Meshless Technique for the Solution of Time-Fractional Partial Differential Equations Having Real-World Applications
In this article, radial basis function collocation scheme is adopted for the numerical solution of fractional partial differential equations. This method is highly demanding because of its meshless nature and ease of implementation in high dimensions and complex geometries. Time derivative is approx...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/8898309 |
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| _version_ | 1832561171340722176 |
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| author | Mehnaz Shakeel Iltaf Hussain Hijaz Ahmad Imtiaz Ahmad Phatiphat Thounthong Ying-Fang Zhang |
| author_facet | Mehnaz Shakeel Iltaf Hussain Hijaz Ahmad Imtiaz Ahmad Phatiphat Thounthong Ying-Fang Zhang |
| author_sort | Mehnaz Shakeel |
| collection | DOAJ |
| description | In this article, radial basis function collocation scheme is adopted for the numerical solution of fractional partial differential equations. This method is highly demanding because of its meshless nature and ease of implementation in high dimensions and complex geometries. Time derivative is approximated by Caputo derivative for the values of α∈0,1 and α∈1,2. Forward difference scheme is applied to approximate the 1st order derivative appearing in the definition of Caputo derivative for α∈0,1, whereas central difference scheme is used for the 2nd order derivative in the definition of Caputo derivative for α∈1,2. Numerical problems are given to judge the behaviour of the proposed method for both the cases of α. Error norms are used to asses the accuracy of the method. Both uniform and nonuniform nodes are considered. Numerical simulation is carried out for irregular domain as well. Results are also compared with the existing methods in the literature. |
| format | Article |
| id | doaj-art-b3f2a840990e452c95cf4b21f7c4478c |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-b3f2a840990e452c95cf4b21f7c4478c2025-02-03T01:25:47ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/88983098898309Meshless Technique for the Solution of Time-Fractional Partial Differential Equations Having Real-World ApplicationsMehnaz Shakeel0Iltaf Hussain1Hijaz Ahmad2Imtiaz Ahmad3Phatiphat Thounthong4Ying-Fang Zhang5Department of Basic Sciences, University of Engineering and Technology, Peshawar, PakistanDepartment of Basic Sciences, University of Engineering and Technology, Peshawar, PakistanDepartment of Basic Sciences, University of Engineering and Technology, Peshawar, PakistanDepartment of Mathematics, University of Swabi, Khyber Pakhtunkhwa, PakistanRenewable Energy Research Centre, Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok, 1518 Pracharat 1 Road, Bangsue, Bangkok 10800, ThailandSchool of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, ChinaIn this article, radial basis function collocation scheme is adopted for the numerical solution of fractional partial differential equations. This method is highly demanding because of its meshless nature and ease of implementation in high dimensions and complex geometries. Time derivative is approximated by Caputo derivative for the values of α∈0,1 and α∈1,2. Forward difference scheme is applied to approximate the 1st order derivative appearing in the definition of Caputo derivative for α∈0,1, whereas central difference scheme is used for the 2nd order derivative in the definition of Caputo derivative for α∈1,2. Numerical problems are given to judge the behaviour of the proposed method for both the cases of α. Error norms are used to asses the accuracy of the method. Both uniform and nonuniform nodes are considered. Numerical simulation is carried out for irregular domain as well. Results are also compared with the existing methods in the literature.http://dx.doi.org/10.1155/2020/8898309 |
| spellingShingle | Mehnaz Shakeel Iltaf Hussain Hijaz Ahmad Imtiaz Ahmad Phatiphat Thounthong Ying-Fang Zhang Meshless Technique for the Solution of Time-Fractional Partial Differential Equations Having Real-World Applications Journal of Function Spaces |
| title | Meshless Technique for the Solution of Time-Fractional Partial Differential Equations Having Real-World Applications |
| title_full | Meshless Technique for the Solution of Time-Fractional Partial Differential Equations Having Real-World Applications |
| title_fullStr | Meshless Technique for the Solution of Time-Fractional Partial Differential Equations Having Real-World Applications |
| title_full_unstemmed | Meshless Technique for the Solution of Time-Fractional Partial Differential Equations Having Real-World Applications |
| title_short | Meshless Technique for the Solution of Time-Fractional Partial Differential Equations Having Real-World Applications |
| title_sort | meshless technique for the solution of time fractional partial differential equations having real world applications |
| url | http://dx.doi.org/10.1155/2020/8898309 |
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