A numerical approach for 2D time-fractional diffusion damped wave model
In this article, we introduce an approximation of the rotated five-point difference Crank-Nicolson R(FPCN) approach for treating the second-order two-dimensional (2D) time-fractional diffusion-wave equation (TFDWE) with damping, which is constructed from two separate sets of equations, namely transv...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023416?viewType=HTML |
| _version_ | 1828014674902253568 |
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| author | Ajmal Ali Tayyaba Akram Azhar Iqbal Poom Kumam Thana Sutthibutpong |
| author_facet | Ajmal Ali Tayyaba Akram Azhar Iqbal Poom Kumam Thana Sutthibutpong |
| author_sort | Ajmal Ali |
| collection | DOAJ |
| description | In this article, we introduce an approximation of the rotated five-point difference Crank-Nicolson R(FPCN) approach for treating the second-order two-dimensional (2D) time-fractional diffusion-wave equation (TFDWE) with damping, which is constructed from two separate sets of equations, namely transverse electric and transverse magnetic phases. Such a category of equations can be achieved by altering second-order time derivative in the ordinary diffusion damped wave model by fractional Caputo derivative of order α while 1<α<2. The suggested methodology is developed from the standard five-points difference Crank-Nicolson S(FPCN) scheme by rotating clockwise 45o with respect to the standard knots. Numerical analysis is presented to demonstrate the applicability and feasibility of the R(FPCN) formulation over the S(FPCN) technique. The stability and convergence of the presented methodology are also performed. |
| first_indexed | 2024-04-10T10:05:38Z |
| format | Article |
| id | doaj.art-5f2bbdc492bd4613b673f17dee4e7e2f |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T10:05:38Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj.art-5f2bbdc492bd4613b673f17dee4e7e2f2023-02-16T01:08:40ZengAIMS PressAIMS Mathematics2473-69882023-01-01848249827310.3934/math.2023416A numerical approach for 2D time-fractional diffusion damped wave modelAjmal Ali 0Tayyaba Akram 1Azhar Iqbal2Poom Kumam3Thana Sutthibutpong 41. Department of Mathematics, Virtual University of Pakistan, Lahore 54000, Pakistan2. Departments of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, Bangkok 10140, Thailand3. Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia4. Center of Excellence in Theoretical and Computational Science & KMUTT Fixed Point Research Laboratory, Departments of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, Bangkok 10140, Thailand 5. Department of Medical Research, China Medical University, Taichung 40402, Taiwan6. Theoretical and Computational Physics Group, Department of Physics, King Mongkut's University of Technology Thonburi, Bangkok, Thailand 7. Center of Excellence in Theoretical and Computational Science Center, Faculty of Science, King Mongkut's University of Technology Thonburi, Bangkok 10140, ThailandIn this article, we introduce an approximation of the rotated five-point difference Crank-Nicolson R(FPCN) approach for treating the second-order two-dimensional (2D) time-fractional diffusion-wave equation (TFDWE) with damping, which is constructed from two separate sets of equations, namely transverse electric and transverse magnetic phases. Such a category of equations can be achieved by altering second-order time derivative in the ordinary diffusion damped wave model by fractional Caputo derivative of order α while 1<α<2. The suggested methodology is developed from the standard five-points difference Crank-Nicolson S(FPCN) scheme by rotating clockwise 45o with respect to the standard knots. Numerical analysis is presented to demonstrate the applicability and feasibility of the R(FPCN) formulation over the S(FPCN) technique. The stability and convergence of the presented methodology are also performed.https://www.aimspress.com/article/doi/10.3934/math.2023416?viewType=HTMLfractional derivativestandard and rotated five-point crank-nicolson approximationsfractional diffusion damped wave model |
| spellingShingle | Ajmal Ali Tayyaba Akram Azhar Iqbal Poom Kumam Thana Sutthibutpong A numerical approach for 2D time-fractional diffusion damped wave model AIMS Mathematics fractional derivative standard and rotated five-point crank-nicolson approximations fractional diffusion damped wave model |
| title | A numerical approach for 2D time-fractional diffusion damped wave model |
| title_full | A numerical approach for 2D time-fractional diffusion damped wave model |
| title_fullStr | A numerical approach for 2D time-fractional diffusion damped wave model |
| title_full_unstemmed | A numerical approach for 2D time-fractional diffusion damped wave model |
| title_short | A numerical approach for 2D time-fractional diffusion damped wave model |
| title_sort | numerical approach for 2d time fractional diffusion damped wave model |
| topic | fractional derivative standard and rotated five-point crank-nicolson approximations fractional diffusion damped wave model |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023416?viewType=HTML |
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