On Unconditionally Stable New Modified Fractional Group Iterative Scheme for the Solution of 2D Time-Fractional Telegraph Model
In this study, a new modified group iterative scheme for solving the two-dimensional (2D) fractional hyperbolic telegraph differential equation with Dirichlet boundary conditions is obtained from the <i>2h</i>-spaced standard and rotated Crank–Nicolson FD approximations. The findings of...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/11/2078 |
| _version_ | 1797508367823929344 |
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| author | Ajmal Ali Thabet Abdeljawad Azhar Iqbal Tayyaba Akram Muhammad Abbas |
| author_facet | Ajmal Ali Thabet Abdeljawad Azhar Iqbal Tayyaba Akram Muhammad Abbas |
| author_sort | Ajmal Ali |
| collection | DOAJ |
| description | In this study, a new modified group iterative scheme for solving the two-dimensional (2D) fractional hyperbolic telegraph differential equation with Dirichlet boundary conditions is obtained from the <i>2h</i>-spaced standard and rotated Crank–Nicolson FD approximations. The findings of new four-point modified explicit group relaxation method demonstrates the rapid rate of convergence of proposed method as compared to the existing schemes. Numerical tests are performed to test the capability of the group iterative scheme in comparison with the point iterative scheme counterparts. The stability of the derived modified group method is proven by the matrix norm algorithm. The obtained results are tabulated and concluded that exact solutions are exactly symmetric with approximate solutions. |
| first_indexed | 2024-03-10T05:01:08Z |
| format | Article |
| id | doaj.art-61c811ef1861483f868ea380fbb344b9 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T05:01:08Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-61c811ef1861483f868ea380fbb344b92023-11-23T01:44:33ZengMDPI AGSymmetry2073-89942021-11-011311207810.3390/sym13112078On Unconditionally Stable New Modified Fractional Group Iterative Scheme for the Solution of 2D Time-Fractional Telegraph ModelAjmal Ali0Thabet Abdeljawad1Azhar Iqbal2Tayyaba Akram3Muhammad Abbas4Department of Mathematics, Virtual University of Pakistan, Lahore 54000, PakistanDepartment of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaMathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi ArabiaSchool of Mathematical Sciences, Universiti Sains Malaysia, Gelugor 11800, MalaysiaDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanIn this study, a new modified group iterative scheme for solving the two-dimensional (2D) fractional hyperbolic telegraph differential equation with Dirichlet boundary conditions is obtained from the <i>2h</i>-spaced standard and rotated Crank–Nicolson FD approximations. The findings of new four-point modified explicit group relaxation method demonstrates the rapid rate of convergence of proposed method as compared to the existing schemes. Numerical tests are performed to test the capability of the group iterative scheme in comparison with the point iterative scheme counterparts. The stability of the derived modified group method is proven by the matrix norm algorithm. The obtained results are tabulated and concluded that exact solutions are exactly symmetric with approximate solutions.https://www.mdpi.com/2073-8994/13/11/2078Caputo’s fractional derivativestandard and rotated schemesfractional telegraph equationmodified group iterative methodmatrix norm |
| spellingShingle | Ajmal Ali Thabet Abdeljawad Azhar Iqbal Tayyaba Akram Muhammad Abbas On Unconditionally Stable New Modified Fractional Group Iterative Scheme for the Solution of 2D Time-Fractional Telegraph Model Symmetry Caputo’s fractional derivative standard and rotated schemes fractional telegraph equation modified group iterative method matrix norm |
| title | On Unconditionally Stable New Modified Fractional Group Iterative Scheme for the Solution of 2D Time-Fractional Telegraph Model |
| title_full | On Unconditionally Stable New Modified Fractional Group Iterative Scheme for the Solution of 2D Time-Fractional Telegraph Model |
| title_fullStr | On Unconditionally Stable New Modified Fractional Group Iterative Scheme for the Solution of 2D Time-Fractional Telegraph Model |
| title_full_unstemmed | On Unconditionally Stable New Modified Fractional Group Iterative Scheme for the Solution of 2D Time-Fractional Telegraph Model |
| title_short | On Unconditionally Stable New Modified Fractional Group Iterative Scheme for the Solution of 2D Time-Fractional Telegraph Model |
| title_sort | on unconditionally stable new modified fractional group iterative scheme for the solution of 2d time fractional telegraph model |
| topic | Caputo’s fractional derivative standard and rotated schemes fractional telegraph equation modified group iterative method matrix norm |
| url | https://www.mdpi.com/2073-8994/13/11/2078 |
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