A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters
A numerical treatment via a difference scheme constructed by the Crank–Nicolson scheme for the time derivative and cubic spline in tension for the spatial derivatives on a layer resolving nonuniform Bakhvalov-type mesh for a singularly perturbed unsteady-state initial-boundary-value problem with two...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2022/5410754 |
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| author | Tariku Birabasa Mekonnen Gemechis File Duressa |
| author_facet | Tariku Birabasa Mekonnen Gemechis File Duressa |
| author_sort | Tariku Birabasa Mekonnen |
| collection | DOAJ |
| description | A numerical treatment via a difference scheme constructed by the Crank–Nicolson scheme for the time derivative and cubic spline in tension for the spatial derivatives on a layer resolving nonuniform Bakhvalov-type mesh for a singularly perturbed unsteady-state initial-boundary-value problem with two small parameters is presented. Error analysis of the constructed scheme is discussed and shown to be parameter-uniformly convergent with second-order convergence. Numerical experimentation is taken to confirm the theoretical findings. |
| format | Article |
| id | doaj-art-6000ca422d5f45c9bbd4e64338ccaa6e |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-6000ca422d5f45c9bbd4e64338ccaa6e2025-08-20T03:34:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252022-01-01202210.1155/2022/5410754A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two ParametersTariku Birabasa Mekonnen0Gemechis File Duressa1Department of MathematicsDepartment of MathematicsA numerical treatment via a difference scheme constructed by the Crank–Nicolson scheme for the time derivative and cubic spline in tension for the spatial derivatives on a layer resolving nonuniform Bakhvalov-type mesh for a singularly perturbed unsteady-state initial-boundary-value problem with two small parameters is presented. Error analysis of the constructed scheme is discussed and shown to be parameter-uniformly convergent with second-order convergence. Numerical experimentation is taken to confirm the theoretical findings.http://dx.doi.org/10.1155/2022/5410754 |
| spellingShingle | Tariku Birabasa Mekonnen Gemechis File Duressa A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters International Journal of Mathematics and Mathematical Sciences |
| title | A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters |
| title_full | A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters |
| title_fullStr | A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters |
| title_full_unstemmed | A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters |
| title_short | A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters |
| title_sort | fitted mesh cubic spline in tension method for singularly perturbed problems with two parameters |
| url | http://dx.doi.org/10.1155/2022/5410754 |
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