Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition
In this paper, we consider a class of singularly perturbed differential equations of convection diffusion type with integral boundary condition. An accelerated uniformly convergent numerical method is constructed via exponentially fitted operator method using Richardson extrapolation techniques and...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2020/9268181 |
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| _version_ | 1832554986204037120 |
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| author | Habtamu Garoma Debela Gemechis File Duressa |
| author_facet | Habtamu Garoma Debela Gemechis File Duressa |
| author_sort | Habtamu Garoma Debela |
| collection | DOAJ |
| description | In this paper, we consider a class of singularly perturbed differential equations of convection diffusion type with integral boundary condition. An accelerated uniformly convergent numerical method is constructed via exponentially fitted operator method using Richardson extrapolation techniques and numerical integration methods to solve the problem. The integral boundary condition is treated using numerical integration techniques. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. |
| format | Article |
| id | doaj-art-1b3484f4c75545f9917e17a83e99f145 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-1b3484f4c75545f9917e17a83e99f1452025-02-03T05:49:52ZengWileyInternational Journal of Differential Equations1687-96431687-96512020-01-01202010.1155/2020/92681819268181Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary ConditionHabtamu Garoma Debela0Gemechis File Duressa1Department of Mathematics, College of Natural Sciences, Jimma University, Jimma, EthiopiaDepartment of Mathematics, College of Natural Sciences, Jimma University, Jimma, EthiopiaIn this paper, we consider a class of singularly perturbed differential equations of convection diffusion type with integral boundary condition. An accelerated uniformly convergent numerical method is constructed via exponentially fitted operator method using Richardson extrapolation techniques and numerical integration methods to solve the problem. The integral boundary condition is treated using numerical integration techniques. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent.http://dx.doi.org/10.1155/2020/9268181 |
| spellingShingle | Habtamu Garoma Debela Gemechis File Duressa Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition International Journal of Differential Equations |
| title | Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition |
| title_full | Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition |
| title_fullStr | Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition |
| title_full_unstemmed | Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition |
| title_short | Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition |
| title_sort | accelerated exponentially fitted operator method for singularly perturbed problems with integral boundary condition |
| url | http://dx.doi.org/10.1155/2020/9268181 |
| work_keys_str_mv | AT habtamugaromadebela acceleratedexponentiallyfittedoperatormethodforsingularlyperturbedproblemswithintegralboundarycondition AT gemechisfileduressa acceleratedexponentiallyfittedoperatormethodforsingularlyperturbedproblemswithintegralboundarycondition |