An efficient numerical scheme for fractional model of telegraph equation
The present attempt is to design a novel approach for the numerical solution of fractional telegraph equation. The novelty of the paper exist in solving the time fractional telegraph equation with differential quadrature method based on cubic B-spline (MHB-DQM) for the fractional parameter 1<γ<...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-08-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016821007997 |
| _version_ | 1818521045995356160 |
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| author | M.S. Hashmi Urfa Aslam Jagdev Singh Kottakkaran Sooppy Nisar |
| author_facet | M.S. Hashmi Urfa Aslam Jagdev Singh Kottakkaran Sooppy Nisar |
| author_sort | M.S. Hashmi |
| collection | DOAJ |
| description | The present attempt is to design a novel approach for the numerical solution of fractional telegraph equation. The novelty of the paper exist in solving the time fractional telegraph equation with differential quadrature method based on cubic B-spline (MHB-DQM) for the fractional parameter 1<γ<2. Telegraph equation is used in electric transmission line to find distance and time. The fractional derivative involved in the equation is discretized using Caputo derivative. On the other hand, the terms involving space derivatives are approximated by fusion of differential quadrature method with modified version of cubic B-spline. Here B-spline acts as a basis to compute the weighted coefficients of differential quadrature method. This phenomenon reduce the PDE to the system of equations, which then are solved using suitable numerical technique. A matrix based technique is used to ensure the stability of the proposed scheme. Feasibility and applicability of this algorithm is performed using test problems. Approximate solutions obtained by MHB-DQM is portrayed through graph and tables in an interactive way. These results show that solution converges for smaller values of time and at various values of fractional parameter. |
| first_indexed | 2024-12-11T01:45:45Z |
| format | Article |
| id | doaj.art-20fb57f9a7194361a02ce3c5faa8d737 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-12-11T01:45:45Z |
| publishDate | 2022-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-20fb57f9a7194361a02ce3c5faa8d7372022-12-22T01:24:55ZengElsevierAlexandria Engineering Journal1110-01682022-08-0161863836393An efficient numerical scheme for fractional model of telegraph equationM.S. Hashmi0Urfa Aslam1Jagdev Singh2Kottakkaran Sooppy Nisar3Department of Mathematics, The Government Sadiq College Women University, Bahawalpur 63100, PakistanDepartment of Mathematics, The Government Sadiq College Women University, Bahawalpur 63100, PakistanDepartment of Mathematics, JECRC University, Jaipur 303905, Rajasthan, IndiaDepartment of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia; Corresponding author.The present attempt is to design a novel approach for the numerical solution of fractional telegraph equation. The novelty of the paper exist in solving the time fractional telegraph equation with differential quadrature method based on cubic B-spline (MHB-DQM) for the fractional parameter 1<γ<2. Telegraph equation is used in electric transmission line to find distance and time. The fractional derivative involved in the equation is discretized using Caputo derivative. On the other hand, the terms involving space derivatives are approximated by fusion of differential quadrature method with modified version of cubic B-spline. Here B-spline acts as a basis to compute the weighted coefficients of differential quadrature method. This phenomenon reduce the PDE to the system of equations, which then are solved using suitable numerical technique. A matrix based technique is used to ensure the stability of the proposed scheme. Feasibility and applicability of this algorithm is performed using test problems. Approximate solutions obtained by MHB-DQM is portrayed through graph and tables in an interactive way. These results show that solution converges for smaller values of time and at various values of fractional parameter.http://www.sciencedirect.com/science/article/pii/S1110016821007997Fractional telegraph equationHybrid B-spline differential quadrature methodCaputo fractional derivativeNumerical approximation |
| spellingShingle | M.S. Hashmi Urfa Aslam Jagdev Singh Kottakkaran Sooppy Nisar An efficient numerical scheme for fractional model of telegraph equation Alexandria Engineering Journal Fractional telegraph equation Hybrid B-spline differential quadrature method Caputo fractional derivative Numerical approximation |
| title | An efficient numerical scheme for fractional model of telegraph equation |
| title_full | An efficient numerical scheme for fractional model of telegraph equation |
| title_fullStr | An efficient numerical scheme for fractional model of telegraph equation |
| title_full_unstemmed | An efficient numerical scheme for fractional model of telegraph equation |
| title_short | An efficient numerical scheme for fractional model of telegraph equation |
| title_sort | efficient numerical scheme for fractional model of telegraph equation |
| topic | Fractional telegraph equation Hybrid B-spline differential quadrature method Caputo fractional derivative Numerical approximation |
| url | http://www.sciencedirect.com/science/article/pii/S1110016821007997 |
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