Research Article
Year 2025,
Volume: 24 Issue: 47, 249 - 260, 30.06.2025
Abstract
Bilimde çeşitli problemlerde Burgers-Huxley denklemi ile karşılaşılmaktadır. Bu çalışmada kompakt sonlu fark şeması, Burgers-Huxley denkleminin çözümü için uygulanmıştır. Çözümler farklı yöntemlerle elde edilen sonuçlarla karşılaştırılmıştır. Lineer olmayan denklem diskrize edildikten sonra çözümün doğruluğunu analiz etmek için dağılım analiz yapılmıştır. İncelenen problemler üzerinde kompakt sonlu fark şemasının doğruluğu ve hesaplama verimliliği gösterilmiştir.
References
- Anjali, K., Vivek. S. & Rajesh, K. G. (2025). Comparative Analysis of the Singularly Perturbed Generalized Burgers-Huxley Problem via Approximate Lie Symmetry and Exponentially Fitted Finite Element Method. International Journal of Theoretical Physics, 64, https://doi.org/10.1007/s10773-025-05882-1. Aydın, A. & Karasozen, B. (2010). Multisymplectic box schemes for the complex modified Korteweg-de Varies equation. Journal of Mathematical Physics, 51, 083511.
- Batiha, B., Noorani, M.S.M. & Hashim, I. (2008). Application of variational iteration method to the generalized Burgers-Huxley equation. Chaos Solitons @ Fractals , 36, 660-663.
- Bratsos, A.G. (2011). A fourth order improved numerical scheme for the generalized Burgers-Huxley equation. Am J Comput Math, 1, 152-158.
- Celikten, G. & Cankurt, A. (2022). A Numerical Solution of the Generalized Burgers-Huxley Equation. AKÜ FEMUBID, 22, 75-84.
- Chin, PWM. (2023). The analysis of the solution of the Burgers-Huxley equation using the Galerkin method. Numerical Methods For Partial Differential Equations, 39, 2787-2807.
- Hashim, I., Noorani, M.S.M. & Al-Hadidi, MRS. (2006). Solving the generalized Burgers-Huxley equation using the adomain decomposition method. Math Comput Model, 43, 1404-1411.
- Ismail, H.N.A., Raslan, K. & Rabboh, A.A.A. (2004). Adomain decomposition method for Burgers-Huxley and Burgers-Fisher equations. Appl Math Comput , 159, 291-301.
- Javidi, M. (2006). A numerical solution of the generalized Burgers-Huxley equation by pseudospectral method and darvishi’s preconditioning. Appl Math Comput, 175, 1619-1628.
- Javidi, M. (2006). A numerical solution of the generalized Burgers-Huxley equation by spectral collocation method. Appl Math Comput, 178, 338-344.
- Javidi, M. & Golbabai, A. (2009). A new domain decomposition algorithm for generalized Burger’s-Huxley equation based on Chebyshev polynomials and preconditioning. Chaos Solitons and Fractals, 39, 849-857.
- Lele, S.K. (1992). Compact finite difference schemes with Spectral-like. Resolution, Journal of Computational Physics, 103, 16-42.
- Mohanty, R.K. Weizhong, D. & Donn, L. (2015). Operator compact method of accuracy two time in time and four in space for the solution of time dependent Burgers-Huxley equation. Numer Algor, 70, 591-605.
- Molabahramin, A. & Khani, F. (2009). The homotopy analysisi method to solved the Burgers-Huxley equation. Nonlinear Analysis, Real World Applications, 2, 589-600.
- Rusli, R., Nasir, M. A. S., Harun, N., Rathi, S. & Zubaidah, S. (2025). A new modified compact finite difference scheme for solving the generalized Burgers-Huxley equation in teaching and learning processes. Journal of Quality Measurement and Analysis, 21, 195-205.
- Satsuma, J. (1986). Exact Solutions of Burgers Equation with Reaction Terms. Topics in Soliton Theory and Exactly Solvable Nonlinear Equations, World Sci Pub, Singapore.
- Shenggao, Z. & Xiaoliang, C. (2011). A linearly semi-implicit compact scheme for the Burgers-Huxley equation. International Journal of Computer Mathematics, 88, 795-804.
- Singh, A., Dahiya, S. & Emdifar, H. (2024). Numerical Solution of Burgers-Huxley Equation Using a Higher Order Collocation Method. Journal of Mathematics, doi.org/10.1155/2024/2439343.
- Yefimova, O.Y. & Kudryashov, N.A. (2004). Exact solutions of the Burgers-Huxley equation. J Appl Math Mech., 3, 413-420.
- Zhang, R., Yu, X. & Zhao, G. (2012). The local discontinuous Galerkin Method for Burger’s-Huxley and Burger’s-Fisher equations. Applied Mathematics and Computation, 17, 8773-8778.
- Zibaei, S., Zeinadini, M. & Namjoo, M. (2016). Numerical solutions of Burgers-Huxley equation by exact finite difference and NSFD schemes. Journal of Difference Equations and Applications, 22, 1098-1113.
- Wazwaz, A.M. (2008). Analytic study on Burgers, Fisher, Huxley equations and combined forms of these equations. Applied Mathematics and Computation, 2, 754-761.
