Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition
This paper presents the study of singularly perturbed differential equations of convection-diffusion type with nonlocal boundary condition. The proposed numerical scheme is a combination of the classical finite difference method for the boundary conditions and exponential fitted operator method for...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2021/5559486 |
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| _version_ | 1832552522908172288 |
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| author | Habtamu Garoma Debela |
| author_facet | Habtamu Garoma Debela |
| author_sort | Habtamu Garoma Debela |
| collection | DOAJ |
| description | This paper presents the study of singularly perturbed differential equations of convection-diffusion type with nonlocal boundary condition. The proposed numerical scheme is a combination of the classical finite difference method for the boundary conditions and exponential fitted operator method for the differential equations at the interior points. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical examples considered. The method is shown to be first-order accuracy independent of the perturbation parameter ε. |
| format | Article |
| id | doaj-art-b23a980982ee4b72a3a9b3bd23882fcf |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b23a980982ee4b72a3a9b3bd23882fcf2025-02-03T05:58:31ZengWileyAbstract and Applied Analysis1085-33751687-04092021-01-01202110.1155/2021/55594865559486Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary ConditionHabtamu Garoma Debela0Department of Mathematics, College of Natural Sciences, Jimma University, Jimma, EthiopiaThis paper presents the study of singularly perturbed differential equations of convection-diffusion type with nonlocal boundary condition. The proposed numerical scheme is a combination of the classical finite difference method for the boundary conditions and exponential fitted operator method for the differential equations at the interior points. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical examples considered. The method is shown to be first-order accuracy independent of the perturbation parameter ε.http://dx.doi.org/10.1155/2021/5559486 |
| spellingShingle | Habtamu Garoma Debela Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition Abstract and Applied Analysis |
| title | Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition |
| title_full | Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition |
| title_fullStr | Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition |
| title_full_unstemmed | Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition |
| title_short | Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition |
| title_sort | exponential fitted operator method for singularly perturbed convection diffusion type problems with nonlocal boundary condition |
| url | http://dx.doi.org/10.1155/2021/5559486 |
| work_keys_str_mv | AT habtamugaromadebela exponentialfittedoperatormethodforsingularlyperturbedconvectiondiffusiontypeproblemswithnonlocalboundarycondition |