A new fourth-order grouping iterative method for the time fractional sub-diffusion equation having a weak singularity at initial time
A new fourth-order explicit grouping iterative method is constructed for the numerical solution of the fractional sub-diffusion equation. The discretization of the equation is based on fourth-order finite difference method. Captive fractional discretization having functions with a weak singularity a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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American Institute of Mathematical Sciences
2023
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| Online Access: | http://eprints.utm.my/104941/1/NormaAlias2023_ANewFourthOrderGroupingIterativeMethod.pdf |
| _version_ | 1796867757089751040 |
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| author | Khan, Muhammad Asim Alias, Norma Ali, Umair |
| author_facet | Khan, Muhammad Asim Alias, Norma Ali, Umair |
| author_sort | Khan, Muhammad Asim |
| collection | ePrints |
| description | A new fourth-order explicit grouping iterative method is constructed for the numerical solution of the fractional sub-diffusion equation. The discretization of the equation is based on fourth-order finite difference method. Captive fractional discretization having functions with a weak singularity at t = 0 is used for time and similarly, the space derivative is approximated with the help of fourth-order approximation. Furthermore, the convergence and stability of the scheme are analyzed. Finally, the accuracy and validity are investigated by some numerical examples. |
| first_indexed | 2024-04-09T03:45:39Z |
| format | Article |
| id | utm.eprints-104941 |
| institution | Universiti Teknologi Malaysia - ePrints |
| language | English |
| last_indexed | 2024-04-09T03:45:39Z |
| publishDate | 2023 |
| publisher | American Institute of Mathematical Sciences |
| record_format | dspace |
| spelling | utm.eprints-1049412024-04-01T06:14:21Z http://eprints.utm.my/104941/ A new fourth-order grouping iterative method for the time fractional sub-diffusion equation having a weak singularity at initial time Khan, Muhammad Asim Alias, Norma Ali, Umair QA Mathematics A new fourth-order explicit grouping iterative method is constructed for the numerical solution of the fractional sub-diffusion equation. The discretization of the equation is based on fourth-order finite difference method. Captive fractional discretization having functions with a weak singularity at t = 0 is used for time and similarly, the space derivative is approximated with the help of fourth-order approximation. Furthermore, the convergence and stability of the scheme are analyzed. Finally, the accuracy and validity are investigated by some numerical examples. American Institute of Mathematical Sciences 2023 Article PeerReviewed application/pdf en http://eprints.utm.my/104941/1/NormaAlias2023_ANewFourthOrderGroupingIterativeMethod.pdf Khan, Muhammad Asim and Alias, Norma and Ali, Umair (2023) A new fourth-order grouping iterative method for the time fractional sub-diffusion equation having a weak singularity at initial time. AIMS Mathematics, 8 (6). pp. 13725-13746. ISSN 2473-6988 http://dx.doi.org/10.3934/math.2023697 DOI : 10.3934/math.2023697 |
| spellingShingle | QA Mathematics Khan, Muhammad Asim Alias, Norma Ali, Umair A new fourth-order grouping iterative method for the time fractional sub-diffusion equation having a weak singularity at initial time |
| title | A new fourth-order grouping iterative method for the time fractional sub-diffusion equation having a weak singularity at initial time |
| title_full | A new fourth-order grouping iterative method for the time fractional sub-diffusion equation having a weak singularity at initial time |
| title_fullStr | A new fourth-order grouping iterative method for the time fractional sub-diffusion equation having a weak singularity at initial time |
| title_full_unstemmed | A new fourth-order grouping iterative method for the time fractional sub-diffusion equation having a weak singularity at initial time |
| title_short | A new fourth-order grouping iterative method for the time fractional sub-diffusion equation having a weak singularity at initial time |
| title_sort | new fourth order grouping iterative method for the time fractional sub diffusion equation having a weak singularity at initial time |
| topic | QA Mathematics |
| url | http://eprints.utm.my/104941/1/NormaAlias2023_ANewFourthOrderGroupingIterativeMethod.pdf |
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