A New Variant of B-Spline for the Solution of Modified Fractional Anomalous Subdiffusion Equation
The objective of this paper is to present an efficient numerical technique for solving time fractional modified anomalous subdiffusion equation. Anomalous diffusion equation has its role in various branches of biological sciences. B-spline is a piecewise function to draw curves and surfaces, which m...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/8047727 |
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| author | M. S. Hashmi Zainab Shehzad Asifa Ashraf Zhiyue Zhang Yu-Pei Lv Abdul Ghaffar Mustafa Inc Ayman A. Aly |
| author_facet | M. S. Hashmi Zainab Shehzad Asifa Ashraf Zhiyue Zhang Yu-Pei Lv Abdul Ghaffar Mustafa Inc Ayman A. Aly |
| author_sort | M. S. Hashmi |
| collection | DOAJ |
| description | The objective of this paper is to present an efficient numerical technique for solving time fractional modified anomalous subdiffusion equation. Anomalous diffusion equation has its role in various branches of biological sciences. B-spline is a piecewise function to draw curves and surfaces, which maintain its degree of smoothness at the connecting points. B-spline provides an active process of approximation to the limit curve. In current attempt, B-spline curve is used to approximate the solution curve of time fractional modified anomalous subdiffusion equation. The process is kept simple involving collocation procedure to the data points. The time fractional derivative is approximated with the discretized form of the Riemann-Liouville derivative. The process results in the form of system of algebraic equations, which is solved using a variant of Thomas algorithm. In order to ensure the convergence of the procedure, a valid method named Von Neumann stability analysis is attempted. The graphical and tabular display of results for the illustrated examples is presented, which stamped the efficiency of the proposed algorithm. |
| format | Article |
| id | doaj-art-3366a963d3d84b04b3143860633982fe |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-3366a963d3d84b04b3143860633982fe2025-02-03T07:23:53ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/80477278047727A New Variant of B-Spline for the Solution of Modified Fractional Anomalous Subdiffusion EquationM. S. Hashmi0Zainab Shehzad1Asifa Ashraf2Zhiyue Zhang3Yu-Pei Lv4Abdul Ghaffar5Mustafa Inc6Ayman A. Aly7Department of Mathematics, The Govt. Sadiq College Women University, Bahawalpur, PakistanDepartment of Mathematics, The Govt. Sadiq College Women University, Bahawalpur, PakistanSchool of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210023, ChinaSchool of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210023, ChinaDepartment of Mathematics, Huzhou University, Huzhou 313000, ChinaDepartment of Mathematics, Ghazi University, D G Khan, PakistanDepartment of Computer Engineering, Biruni University, Istanbul, TurkeyDepartment of Mechanical Engineering, College of Engineering, Taif University, P.O.Box 11099, Taif 21944, Saudi ArabiaThe objective of this paper is to present an efficient numerical technique for solving time fractional modified anomalous subdiffusion equation. Anomalous diffusion equation has its role in various branches of biological sciences. B-spline is a piecewise function to draw curves and surfaces, which maintain its degree of smoothness at the connecting points. B-spline provides an active process of approximation to the limit curve. In current attempt, B-spline curve is used to approximate the solution curve of time fractional modified anomalous subdiffusion equation. The process is kept simple involving collocation procedure to the data points. The time fractional derivative is approximated with the discretized form of the Riemann-Liouville derivative. The process results in the form of system of algebraic equations, which is solved using a variant of Thomas algorithm. In order to ensure the convergence of the procedure, a valid method named Von Neumann stability analysis is attempted. The graphical and tabular display of results for the illustrated examples is presented, which stamped the efficiency of the proposed algorithm.http://dx.doi.org/10.1155/2021/8047727 |
| spellingShingle | M. S. Hashmi Zainab Shehzad Asifa Ashraf Zhiyue Zhang Yu-Pei Lv Abdul Ghaffar Mustafa Inc Ayman A. Aly A New Variant of B-Spline for the Solution of Modified Fractional Anomalous Subdiffusion Equation Journal of Function Spaces |
| title | A New Variant of B-Spline for the Solution of Modified Fractional Anomalous Subdiffusion Equation |
| title_full | A New Variant of B-Spline for the Solution of Modified Fractional Anomalous Subdiffusion Equation |
| title_fullStr | A New Variant of B-Spline for the Solution of Modified Fractional Anomalous Subdiffusion Equation |
| title_full_unstemmed | A New Variant of B-Spline for the Solution of Modified Fractional Anomalous Subdiffusion Equation |
| title_short | A New Variant of B-Spline for the Solution of Modified Fractional Anomalous Subdiffusion Equation |
| title_sort | new variant of b spline for the solution of modified fractional anomalous subdiffusion equation |
| url | http://dx.doi.org/10.1155/2021/8047727 |
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