High order approximation on non-uniform meshes for generalized time-fractional telegraph equation
This paper presents a high order approximation scheme to solve the generalized fractional telegraph equation (GFTE) involving the generalized fractional derivative (GFD). The GFD is characterized by a scale function σ(t) and a weight function ω(t). Thus, we study the solution behavior of the GFTE fo...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-01-01
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| Series: | MethodsX |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2215016122002825 |
| _version_ | 1811177834147741696 |
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| author | Farheen Sultana Rajesh K. Pandey Deeksha Singh Om P. Agrawal |
| author_facet | Farheen Sultana Rajesh K. Pandey Deeksha Singh Om P. Agrawal |
| author_sort | Farheen Sultana |
| collection | DOAJ |
| description | This paper presents a high order approximation scheme to solve the generalized fractional telegraph equation (GFTE) involving the generalized fractional derivative (GFD). The GFD is characterized by a scale function σ(t) and a weight function ω(t). Thus, we study the solution behavior of the GFTE for different σ(t) and ω(t). The scale function either stretches or contracts the solution while the weight function dramatically shifts the numerical solution of the GFTE. The time fractional GFTE is approximated using quadratic scheme in the temporal direction and the compact finite difference scheme in the spatial direction. To improve the numerical scheme’s accuracy, we use the non-uniform mesh. The convergence order of the whole discretized scheme is, O(τ2α−3,h4), where τ and h are the temporal and spatial step sizes respectively. The outcomes of the work are as follows: • The error estimate for approximation of the GFD on non-uniform meshes is established. • The numerical scheme’s stability and convergence are examined. • Numerical results for four examples are compared with those obtained using other method. The study shows that the developed scheme achieves higher accuracy than the scheme discussed in literature. |
| first_indexed | 2024-04-11T06:09:01Z |
| format | Article |
| id | doaj.art-c8ae5e9d3c884f8b90bcb121993c1948 |
| institution | Directory Open Access Journal |
| issn | 2215-0161 |
| language | English |
| last_indexed | 2024-04-11T06:09:01Z |
| publishDate | 2022-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | MethodsX |
| spelling | doaj.art-c8ae5e9d3c884f8b90bcb121993c19482022-12-22T04:41:25ZengElsevierMethodsX2215-01612022-01-019101905High order approximation on non-uniform meshes for generalized time-fractional telegraph equationFarheen Sultana0Rajesh K. Pandey1Deeksha Singh2Om P. Agrawal3Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi, 221005, Uttar Pradesh, IndiaCorresponding author.; Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi, 221005, Uttar Pradesh, IndiaDepartment of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi, 221005, Uttar Pradesh, IndiaMechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, IL-62901, USAThis paper presents a high order approximation scheme to solve the generalized fractional telegraph equation (GFTE) involving the generalized fractional derivative (GFD). The GFD is characterized by a scale function σ(t) and a weight function ω(t). Thus, we study the solution behavior of the GFTE for different σ(t) and ω(t). The scale function either stretches or contracts the solution while the weight function dramatically shifts the numerical solution of the GFTE. The time fractional GFTE is approximated using quadratic scheme in the temporal direction and the compact finite difference scheme in the spatial direction. To improve the numerical scheme’s accuracy, we use the non-uniform mesh. The convergence order of the whole discretized scheme is, O(τ2α−3,h4), where τ and h are the temporal and spatial step sizes respectively. The outcomes of the work are as follows: • The error estimate for approximation of the GFD on non-uniform meshes is established. • The numerical scheme’s stability and convergence are examined. • Numerical results for four examples are compared with those obtained using other method. The study shows that the developed scheme achieves higher accuracy than the scheme discussed in literature.http://www.sciencedirect.com/science/article/pii/S2215016122002825High order approximation on non-uniform meshesfor generalized time-fractional telegraph equation |
| spellingShingle | Farheen Sultana Rajesh K. Pandey Deeksha Singh Om P. Agrawal High order approximation on non-uniform meshes for generalized time-fractional telegraph equation MethodsX High order approximation on non-uniform meshesfor generalized time-fractional telegraph equation |
| title | High order approximation on non-uniform meshes for generalized time-fractional telegraph equation |
| title_full | High order approximation on non-uniform meshes for generalized time-fractional telegraph equation |
| title_fullStr | High order approximation on non-uniform meshes for generalized time-fractional telegraph equation |
| title_full_unstemmed | High order approximation on non-uniform meshes for generalized time-fractional telegraph equation |
| title_short | High order approximation on non-uniform meshes for generalized time-fractional telegraph equation |
| title_sort | high order approximation on non uniform meshes for generalized time fractional telegraph equation |
| topic | High order approximation on non-uniform meshesfor generalized time-fractional telegraph equation |
| url | http://www.sciencedirect.com/science/article/pii/S2215016122002825 |
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