Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method
In this study, an iterative approximation is proposed by using the reproducing kernel method (RKM) for the nonlinear advection equation. To apply the iterative RKM, specific reproducing kernel spaces are defined and their kernel functions are presented. The proposed method requires homogenising the...
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| Format: | Article |
| Language: | English |
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Mahmut Akyigit
2024-12-01
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| Series: | Journal of Mathematical Sciences and Modelling |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/4411984 |
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| author | Onur Saldır |
| author_facet | Onur Saldır |
| author_sort | Onur Saldır |
| collection | DOAJ |
| description | In this study, an iterative approximation is proposed by using the reproducing kernel method (RKM) for the nonlinear advection equation. To apply the iterative RKM, specific reproducing kernel spaces are defined and their kernel functions are presented. The proposed method requires homogenising the initial or boundary conditions of the problem under consideration. After homogenising the initial condition of the advection equation, a linear operator selection is made, and then the approximate solution is constructed using orthonormal basis functions in serial form. Convergence analysis of the approximate solution is demonstrated through the lemma and theorem. Numerical outcomes are provided in the form of graphics and tables to show the efficiency and accuracy of the presented method. |
| format | Article |
| id | doaj-art-e57ee92f598d4681a1aa7c1c97ead11f |
| institution | Kabale University |
| issn | 2636-8692 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Mahmut Akyigit |
| record_format | Article |
| series | Journal of Mathematical Sciences and Modelling |
| spelling | doaj-art-e57ee92f598d4681a1aa7c1c97ead11f2024-12-31T09:27:47ZengMahmut AkyigitJournal of Mathematical Sciences and Modelling2636-86922024-12-017315716710.33187/jmsm.15952761408Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel MethodOnur Saldır0https://orcid.org/0000-0002-5292-9458VAN YÜZÜNCÜ YIL ÜNİVERSİTESİIn this study, an iterative approximation is proposed by using the reproducing kernel method (RKM) for the nonlinear advection equation. To apply the iterative RKM, specific reproducing kernel spaces are defined and their kernel functions are presented. The proposed method requires homogenising the initial or boundary conditions of the problem under consideration. After homogenising the initial condition of the advection equation, a linear operator selection is made, and then the approximate solution is constructed using orthonormal basis functions in serial form. Convergence analysis of the approximate solution is demonstrated through the lemma and theorem. Numerical outcomes are provided in the form of graphics and tables to show the efficiency and accuracy of the presented method.https://dergipark.org.tr/en/download/article-file/4411984advection equationconvergenceiterative solutionnumerical solutionreproducing kernel method |
| spellingShingle | Onur Saldır Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method Journal of Mathematical Sciences and Modelling advection equation convergence iterative solution numerical solution reproducing kernel method |
| title | Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method |
| title_full | Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method |
| title_fullStr | Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method |
| title_full_unstemmed | Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method |
| title_short | Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method |
| title_sort | numerical solution of nonlinear advection equation using reproducing kernel method |
| topic | advection equation convergence iterative solution numerical solution reproducing kernel method |
| url | https://dergipark.org.tr/en/download/article-file/4411984 |
| work_keys_str_mv | AT onursaldır numericalsolutionofnonlinearadvectionequationusingreproducingkernelmethod |