Enhanced rational multi-derivative integrator for singular problems with application to advection equations
Singular problems with discontinuities or steep gradients challenge traditional numerical integration methods. This study introduces the Rational Multi-Derivative Integrator (RMDI), designed specifically for such problems in ordinary and partial differential equations. The RMDI employs rational appr...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Ain Shams Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447924004416 |
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| author | Muideen O. Ogunniran Abeer Aljohani Ali Shokri Kamiludeen R. Tijani Yuanheng Wang |
| author_facet | Muideen O. Ogunniran Abeer Aljohani Ali Shokri Kamiludeen R. Tijani Yuanheng Wang |
| author_sort | Muideen O. Ogunniran |
| collection | DOAJ |
| description | Singular problems with discontinuities or steep gradients challenge traditional numerical integration methods. This study introduces the Rational Multi-Derivative Integrator (RMDI), designed specifically for such problems in ordinary and partial differential equations. The RMDI employs rational approximations and neural data to effectively manage singularities, enhancing accuracy and stability. Benchmark tests on singular ODEs and Advection equations show the RMDI reduces error rates by up to 99% and converges at singular points with errors within 1.5% of exact solutions. In real-world applications, the RMDI consistently outperforms existing methods, confirming its potential for practical use in scientific and engineering fields. |
| format | Article |
| id | doaj-art-0de15ebba0fb4839a9c384b97e7c7ece |
| institution | Kabale University |
| issn | 2090-4479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj-art-0de15ebba0fb4839a9c384b97e7c7ece2024-12-18T08:48:16ZengElsevierAin Shams Engineering Journal2090-44792024-12-011512103066Enhanced rational multi-derivative integrator for singular problems with application to advection equationsMuideen O. Ogunniran0Abeer Aljohani1Ali Shokri2Kamiludeen R. Tijani3Yuanheng Wang4Department of Mathematical Sciences, Osun State University, Osogbo, NigeriaDepartment of Computer Science and Informatics, Applied College, Taibah University Medina, 42353, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences, University of Maragheh, Maragheh 83111-55181, IranDepartment of Mathematical Sciences, Osun State University, Osogbo, NigeriaSchool of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China; Corresponding author.Singular problems with discontinuities or steep gradients challenge traditional numerical integration methods. This study introduces the Rational Multi-Derivative Integrator (RMDI), designed specifically for such problems in ordinary and partial differential equations. The RMDI employs rational approximations and neural data to effectively manage singularities, enhancing accuracy and stability. Benchmark tests on singular ODEs and Advection equations show the RMDI reduces error rates by up to 99% and converges at singular points with errors within 1.5% of exact solutions. In real-world applications, the RMDI consistently outperforms existing methods, confirming its potential for practical use in scientific and engineering fields.http://www.sciencedirect.com/science/article/pii/S2090447924004416Multi-derivative Hybrid methodsAdaptive algorithmsRational functionsError estimationConvergence and stability |
| spellingShingle | Muideen O. Ogunniran Abeer Aljohani Ali Shokri Kamiludeen R. Tijani Yuanheng Wang Enhanced rational multi-derivative integrator for singular problems with application to advection equations Ain Shams Engineering Journal Multi-derivative Hybrid methods Adaptive algorithms Rational functions Error estimation Convergence and stability |
| title | Enhanced rational multi-derivative integrator for singular problems with application to advection equations |
| title_full | Enhanced rational multi-derivative integrator for singular problems with application to advection equations |
| title_fullStr | Enhanced rational multi-derivative integrator for singular problems with application to advection equations |
| title_full_unstemmed | Enhanced rational multi-derivative integrator for singular problems with application to advection equations |
| title_short | Enhanced rational multi-derivative integrator for singular problems with application to advection equations |
| title_sort | enhanced rational multi derivative integrator for singular problems with application to advection equations |
| topic | Multi-derivative Hybrid methods Adaptive algorithms Rational functions Error estimation Convergence and stability |
| url | http://www.sciencedirect.com/science/article/pii/S2090447924004416 |
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