Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients
Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values. A comparison is shown between the weigh...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/542897 |
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| _version_ | 1832554284427771904 |
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| author | Nauman Raza Asma Rashid Butt |
| author_facet | Nauman Raza Asma Rashid Butt |
| author_sort | Nauman Raza |
| collection | DOAJ |
| description | Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values. A comparison is shown between the weighted and unweighted Sobolev gradients in two and three dimensions. The superiority of the method is also demonstrated by showing comparison with Newton's method. |
| format | Article |
| id | doaj-art-61bcb6da884b48c79853a56314924474 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-61bcb6da884b48c79853a563149244742025-02-03T05:51:55ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/542897542897Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev GradientsNauman Raza0Asma Rashid Butt1Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, CanadaDepartment of Mathematics, Brock University, St. Catharines, ON, L2S 3A1, CanadaCritical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values. A comparison is shown between the weighted and unweighted Sobolev gradients in two and three dimensions. The superiority of the method is also demonstrated by showing comparison with Newton's method.http://dx.doi.org/10.1155/2013/542897 |
| spellingShingle | Nauman Raza Asma Rashid Butt Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients Journal of Function Spaces and Applications |
| title | Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients |
| title_full | Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients |
| title_fullStr | Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients |
| title_full_unstemmed | Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients |
| title_short | Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients |
| title_sort | numerical solutions of singularly perturbed reaction diffusion equation with sobolev gradients |
| url | http://dx.doi.org/10.1155/2013/542897 |
| work_keys_str_mv | AT naumanraza numericalsolutionsofsingularlyperturbedreactiondiffusionequationwithsobolevgradients AT asmarashidbutt numericalsolutionsofsingularlyperturbedreactiondiffusionequationwithsobolevgradients |