Operational matrices based on the shifted fifth-kind Chebyshev polynomials for solving nonlinear variable order integro-differential equations
Abstract In this research, we study a general class of variable order integro-differential equations (VO-IDEs). We propose a numerical scheme based on the shifted fifth-kind Chebyshev polynomials (SFKCPs). First, in this scheme, we expand the unknown function and its derivatives in terms of the SFKC...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03588-2 |
| _version_ | 1819242636312051712 |
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| author | H. Jafari S. Nemati R. M. Ganji |
| author_facet | H. Jafari S. Nemati R. M. Ganji |
| author_sort | H. Jafari |
| collection | DOAJ |
| description | Abstract In this research, we study a general class of variable order integro-differential equations (VO-IDEs). We propose a numerical scheme based on the shifted fifth-kind Chebyshev polynomials (SFKCPs). First, in this scheme, we expand the unknown function and its derivatives in terms of the SFKCPs. To carry out the proposed scheme, we calculate the operational matrices depending on the SFKCPs to find an approximate solution of the original problem. These matrices, together with the collocation points, are used to transform the original problem to form a system of linear or nonlinear algebraic equations. We discuss the convergence of the method and then give an estimation of the error. We end by solving numerical tests, which show the high accuracy of our results. |
| first_indexed | 2024-12-23T14:42:57Z |
| format | Article |
| id | doaj.art-1cf4d41069424a4cb1fd3f2674b4b273 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-23T14:42:57Z |
| publishDate | 2021-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-1cf4d41069424a4cb1fd3f2674b4b2732022-12-21T17:43:10ZengSpringerOpenAdvances in Difference Equations1687-18472021-10-012021111410.1186/s13662-021-03588-2Operational matrices based on the shifted fifth-kind Chebyshev polynomials for solving nonlinear variable order integro-differential equationsH. Jafari0S. Nemati1R. M. Ganji2Department of Applied Mathematics, Faculty of Mathematical Sciences, University of MazandaranDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of MazandaranDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of MazandaranAbstract In this research, we study a general class of variable order integro-differential equations (VO-IDEs). We propose a numerical scheme based on the shifted fifth-kind Chebyshev polynomials (SFKCPs). First, in this scheme, we expand the unknown function and its derivatives in terms of the SFKCPs. To carry out the proposed scheme, we calculate the operational matrices depending on the SFKCPs to find an approximate solution of the original problem. These matrices, together with the collocation points, are used to transform the original problem to form a system of linear or nonlinear algebraic equations. We discuss the convergence of the method and then give an estimation of the error. We end by solving numerical tests, which show the high accuracy of our results.https://doi.org/10.1186/s13662-021-03588-2Shifted fifth-kind Chebyshev polynomialsVariable orderNonlinear integro-differential equationsOperational matrixConvergence analysis |
| spellingShingle | H. Jafari S. Nemati R. M. Ganji Operational matrices based on the shifted fifth-kind Chebyshev polynomials for solving nonlinear variable order integro-differential equations Advances in Difference Equations Shifted fifth-kind Chebyshev polynomials Variable order Nonlinear integro-differential equations Operational matrix Convergence analysis |
| title | Operational matrices based on the shifted fifth-kind Chebyshev polynomials for solving nonlinear variable order integro-differential equations |
| title_full | Operational matrices based on the shifted fifth-kind Chebyshev polynomials for solving nonlinear variable order integro-differential equations |
| title_fullStr | Operational matrices based on the shifted fifth-kind Chebyshev polynomials for solving nonlinear variable order integro-differential equations |
| title_full_unstemmed | Operational matrices based on the shifted fifth-kind Chebyshev polynomials for solving nonlinear variable order integro-differential equations |
| title_short | Operational matrices based on the shifted fifth-kind Chebyshev polynomials for solving nonlinear variable order integro-differential equations |
| title_sort | operational matrices based on the shifted fifth kind chebyshev polynomials for solving nonlinear variable order integro differential equations |
| topic | Shifted fifth-kind Chebyshev polynomials Variable order Nonlinear integro-differential equations Operational matrix Convergence analysis |
| url | https://doi.org/10.1186/s13662-021-03588-2 |
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