Compact implicit difference approximation for time-fractional diffusion-wave equation
In this article, developed the compact implicit difference method based Grünwald Letnikov formula (GLF) to compute the solution of the time-fractional diffusion-wave equation (TFDWE) describing wave propagation phenomenan having order α (1<α<2). The fractional derivative is in Caputo sense. Th...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-05-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016821006074 |
| _version_ | 1811303075393044480 |
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| author | Umair Ali Azhar Iqbal Muhammad Sohail Farah Aini Abdullah Zohaib Khan |
| author_facet | Umair Ali Azhar Iqbal Muhammad Sohail Farah Aini Abdullah Zohaib Khan |
| author_sort | Umair Ali |
| collection | DOAJ |
| description | In this article, developed the compact implicit difference method based Grünwald Letnikov formula (GLF) to compute the solution of the time-fractional diffusion-wave equation (TFDWE) describing wave propagation phenomenan having order α (1<α<2). The fractional derivative is in Caputo sense. The theoretical analysis such as stability, consistency, convergence and solvability of the said scheme are discussed and proved that the scheme is conditionally stable and convergent with the order (τ2+(Δx)4). The numerical results compared with the recent existed method. The results of the numerical examples show that the GLF and the proposed method is very accurate and efficient for time fractional diffusion-wave equation. |
| first_indexed | 2024-04-13T07:40:08Z |
| format | Article |
| id | doaj.art-61bf3e3177ab43e7b6e69738562ae7c8 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-13T07:40:08Z |
| publishDate | 2022-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-61bf3e3177ab43e7b6e69738562ae7c82022-12-22T02:55:55ZengElsevierAlexandria Engineering Journal1110-01682022-05-0161541194126Compact implicit difference approximation for time-fractional diffusion-wave equationUmair Ali0Azhar Iqbal1Muhammad Sohail2Farah Aini Abdullah3Zohaib Khan4Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad 44000, PakistanMathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia; Corresponding author.Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad 44000, PakistanSchool of Mathematical Sciences, Universiti Sains Malaysia, Pulau Pinang 11800, MalaysiaFaculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat, Johor, Malaysia; Department of Mechanical Engineering, Quaid e Awam University of Engineering, Science and Technology Larkana (Campus) Sindh, PakistanIn this article, developed the compact implicit difference method based Grünwald Letnikov formula (GLF) to compute the solution of the time-fractional diffusion-wave equation (TFDWE) describing wave propagation phenomenan having order α (1<α<2). The fractional derivative is in Caputo sense. The theoretical analysis such as stability, consistency, convergence and solvability of the said scheme are discussed and proved that the scheme is conditionally stable and convergent with the order (τ2+(Δx)4). The numerical results compared with the recent existed method. The results of the numerical examples show that the GLF and the proposed method is very accurate and efficient for time fractional diffusion-wave equation.http://www.sciencedirect.com/science/article/pii/S1110016821006074Compact approximationImplicit difference schemeFractional diffusion-wave equationGrünwald Letnikov formulaStabilityConsistency |
| spellingShingle | Umair Ali Azhar Iqbal Muhammad Sohail Farah Aini Abdullah Zohaib Khan Compact implicit difference approximation for time-fractional diffusion-wave equation Alexandria Engineering Journal Compact approximation Implicit difference scheme Fractional diffusion-wave equation Grünwald Letnikov formula Stability Consistency |
| title | Compact implicit difference approximation for time-fractional diffusion-wave equation |
| title_full | Compact implicit difference approximation for time-fractional diffusion-wave equation |
| title_fullStr | Compact implicit difference approximation for time-fractional diffusion-wave equation |
| title_full_unstemmed | Compact implicit difference approximation for time-fractional diffusion-wave equation |
| title_short | Compact implicit difference approximation for time-fractional diffusion-wave equation |
| title_sort | compact implicit difference approximation for time fractional diffusion wave equation |
| topic | Compact approximation Implicit difference scheme Fractional diffusion-wave equation Grünwald Letnikov formula Stability Consistency |
| url | http://www.sciencedirect.com/science/article/pii/S1110016821006074 |
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