Parameter Uniform Numerical Method for Singularly Perturbed 2D Parabolic PDE with Shift in Space
Singularly perturbed 2D parabolic delay differential equations with the discontinuous source term and convection coefficient are taken into consideration in this paper. For the time derivative, we use the fractional implicit Euler method, followed by the fitted finite difference method with bilinear...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/18/3310 |
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| author | V. Subburayan S. Natesan |
| author_facet | V. Subburayan S. Natesan |
| author_sort | V. Subburayan |
| collection | DOAJ |
| description | Singularly perturbed 2D parabolic delay differential equations with the discontinuous source term and convection coefficient are taken into consideration in this paper. For the time derivative, we use the fractional implicit Euler method, followed by the fitted finite difference method with bilinear interpolation for locally one-dimensional problems. The proposed method is shown to be almost first-order convergent in the spatial direction and first-order convergent in the temporal direction. Theoretical results are illustrated with numerical examples. |
| first_indexed | 2024-03-09T23:15:30Z |
| format | Article |
| id | doaj.art-514178f2dd114704ad9a0bdc1ea29a10 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:15:30Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-514178f2dd114704ad9a0bdc1ea29a102023-11-23T17:36:23ZengMDPI AGMathematics2227-73902022-09-011018331010.3390/math10183310Parameter Uniform Numerical Method for Singularly Perturbed 2D Parabolic PDE with Shift in SpaceV. Subburayan0S. Natesan1Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamilnadu, IndiaDepartment of Mathematics, Indian Institute of Technology, Guwahati 781039, Assam, IndiaSingularly perturbed 2D parabolic delay differential equations with the discontinuous source term and convection coefficient are taken into consideration in this paper. For the time derivative, we use the fractional implicit Euler method, followed by the fitted finite difference method with bilinear interpolation for locally one-dimensional problems. The proposed method is shown to be almost first-order convergent in the spatial direction and first-order convergent in the temporal direction. Theoretical results are illustrated with numerical examples.https://www.mdpi.com/2227-7390/10/18/3310delay differential equations2D parabolic equationsfractional step methodconvection diffusion problems |
| spellingShingle | V. Subburayan S. Natesan Parameter Uniform Numerical Method for Singularly Perturbed 2D Parabolic PDE with Shift in Space Mathematics delay differential equations 2D parabolic equations fractional step method convection diffusion problems |
| title | Parameter Uniform Numerical Method for Singularly Perturbed 2D Parabolic PDE with Shift in Space |
| title_full | Parameter Uniform Numerical Method for Singularly Perturbed 2D Parabolic PDE with Shift in Space |
| title_fullStr | Parameter Uniform Numerical Method for Singularly Perturbed 2D Parabolic PDE with Shift in Space |
| title_full_unstemmed | Parameter Uniform Numerical Method for Singularly Perturbed 2D Parabolic PDE with Shift in Space |
| title_short | Parameter Uniform Numerical Method for Singularly Perturbed 2D Parabolic PDE with Shift in Space |
| title_sort | parameter uniform numerical method for singularly perturbed 2d parabolic pde with shift in space |
| topic | delay differential equations 2D parabolic equations fractional step method convection diffusion problems |
| url | https://www.mdpi.com/2227-7390/10/18/3310 |
| work_keys_str_mv | AT vsubburayan parameteruniformnumericalmethodforsingularlyperturbed2dparabolicpdewithshiftinspace AT snatesan parameteruniformnumericalmethodforsingularlyperturbed2dparabolicpdewithshiftinspace |