Parameter-Uniform Numerical Scheme for Singularly Perturbed Delay Parabolic Reaction Diffusion Equations with Integral Boundary Condition
Numerical computation for the class of singularly perturbed delay parabolic reaction diffusion equations with integral boundary condition has been considered. A parameter-uniform numerical method is constructed via the nonstandard finite difference method for the spatial direction, and the backward...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2021/9993644 |
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| _version_ | 1832545979535982592 |
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| author | Wakjira Tolassa Gobena Gemechis File Duressa |
| author_facet | Wakjira Tolassa Gobena Gemechis File Duressa |
| author_sort | Wakjira Tolassa Gobena |
| collection | DOAJ |
| description | Numerical computation for the class of singularly perturbed delay parabolic reaction diffusion equations with integral boundary condition has been considered. A parameter-uniform numerical method is constructed via the nonstandard finite difference method for the spatial direction, and the backward Euler method for the resulting system of initial value problems in temporal direction is used. The integral boundary condition is treated using numerical integration techniques. Maximum absolute errors and the rate of convergence for different values of perturbation parameter ε and mesh sizes are tabulated for two model examples. The proposed method is shown to be parameter-uniformly convergent. |
| format | Article |
| id | doaj-art-364d5b28add44e02be3e1bce2fee9e3e |
| institution | Kabale University |
| issn | 1687-9651 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-364d5b28add44e02be3e1bce2fee9e3e2025-02-03T07:24:13ZengWileyInternational Journal of Differential Equations1687-96512021-01-01202110.1155/2021/9993644Parameter-Uniform Numerical Scheme for Singularly Perturbed Delay Parabolic Reaction Diffusion Equations with Integral Boundary ConditionWakjira Tolassa Gobena0Gemechis File Duressa1Department of MathematicsDepartment of MathematicsNumerical computation for the class of singularly perturbed delay parabolic reaction diffusion equations with integral boundary condition has been considered. A parameter-uniform numerical method is constructed via the nonstandard finite difference method for the spatial direction, and the backward Euler method for the resulting system of initial value problems in temporal direction is used. The integral boundary condition is treated using numerical integration techniques. Maximum absolute errors and the rate of convergence for different values of perturbation parameter ε and mesh sizes are tabulated for two model examples. The proposed method is shown to be parameter-uniformly convergent.http://dx.doi.org/10.1155/2021/9993644 |
| spellingShingle | Wakjira Tolassa Gobena Gemechis File Duressa Parameter-Uniform Numerical Scheme for Singularly Perturbed Delay Parabolic Reaction Diffusion Equations with Integral Boundary Condition International Journal of Differential Equations |
| title | Parameter-Uniform Numerical Scheme for Singularly Perturbed Delay Parabolic Reaction Diffusion Equations with Integral Boundary Condition |
| title_full | Parameter-Uniform Numerical Scheme for Singularly Perturbed Delay Parabolic Reaction Diffusion Equations with Integral Boundary Condition |
| title_fullStr | Parameter-Uniform Numerical Scheme for Singularly Perturbed Delay Parabolic Reaction Diffusion Equations with Integral Boundary Condition |
| title_full_unstemmed | Parameter-Uniform Numerical Scheme for Singularly Perturbed Delay Parabolic Reaction Diffusion Equations with Integral Boundary Condition |
| title_short | Parameter-Uniform Numerical Scheme for Singularly Perturbed Delay Parabolic Reaction Diffusion Equations with Integral Boundary Condition |
| title_sort | parameter uniform numerical scheme for singularly perturbed delay parabolic reaction diffusion equations with integral boundary condition |
| url | http://dx.doi.org/10.1155/2021/9993644 |
| work_keys_str_mv | AT wakjiratolassagobena parameteruniformnumericalschemeforsingularlyperturbeddelayparabolicreactiondiffusionequationswithintegralboundarycondition AT gemechisfileduressa parameteruniformnumericalschemeforsingularlyperturbeddelayparabolicreactiondiffusionequationswithintegralboundarycondition |