A numerical approach to solve hyperbolic telegraph equations via Pell–Lucas polynomials
In this article, a collocation approximation is investigated for approximate solutions of hyperbolic telegraph partial differential equations (HTPDEs). The method is based on evenly spaced collocation points and Pell–Lucas polynomials (PLPs). The form of solution, derivatives of unknown function in...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2023-12-01
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| Series: | Journal of Taibah University for Science |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/16583655.2023.2255404 |
| _version_ | 1797215151920775168 |
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| author | Şuayip Yüzbaşı Gamze Yıldırım |
| author_facet | Şuayip Yüzbaşı Gamze Yıldırım |
| author_sort | Şuayip Yüzbaşı |
| collection | DOAJ |
| description | In this article, a collocation approximation is investigated for approximate solutions of hyperbolic telegraph partial differential equations (HTPDEs). The method is based on evenly spaced collocation points and Pell–Lucas polynomials (PLPs). The form of solution, derivatives of unknown function in equation and conditions are expressed in matrix forms which depend on PLMs. By the help of these matrix forms and collocation points, problem is reduced to a system of linear algebraic equations. In addition, error analysis is performed for method. Thus, errors are bound by an upper bound. By making the applications of these techniques, the computed outcomes are offered in tables and graphs. Also the obtained outcomes by method are also compared with outcomes of other methods in the literature. These comparisons show that our method is more influential than other methods. All results have been computed by the aid of a code generated in MATLAB. |
| first_indexed | 2024-03-10T08:13:34Z |
| format | Article |
| id | doaj.art-55757b0705cc4bca863a3d3de3e51f7d |
| institution | Directory Open Access Journal |
| issn | 1658-3655 |
| language | English |
| last_indexed | 2024-04-24T11:25:31Z |
| publishDate | 2023-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Taibah University for Science |
| spelling | doaj.art-55757b0705cc4bca863a3d3de3e51f7d2024-04-10T20:17:48ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552023-12-0117110.1080/16583655.2023.2255404A numerical approach to solve hyperbolic telegraph equations via Pell–Lucas polynomialsŞuayip Yüzbaşı0Gamze Yıldırım1Faculty of Science, Department of Mathematics, Akdeniz University, Antalya, TurkeyFaculty of Science, Department of Mathematics, Akdeniz University, Antalya, TurkeyIn this article, a collocation approximation is investigated for approximate solutions of hyperbolic telegraph partial differential equations (HTPDEs). The method is based on evenly spaced collocation points and Pell–Lucas polynomials (PLPs). The form of solution, derivatives of unknown function in equation and conditions are expressed in matrix forms which depend on PLMs. By the help of these matrix forms and collocation points, problem is reduced to a system of linear algebraic equations. In addition, error analysis is performed for method. Thus, errors are bound by an upper bound. By making the applications of these techniques, the computed outcomes are offered in tables and graphs. Also the obtained outcomes by method are also compared with outcomes of other methods in the literature. These comparisons show that our method is more influential than other methods. All results have been computed by the aid of a code generated in MATLAB.https://www.tandfonline.com/doi/10.1080/16583655.2023.2255404Collocation methoderror analysishyperbolic equationspartial differential equationsPell–Lucas polynomials35L20 |
| spellingShingle | Şuayip Yüzbaşı Gamze Yıldırım A numerical approach to solve hyperbolic telegraph equations via Pell–Lucas polynomials Journal of Taibah University for Science Collocation method error analysis hyperbolic equations partial differential equations Pell–Lucas polynomials 35L20 |
| title | A numerical approach to solve hyperbolic telegraph equations via Pell–Lucas polynomials |
| title_full | A numerical approach to solve hyperbolic telegraph equations via Pell–Lucas polynomials |
| title_fullStr | A numerical approach to solve hyperbolic telegraph equations via Pell–Lucas polynomials |
| title_full_unstemmed | A numerical approach to solve hyperbolic telegraph equations via Pell–Lucas polynomials |
| title_short | A numerical approach to solve hyperbolic telegraph equations via Pell–Lucas polynomials |
| title_sort | numerical approach to solve hyperbolic telegraph equations via pell lucas polynomials |
| topic | Collocation method error analysis hyperbolic equations partial differential equations Pell–Lucas polynomials 35L20 |
| url | https://www.tandfonline.com/doi/10.1080/16583655.2023.2255404 |
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