Hybrid Finite Differences Technique for Solving the Nonlinear Fractional Korteweg-De Vries-Burger Equation
This study presents a new algorithm for effectively solving the nonlinear fractional Korteweg-de Vries-Burger equation (NFKDV-B) using a hybrid explicit finite difference technique with the Adomian polynomial (HEFD). The suggested technique addresses the problem of accurately solving the FKDV-B equa...
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| Format: | Article |
| Language: | English |
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Mosul University
2023-12-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
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| Online Access: | https://csmj.mosuljournals.com/article_181636_b4f6d4b40af37e52ad0e178ee4ee1e61.pdf |
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| _version_ | 1850238067041894400 |
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| author | almutasim Hamed Ekhlass Al-Rawi |
| author_facet | almutasim Hamed Ekhlass Al-Rawi |
| author_sort | almutasim Hamed |
| collection | DOAJ |
| description | This study presents a new algorithm for effectively solving the nonlinear fractional Korteweg-de Vries-Burger equation (NFKDV-B) using a hybrid explicit finite difference technique with the Adomian polynomial (HEFD). The suggested technique addresses the problem of accurately solving the FKDV-B equation with fractional nonlinear space derivatives in numerical solutions. Numerical results are obtained by comparing the exact solution with absolute and mean square errors. The fractional time and space derivatives are estimated using two widely used techniques: the Caputo derivative and the shifted Grünwald-Letnikov (G-L) formulas.
Using a test problem to asses the HEFD method accuracy against the exact solution and the conventional explicit finite difference (EFD) method. The results exhibit excellent agreement between the approximate and exact solutions at different time values. The findings highlight the effectiveness of the proposed method across a range of fractional derivative values when compared to the exact solution and conventional explicit finite difference methods. |
| format | Article |
| id | doaj-art-30e673961362457d8ff4d2f64ecde250 |
| institution | OA Journals |
| issn | 1815-4816 2311-7990 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Mosul University |
| record_format | Article |
| series | Al-Rafidain Journal of Computer Sciences and Mathematics |
| spelling | doaj-art-30e673961362457d8ff4d2f64ecde2502025-08-20T02:01:34ZengMosul UniversityAl-Rafidain Journal of Computer Sciences and Mathematics1815-48162311-79902023-12-0117210510910.33899/csmj.2023.141335.1075181636Hybrid Finite Differences Technique for Solving the Nonlinear Fractional Korteweg-De Vries-Burger Equationalmutasim Hamed0Ekhlass Al-Rawi1Department of mathematics, College of computer science and mathematics, University of MosulCollege of Computer Sciences and Mathematics University of Mosul, Mosul, IraqThis study presents a new algorithm for effectively solving the nonlinear fractional Korteweg-de Vries-Burger equation (NFKDV-B) using a hybrid explicit finite difference technique with the Adomian polynomial (HEFD). The suggested technique addresses the problem of accurately solving the FKDV-B equation with fractional nonlinear space derivatives in numerical solutions. Numerical results are obtained by comparing the exact solution with absolute and mean square errors. The fractional time and space derivatives are estimated using two widely used techniques: the Caputo derivative and the shifted Grünwald-Letnikov (G-L) formulas. Using a test problem to asses the HEFD method accuracy against the exact solution and the conventional explicit finite difference (EFD) method. The results exhibit excellent agreement between the approximate and exact solutions at different time values. The findings highlight the effectiveness of the proposed method across a range of fractional derivative values when compared to the exact solution and conventional explicit finite difference methods.https://csmj.mosuljournals.com/article_181636_b4f6d4b40af37e52ad0e178ee4ee1e61.pdfhybrid finite differencefkdv-b equationadomian polynomialcaputo sensegrünwald-letnikov |
| spellingShingle | almutasim Hamed Ekhlass Al-Rawi Hybrid Finite Differences Technique for Solving the Nonlinear Fractional Korteweg-De Vries-Burger Equation Al-Rafidain Journal of Computer Sciences and Mathematics hybrid finite difference fkdv-b equation adomian polynomial caputo sense grünwald-letnikov |
| title | Hybrid Finite Differences Technique for Solving the Nonlinear Fractional Korteweg-De Vries-Burger Equation |
| title_full | Hybrid Finite Differences Technique for Solving the Nonlinear Fractional Korteweg-De Vries-Burger Equation |
| title_fullStr | Hybrid Finite Differences Technique for Solving the Nonlinear Fractional Korteweg-De Vries-Burger Equation |
| title_full_unstemmed | Hybrid Finite Differences Technique for Solving the Nonlinear Fractional Korteweg-De Vries-Burger Equation |
| title_short | Hybrid Finite Differences Technique for Solving the Nonlinear Fractional Korteweg-De Vries-Burger Equation |
| title_sort | hybrid finite differences technique for solving the nonlinear fractional korteweg de vries burger equation |
| topic | hybrid finite difference fkdv-b equation adomian polynomial caputo sense grünwald-letnikov |
| url | https://csmj.mosuljournals.com/article_181636_b4f6d4b40af37e52ad0e178ee4ee1e61.pdf |
| work_keys_str_mv | AT almutasimhamed hybridfinitedifferencestechniqueforsolvingthenonlinearfractionalkortewegdevriesburgerequation AT ekhlassalrawi hybridfinitedifferencestechniqueforsolvingthenonlinearfractionalkortewegdevriesburgerequation |