Year 2025,
Volume: 24 Issue: 47, 249 - 260, 30.06.2025
Abstract
The Burgers-Huxley equation arises in several problems in science. The compact finite difference scheme (CFDS) has been developed for the Burgers-Huxley equation. This scheme has been compared different methods for the Burgers-Huxley equation. Dispersive properties are investigated for the linearized equations to examine the nonlinear dynamics after discretisation. The accuracy and computational efficiency of the compact finite differences scheme are shown in numerical test problems.
References
- Anjali, K., Vivek. S. & Rajesh, K. G. (2025). Comparative Analysis of the Singularly Perturbed Generalized Burgers-Huxley Problem via Approximate Lie Symmetry and Exponentially Fitted Finite Element Method. International Journal of Theoretical Physics, 64, https://doi.org/10.1007/s10773-025-05882-1. Aydın, A. & Karasozen, B. (2010). Multisymplectic box schemes for the complex modified Korteweg-de Varies equation. Journal of Mathematical Physics, 51, 083511.
- Batiha, B., Noorani, M.S.M. & Hashim, I. (2008). Application of variational iteration method to the generalized Burgers-Huxley equation. Chaos Solitons @ Fractals , 36, 660-663.
- Bratsos, A.G. (2011). A fourth order improved numerical scheme for the generalized Burgers-Huxley equation. Am J Comput Math, 1, 152-158.
- Celikten, G. & Cankurt, A. (2022). A Numerical Solution of the Generalized Burgers-Huxley Equation. AKÜ FEMUBID, 22, 75-84.
- Chin, PWM. (2023). The analysis of the solution of the Burgers-Huxley equation using the Galerkin method. Numerical Methods For Partial Differential Equations, 39, 2787-2807.
- Hashim, I., Noorani, M.S.M. & Al-Hadidi, MRS. (2006). Solving the generalized Burgers-Huxley equation using the adomain decomposition method. Math Comput Model, 43, 1404-1411.
- Ismail, H.N.A., Raslan, K. & Rabboh, A.A.A. (2004). Adomain decomposition method for Burgers-Huxley and Burgers-Fisher equations. Appl Math Comput , 159, 291-301.
- Javidi, M. (2006). A numerical solution of the generalized Burgers-Huxley equation by pseudospectral method and darvishi’s preconditioning. Appl Math Comput, 175, 1619-1628.
- Javidi, M. (2006). A numerical solution of the generalized Burgers-Huxley equation by spectral collocation method. Appl Math Comput, 178, 338-344.
- Javidi, M. & Golbabai, A. (2009). A new domain decomposition algorithm for generalized Burger’s-Huxley equation based on Chebyshev polynomials and preconditioning. Chaos Solitons and Fractals, 39, 849-857.
- Lele, S.K. (1992). Compact finite difference schemes with Spectral-like. Resolution, Journal of Computational Physics, 103, 16-42.
- Mohanty, R.K. Weizhong, D. & Donn, L. (2015). Operator compact method of accuracy two time in time and four in space for the solution of time dependent Burgers-Huxley equation. Numer Algor, 70, 591-605.
- Molabahramin, A. & Khani, F. (2009). The homotopy analysisi method to solved the Burgers-Huxley equation. Nonlinear Analysis, Real World Applications, 2, 589-600.
- Rusli, R., Nasir, M. A. S., Harun, N., Rathi, S. & Zubaidah, S. (2025). A new modified compact finite difference scheme for solving the generalized Burgers-Huxley equation in teaching and learning processes. Journal of Quality Measurement and Analysis, 21, 195-205.
- Satsuma, J. (1986). Exact Solutions of Burgers Equation with Reaction Terms. Topics in Soliton Theory and Exactly Solvable Nonlinear Equations, World Sci Pub, Singapore.
- Shenggao, Z. & Xiaoliang, C. (2011). A linearly semi-implicit compact scheme for the Burgers-Huxley equation. International Journal of Computer Mathematics, 88, 795-804.
- Singh, A., Dahiya, S. & Emdifar, H. (2024). Numerical Solution of Burgers-Huxley Equation Using a Higher Order Collocation Method. Journal of Mathematics, doi.org/10.1155/2024/2439343.
- Yefimova, O.Y. & Kudryashov, N.A. (2004). Exact solutions of the Burgers-Huxley equation. J Appl Math Mech., 3, 413-420.
- Zhang, R., Yu, X. & Zhao, G. (2012). The local discontinuous Galerkin Method for Burger’s-Huxley and Burger’s-Fisher equations. Applied Mathematics and Computation, 17, 8773-8778.
- Zibaei, S., Zeinadini, M. & Namjoo, M. (2016). Numerical solutions of Burgers-Huxley equation by exact finite difference and NSFD schemes. Journal of Difference Equations and Applications, 22, 1098-1113.
- Wazwaz, A.M. (2008). Analytic study on Burgers, Fisher, Huxley equations and combined forms of these equations. Applied Mathematics and Computation, 2, 754-761.
There are 21 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Numerical Analysis |
| Journal Section | Research Article |
| Authors | |
| Early Pub Date | June 14, 2025 |
| Publication Date | June 30, 2025 |
| Submission Date | January 27, 2025 |
| Acceptance Date | April 16, 2025 |
| Published in Issue | Year 2025 Volume: 24 Issue: 47 |
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