Numerical solution of a boundary value problem including both delay and boundary layer
Difference method on a piecewise uniform mesh of Shishkin type, for a singularly perturbed boundary-value problem for a nonlinear second order delay differential equation is analyzed. Also, the method is proved that it gives essentially first order parameter-uniform convergence in the discrete maxim...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2018-10-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/5367 |
| _version_ | 1818386722693578752 |
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| author | Erkan Cimen |
| author_facet | Erkan Cimen |
| author_sort | Erkan Cimen |
| collection | DOAJ |
| description | Difference method on a piecewise uniform mesh of Shishkin type, for a singularly perturbed boundary-value problem for a nonlinear second order delay differential equation is analyzed. Also, the method is proved that it gives essentially first order parameter-uniform convergence in the discrete maximum norm. Furthermore, numerical results are presented in support of the theory. |
| first_indexed | 2024-12-14T03:58:34Z |
| format | Article |
| id | doaj.art-e07dee38bf184c839e1e75f3ab8b6f81 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-14T03:58:34Z |
| publishDate | 2018-10-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-e07dee38bf184c839e1e75f3ab8b6f812022-12-21T23:18:01ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102018-10-0123410.3846/mma.2018.034Numerical solution of a boundary value problem including both delay and boundary layerErkan Cimen0Van Yuzuncu Yil University 65080, Van, TurkeyDifference method on a piecewise uniform mesh of Shishkin type, for a singularly perturbed boundary-value problem for a nonlinear second order delay differential equation is analyzed. Also, the method is proved that it gives essentially first order parameter-uniform convergence in the discrete maximum norm. Furthermore, numerical results are presented in support of the theory.https://journals.vgtu.lt/index.php/MMA/article/view/5367singular perturbationboundary-value problemfinite difference methoddelay differential equationShishkin mesh |
| spellingShingle | Erkan Cimen Numerical solution of a boundary value problem including both delay and boundary layer Mathematical Modelling and Analysis singular perturbation boundary-value problem finite difference method delay differential equation Shishkin mesh |
| title | Numerical solution of a boundary value problem including both delay and boundary layer |
| title_full | Numerical solution of a boundary value problem including both delay and boundary layer |
| title_fullStr | Numerical solution of a boundary value problem including both delay and boundary layer |
| title_full_unstemmed | Numerical solution of a boundary value problem including both delay and boundary layer |
| title_short | Numerical solution of a boundary value problem including both delay and boundary layer |
| title_sort | numerical solution of a boundary value problem including both delay and boundary layer |
| topic | singular perturbation boundary-value problem finite difference method delay differential equation Shishkin mesh |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/5367 |
| work_keys_str_mv | AT erkancimen numericalsolutionofaboundaryvalueproblemincludingbothdelayandboundarylayer |