Numerical Solution of Heat Equation in Polar Cylindrical Coordinates by the Meshless Method of Lines
We propose a numerical solution to the heat equation in polar cylindrical coordinates by using the meshless method of lines approach. The space variables are discretized by multiquadric radial basis function, and time integration is performed by using the Runge-Kutta method of order 4. In radial bas...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/8862139 |
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| author | Arshad Hussain Marjan Uddin Sirajul Haq Hameed Ullah Jan |
| author_facet | Arshad Hussain Marjan Uddin Sirajul Haq Hameed Ullah Jan |
| author_sort | Arshad Hussain |
| collection | DOAJ |
| description | We propose a numerical solution to the heat equation in polar cylindrical coordinates by using the meshless method of lines approach. The space variables are discretized by multiquadric radial basis function, and time integration is performed by using the Runge-Kutta method of order 4. In radial basis functions (RBFs), much of the research are devoted to the partial differential equations in rectangular coordinates. This work is an attempt to explore the versatility of RBFs in nonrectangular coordinates as well. The results show that application of RBFs is equally good in polar cylindrical coordinates. Comparison with other cited works confirms that the present approach is accurate as well as easy to implement to problems in higher dimensions. |
| format | Article |
| id | doaj-art-0754a8d1e4844be2a150618cb12528a5 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-0754a8d1e4844be2a150618cb12528a52025-08-20T03:55:28ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/8862139Numerical Solution of Heat Equation in Polar Cylindrical Coordinates by the Meshless Method of LinesArshad Hussain0Marjan Uddin1Sirajul Haq2Hameed Ullah Jan3Department of MathematicsDepartment of Basic Sciences and IslamiatFaculty of Engineering SciencesDepartment of Basic Sciences and IslamiatWe propose a numerical solution to the heat equation in polar cylindrical coordinates by using the meshless method of lines approach. The space variables are discretized by multiquadric radial basis function, and time integration is performed by using the Runge-Kutta method of order 4. In radial basis functions (RBFs), much of the research are devoted to the partial differential equations in rectangular coordinates. This work is an attempt to explore the versatility of RBFs in nonrectangular coordinates as well. The results show that application of RBFs is equally good in polar cylindrical coordinates. Comparison with other cited works confirms that the present approach is accurate as well as easy to implement to problems in higher dimensions.http://dx.doi.org/10.1155/2021/8862139 |
| spellingShingle | Arshad Hussain Marjan Uddin Sirajul Haq Hameed Ullah Jan Numerical Solution of Heat Equation in Polar Cylindrical Coordinates by the Meshless Method of Lines Journal of Mathematics |
| title | Numerical Solution of Heat Equation in Polar Cylindrical Coordinates by the Meshless Method of Lines |
| title_full | Numerical Solution of Heat Equation in Polar Cylindrical Coordinates by the Meshless Method of Lines |
| title_fullStr | Numerical Solution of Heat Equation in Polar Cylindrical Coordinates by the Meshless Method of Lines |
| title_full_unstemmed | Numerical Solution of Heat Equation in Polar Cylindrical Coordinates by the Meshless Method of Lines |
| title_short | Numerical Solution of Heat Equation in Polar Cylindrical Coordinates by the Meshless Method of Lines |
| title_sort | numerical solution of heat equation in polar cylindrical coordinates by the meshless method of lines |
| url | http://dx.doi.org/10.1155/2021/8862139 |
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