecewise-uniform Shishkin meshes are constructed and analysed for such problems. Numerical results are presented to support the theoretical results and to illustrate the benefits of using a piecewise-uniform Shishkin mesh over the use of uniform meshes in the simulation of a simple semiconductor device.

C. de Falco and E. O'Riordan. (2010). Interior Layers in a Reaction-Diffusion Equation with a Discontinuous Diffusion Coefficient. International Journal of Numerical Analysis and Modeling. 7 (3). 444-461. doi:
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