Numerical Study of the Inverse Problem of Generalized Burgers–Fisher and Generalized Burgers–Huxley Equations
In this paper, the boundary value inverse problem related to the generalized Burgers–Fisher and generalized Burgers–Huxley equations is solved numerically based on a spline approximation tool. B-splines with quasilinearization and Tikhonov regularization methods are used to obtain new numerical solu...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/6652108 |
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| author | Javad Alavi Hossein Aminikhah |
| author_facet | Javad Alavi Hossein Aminikhah |
| author_sort | Javad Alavi |
| collection | DOAJ |
| description | In this paper, the boundary value inverse problem related to the generalized Burgers–Fisher and generalized Burgers–Huxley equations is solved numerically based on a spline approximation tool. B-splines with quasilinearization and Tikhonov regularization methods are used to obtain new numerical solutions to this problem. First, a quasilinearization method is used to linearize the equation in a specific time step. Then, a linear combination of B-splines is used to approximate the largest order of derivatives in the equation. By integrating from this linear combination, some approximations have been obtained for each of the functions and derivatives with respect to time and space. The boundary and additional conditions of the problem are also applied in these approximations. The Tikhonov regularization method is used to solve the system of linear equations using noisy data. Several numerical examples are provided to illustrate the accuracy and efficiency of the method. |
| format | Article |
| id | doaj-art-ad670eee4eda417286ff85c40402582c |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-ad670eee4eda417286ff85c40402582c2025-02-03T01:07:08ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/66521086652108Numerical Study of the Inverse Problem of Generalized Burgers–Fisher and Generalized Burgers–Huxley EquationsJavad Alavi0Hossein Aminikhah1Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht 41938, IranDepartment of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht 41938, IranIn this paper, the boundary value inverse problem related to the generalized Burgers–Fisher and generalized Burgers–Huxley equations is solved numerically based on a spline approximation tool. B-splines with quasilinearization and Tikhonov regularization methods are used to obtain new numerical solutions to this problem. First, a quasilinearization method is used to linearize the equation in a specific time step. Then, a linear combination of B-splines is used to approximate the largest order of derivatives in the equation. By integrating from this linear combination, some approximations have been obtained for each of the functions and derivatives with respect to time and space. The boundary and additional conditions of the problem are also applied in these approximations. The Tikhonov regularization method is used to solve the system of linear equations using noisy data. Several numerical examples are provided to illustrate the accuracy and efficiency of the method.http://dx.doi.org/10.1155/2021/6652108 |
| spellingShingle | Javad Alavi Hossein Aminikhah Numerical Study of the Inverse Problem of Generalized Burgers–Fisher and Generalized Burgers–Huxley Equations Advances in Mathematical Physics |
| title | Numerical Study of the Inverse Problem of Generalized Burgers–Fisher and Generalized Burgers–Huxley Equations |
| title_full | Numerical Study of the Inverse Problem of Generalized Burgers–Fisher and Generalized Burgers–Huxley Equations |
| title_fullStr | Numerical Study of the Inverse Problem of Generalized Burgers–Fisher and Generalized Burgers–Huxley Equations |
| title_full_unstemmed | Numerical Study of the Inverse Problem of Generalized Burgers–Fisher and Generalized Burgers–Huxley Equations |
| title_short | Numerical Study of the Inverse Problem of Generalized Burgers–Fisher and Generalized Burgers–Huxley Equations |
| title_sort | numerical study of the inverse problem of generalized burgers fisher and generalized burgers huxley equations |
| url | http://dx.doi.org/10.1155/2021/6652108 |
| work_keys_str_mv | AT javadalavi numericalstudyoftheinverseproblemofgeneralizedburgersfisherandgeneralizedburgershuxleyequations AT hosseinaminikhah numericalstudyoftheinverseproblemofgeneralizedburgersfisherandgeneralizedburgershuxleyequations |