Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations
Abstract This paper presents a novel approach to numerical solution of a class of fourth-order time fractional partial differential equations (PDEs). The finite difference formulation has been used for temporal discretization, whereas the space discretization is achieved by means of non-polynomial q...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-05-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2125-1 |
| _version_ | 1819146073661243392 |
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| author | Muhammad Amin Muhammad Abbas Muhammad Kashif Iqbal Dumitru Baleanu |
| author_facet | Muhammad Amin Muhammad Abbas Muhammad Kashif Iqbal Dumitru Baleanu |
| author_sort | Muhammad Amin |
| collection | DOAJ |
| description | Abstract This paper presents a novel approach to numerical solution of a class of fourth-order time fractional partial differential equations (PDEs). The finite difference formulation has been used for temporal discretization, whereas the space discretization is achieved by means of non-polynomial quintic spline method. The proposed algorithm is proved to be stable and convergent. In order to corroborate this work, some test problems have been considered, and the computational outcomes are compared with those found in the exiting literature. It is revealed that the presented scheme is more accurate as compared to current variants on the topic. |
| first_indexed | 2024-12-22T13:08:08Z |
| format | Article |
| id | doaj.art-0389f3b19f2a4641aa87e56be25bb753 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-22T13:08:08Z |
| publishDate | 2019-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-0389f3b19f2a4641aa87e56be25bb7532022-12-21T18:24:48ZengSpringerOpenAdvances in Difference Equations1687-18472019-05-012019112210.1186/s13662-019-2125-1Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equationsMuhammad Amin0Muhammad Abbas1Muhammad Kashif Iqbal2Dumitru Baleanu3Department of Mathematics, National College of Business Administration & EconomicsDepartment of Mathematics, University of SargodhaDepartment of Mathematics, Government College UniversityDepartment of Mathematics, Faculty of Arts and Sciences, Cankaya UniversityAbstract This paper presents a novel approach to numerical solution of a class of fourth-order time fractional partial differential equations (PDEs). The finite difference formulation has been used for temporal discretization, whereas the space discretization is achieved by means of non-polynomial quintic spline method. The proposed algorithm is proved to be stable and convergent. In order to corroborate this work, some test problems have been considered, and the computational outcomes are compared with those found in the exiting literature. It is revealed that the presented scheme is more accurate as compared to current variants on the topic.http://link.springer.com/article/10.1186/s13662-019-2125-1Non-polynomial quintic splineBackward Euler methodTime fractional partial differential equationCaputo fractional derivative |
| spellingShingle | Muhammad Amin Muhammad Abbas Muhammad Kashif Iqbal Dumitru Baleanu Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations Advances in Difference Equations Non-polynomial quintic spline Backward Euler method Time fractional partial differential equation Caputo fractional derivative |
| title | Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations |
| title_full | Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations |
| title_fullStr | Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations |
| title_full_unstemmed | Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations |
| title_short | Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations |
| title_sort | non polynomial quintic spline for numerical solution of fourth order time fractional partial differential equations |
| topic | Non-polynomial quintic spline Backward Euler method Time fractional partial differential equation Caputo fractional derivative |
| url | http://link.springer.com/article/10.1186/s13662-019-2125-1 |
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