Numerical Solution of Burgers–Huxley Equation Using a Higher Order Collocation Method
In this paper, the collocation method with cubic B-spline as basis function has been successfully applied to numerically solve the Burgers–Huxley equation. This equation illustrates a model for describing the interaction between reaction mechanisms, convection effects, and diffusion transport. Quasi...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/2439343 |
| _version_ | 1797269180746039296 |
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| author | Aditi Singh Sumita Dahiya Homan Emadifar Masoumeh Khademi |
| author_facet | Aditi Singh Sumita Dahiya Homan Emadifar Masoumeh Khademi |
| author_sort | Aditi Singh |
| collection | DOAJ |
| description | In this paper, the collocation method with cubic B-spline as basis function has been successfully applied to numerically solve the Burgers–Huxley equation. This equation illustrates a model for describing the interaction between reaction mechanisms, convection effects, and diffusion transport. Quasi-linearization has been employed to deal with the nonlinearity of equations. The Crank–Nicolson implicit scheme is used for discretization of the equation and the resulting system turned out to be semi-implicit. The stability of the method is discussed using Fourier series analysis (von Neumann method), and it has been concluded that the method is unconditionally stable. Various numerical experiments have been performed to demonstrate the authenticity of the scheme. We have found that the computed numerical solutions are in good agreement with the exact solutions and are competent with those available in the literature. Accuracy and minimal computational efforts are the key features of the proposed method. |
| first_indexed | 2024-04-25T01:44:17Z |
| format | Article |
| id | doaj.art-5de9115d73354e10bf5c809d9b2478d8 |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2024-04-25T01:44:17Z |
| publishDate | 2024-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-5de9115d73354e10bf5c809d9b2478d82024-03-08T00:00:03ZengHindawi LimitedJournal of Mathematics2314-47852024-01-01202410.1155/2024/2439343Numerical Solution of Burgers–Huxley Equation Using a Higher Order Collocation MethodAditi Singh0Sumita Dahiya1Homan Emadifar2Masoumeh Khademi3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsIn this paper, the collocation method with cubic B-spline as basis function has been successfully applied to numerically solve the Burgers–Huxley equation. This equation illustrates a model for describing the interaction between reaction mechanisms, convection effects, and diffusion transport. Quasi-linearization has been employed to deal with the nonlinearity of equations. The Crank–Nicolson implicit scheme is used for discretization of the equation and the resulting system turned out to be semi-implicit. The stability of the method is discussed using Fourier series analysis (von Neumann method), and it has been concluded that the method is unconditionally stable. Various numerical experiments have been performed to demonstrate the authenticity of the scheme. We have found that the computed numerical solutions are in good agreement with the exact solutions and are competent with those available in the literature. Accuracy and minimal computational efforts are the key features of the proposed method.http://dx.doi.org/10.1155/2024/2439343 |
| spellingShingle | Aditi Singh Sumita Dahiya Homan Emadifar Masoumeh Khademi Numerical Solution of Burgers–Huxley Equation Using a Higher Order Collocation Method Journal of Mathematics |
| title | Numerical Solution of Burgers–Huxley Equation Using a Higher Order Collocation Method |
| title_full | Numerical Solution of Burgers–Huxley Equation Using a Higher Order Collocation Method |
| title_fullStr | Numerical Solution of Burgers–Huxley Equation Using a Higher Order Collocation Method |
| title_full_unstemmed | Numerical Solution of Burgers–Huxley Equation Using a Higher Order Collocation Method |
| title_short | Numerical Solution of Burgers–Huxley Equation Using a Higher Order Collocation Method |
| title_sort | numerical solution of burgers huxley equation using a higher order collocation method |
| url | http://dx.doi.org/10.1155/2024/2439343 |
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