Accelerated Fitted Mesh Scheme for Singularly Perturbed Turning Point Boundary Value Problems
An accelerated fitted mesh scheme is proposed for the numerical solution of the singularly perturbed boundary value problems whose solution exhibits an interior layer near the turning point. To resolve the interior layer, a mesh of the Shishkin type is used with the help of a transition parameter th...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/3767246 |
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| _version_ | 1832564879674834944 |
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| author | Tesfaye Aga Bullo |
| author_facet | Tesfaye Aga Bullo |
| author_sort | Tesfaye Aga Bullo |
| collection | DOAJ |
| description | An accelerated fitted mesh scheme is proposed for the numerical solution of the singularly perturbed boundary value problems whose solution exhibits an interior layer near the turning point. To resolve the interior layer, a mesh of the Shishkin type is used with the help of a transition parameter that separates the layer and regular region. A tridiagonal solver is implemented to solve the system of equation. The stability of the described scheme is analyzed, and the truncation error is obtained. The proposed scheme is of almost second-order convergent and accelerated to almost sixth-order convergent by applying the Richardson extrapolation technique. The numerical results obtained by the present scheme have been compared with some existing methods, and it is observed that it gives better accuracy. |
| format | Article |
| id | doaj-art-3fa9dd39781345e1bd617768ebcefd04 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-3fa9dd39781345e1bd617768ebcefd042025-02-03T01:09:54ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/3767246Accelerated Fitted Mesh Scheme for Singularly Perturbed Turning Point Boundary Value ProblemsTesfaye Aga Bullo0Department of MathematicsAn accelerated fitted mesh scheme is proposed for the numerical solution of the singularly perturbed boundary value problems whose solution exhibits an interior layer near the turning point. To resolve the interior layer, a mesh of the Shishkin type is used with the help of a transition parameter that separates the layer and regular region. A tridiagonal solver is implemented to solve the system of equation. The stability of the described scheme is analyzed, and the truncation error is obtained. The proposed scheme is of almost second-order convergent and accelerated to almost sixth-order convergent by applying the Richardson extrapolation technique. The numerical results obtained by the present scheme have been compared with some existing methods, and it is observed that it gives better accuracy.http://dx.doi.org/10.1155/2022/3767246 |
| spellingShingle | Tesfaye Aga Bullo Accelerated Fitted Mesh Scheme for Singularly Perturbed Turning Point Boundary Value Problems Journal of Mathematics |
| title | Accelerated Fitted Mesh Scheme for Singularly Perturbed Turning Point Boundary Value Problems |
| title_full | Accelerated Fitted Mesh Scheme for Singularly Perturbed Turning Point Boundary Value Problems |
| title_fullStr | Accelerated Fitted Mesh Scheme for Singularly Perturbed Turning Point Boundary Value Problems |
| title_full_unstemmed | Accelerated Fitted Mesh Scheme for Singularly Perturbed Turning Point Boundary Value Problems |
| title_short | Accelerated Fitted Mesh Scheme for Singularly Perturbed Turning Point Boundary Value Problems |
| title_sort | accelerated fitted mesh scheme for singularly perturbed turning point boundary value problems |
| url | http://dx.doi.org/10.1155/2022/3767246 |
| work_keys_str_mv | AT tesfayeagabullo acceleratedfittedmeshschemeforsingularlyperturbedturningpointboundaryvalueproblems |