A Parameter Uniform Almost First Order Convergent Numerical Method for a Semi-Linear System of Singularly Perturbed Delay Differential Equations
In this paper an initial value problem for asemi-linear system of two singularly perturbed first order delay differential equations is considered on the interval(0,2]. The components of the solution of this system exhibit initial layers at 0 and interior layers at 1. A numerical method composed of a...
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| Format: | Article |
| Language: | English |
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Bulgarian Academy of Sciences, Institute of Mathematics and Informatics
2014-12-01
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| Series: | Biomath |
| Subjects: | |
| Online Access: | http://www.biomathforum.org/biomath/index.php/biomath/article/view/355 |
| _version_ | 1797705789323870208 |
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| author | Nagaranjan Shivaranjan John J H Miller Sigmani Valarmathi |
| author_facet | Nagaranjan Shivaranjan John J H Miller Sigmani Valarmathi |
| author_sort | Nagaranjan Shivaranjan |
| collection | DOAJ |
| description | In this paper an initial value problem for asemi-linear system of two singularly perturbed first order delay differential equations is considered on the interval(0,2]. The components of the solution of this system exhibit initial layers at 0 and interior layers at 1. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be first order convergent in the maximum norm uniformly in the perturbation parameters. |
| first_indexed | 2024-03-12T05:41:36Z |
| format | Article |
| id | doaj.art-785ee6eea5ca45e3b6ac448717f32b65 |
| institution | Directory Open Access Journal |
| issn | 1314-684X 1314-7218 |
| language | English |
| last_indexed | 2024-03-12T05:41:36Z |
| publishDate | 2014-12-01 |
| publisher | Bulgarian Academy of Sciences, Institute of Mathematics and Informatics |
| record_format | Article |
| series | Biomath |
| spelling | doaj.art-785ee6eea5ca45e3b6ac448717f32b652023-09-03T05:59:29ZengBulgarian Academy of Sciences, Institute of Mathematics and InformaticsBiomath1314-684X1314-72182014-12-013210.11145/j.biomath.2014.11.04151252A Parameter Uniform Almost First Order Convergent Numerical Method for a Semi-Linear System of Singularly Perturbed Delay Differential EquationsNagaranjan Shivaranjan0John J H Miller1Sigmani Valarmathi2Bishop Heber CollegeTrinity College DublinBishop Heber College TiruchirappalliIn this paper an initial value problem for asemi-linear system of two singularly perturbed first order delay differential equations is considered on the interval(0,2]. The components of the solution of this system exhibit initial layers at 0 and interior layers at 1. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be first order convergent in the maximum norm uniformly in the perturbation parameters.http://www.biomathforum.org/biomath/index.php/biomath/article/view/355Perturbation problems, boundary layers, semi-linear delay differential equations, finite difference schemes, Shishkin mesh, parameter uniform convergence |
| spellingShingle | Nagaranjan Shivaranjan John J H Miller Sigmani Valarmathi A Parameter Uniform Almost First Order Convergent Numerical Method for a Semi-Linear System of Singularly Perturbed Delay Differential Equations Biomath Perturbation problems, boundary layers, semi-linear delay differential equations, finite difference schemes, Shishkin mesh, parameter uniform convergence |
| title | A Parameter Uniform Almost First Order Convergent Numerical Method for a Semi-Linear System of Singularly Perturbed Delay Differential Equations |
| title_full | A Parameter Uniform Almost First Order Convergent Numerical Method for a Semi-Linear System of Singularly Perturbed Delay Differential Equations |
| title_fullStr | A Parameter Uniform Almost First Order Convergent Numerical Method for a Semi-Linear System of Singularly Perturbed Delay Differential Equations |
| title_full_unstemmed | A Parameter Uniform Almost First Order Convergent Numerical Method for a Semi-Linear System of Singularly Perturbed Delay Differential Equations |
| title_short | A Parameter Uniform Almost First Order Convergent Numerical Method for a Semi-Linear System of Singularly Perturbed Delay Differential Equations |
| title_sort | parameter uniform almost first order convergent numerical method for a semi linear system of singularly perturbed delay differential equations |
| topic | Perturbation problems, boundary layers, semi-linear delay differential equations, finite difference schemes, Shishkin mesh, parameter uniform convergence |
| url | http://www.biomathforum.org/biomath/index.php/biomath/article/view/355 |
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