دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,416
تعداد مقالات17,490
تعداد مشاهده مقاله56,485,384
تعداد دریافت فایل اصل مقاله18,742,438
Aghazadeh, Nasser. (1404). A Chebyshev wavelet approach to the generalized time-fractional Burgers-Fisher equation. سامانه مدیریت نشریات علمی, 13(4), 1135-1147. doi: 10.22034/cmde.2024.61020.2617
Nasser Aghazadeh. "A Chebyshev wavelet approach to the generalized time-fractional Burgers-Fisher equation". سامانه مدیریت نشریات علمی, 13, 4, 1404, 1135-1147. doi: 10.22034/cmde.2024.61020.2617
Aghazadeh, Nasser. (1404). 'A Chebyshev wavelet approach to the generalized time-fractional Burgers-Fisher equation', سامانه مدیریت نشریات علمی, 13(4), pp. 1135-1147. doi: 10.22034/cmde.2024.61020.2617
Aghazadeh, Nasser. A Chebyshev wavelet approach to the generalized time-fractional Burgers-Fisher equation. سامانه مدیریت نشریات علمی, 1404; 13(4): 1135-1147. doi: 10.22034/cmde.2024.61020.2617

A Chebyshev wavelet approach to the generalized time-fractional Burgers-Fisher equation

Computational Methods for Differential Equations
مقاله 5، دوره 13، شماره 4، دی 2025، صفحه 1135-1147    اصل مقاله (2.72 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.61020.2617
نویسنده
Nasser Aghazadeh*
1. ‎Department of Mathematics‎, ‎Izmir Institute of Technology‎, ‎Izmir‎, ‎Türkiye. 2. Center for Theoretical Physics, Khazar University, 41 Mehseti Street, Baku, AZ1096, Azerbaijan.
چکیده
This work proposes a new method for obtaining the approximate solution of the time-fractional generalized Burgers Fisher equation. The method’s main idea is based on converting the nonlinear partial differential equation to a linear partial differential equation using the Picard iteration method. Then, the second kind Chebyshev wavelet collocation method is used to solve the linear equation obtained in the previous step. The technique is called the Chebyshev Wavelet Picard Method (CWPM). The proposed method successfully solves the time fractional generalized Burgers-Fisher equation. The obtained numerical results are compared with the exact solutions and with the solutions obtained using the Haar wavelet Picard method and the homotopy perturbation method.
کلیدواژه‌ها
Numerical methods for wavelets؛ Fractional partial differential equations؛ Fractional derivatives and integrals؛ Picard iteration technique؛ Sylvester equation
مراجع
  • [1] N. Aghazadeh, G. Ahmadnezhad, and S. Rezapour, On Time Fractional Modified Camassa-Holm and Degasperis Procesi Equations by Using the Haar Wavelet Iteration Method, Iranian Journal Of Mathematical Sciences And Informatics, 18(1) (2023), 55-71.
  • [2] N. Aghazadeh, A. Mohammadi, G. Ahmadnezhad, and S. Rezapour, Solving partial fractional differential equations by using the Laguerre wavelet-Adomian method, Advances In Difference Equations, 2021 (2021), 1-20.
  • [3] N. Aghazadeh, A. Mohammadi, and G. Tano˘glu, Taylor wavelets collocation technique for solving fractional nonlinear singular PDEs, Mathematical Sciences, 18 (2024), 41-54.
  • [4] N. Aghazadeh, E. Ravash, and S. Rezapour, Existence results and numerical solutions for a multi-term fractional integro-differential equation, Kragujev. J. Math., 43 (2019), 413-426.
  • [5] G. Ahmadnezhad, N. Aghazadeh, and S. Rezapour, Haar wavelet iteration method for solving time fractional Fisher’s equation, Computational Methods For Differential Equations, 8(3) (2020), 505-522.
  • [6] R. Baillie, Long memory processes and fractional integration in econometrics, Journal Of Econometrics, 73 (1996), 5-59.
  • [7] S. Balaji, Legendre wavelet operational matrix method for solution of fractional order Riccati differential equation, Journal Of The Egyptian Mathematical Society, 23 (2015), 263-270.
  • [8] G. Bohannan, Analog Fractional Order Controller in Temperature and Motor Control Applications, Journal Of Vibration And Control, 14 (2008), 1487-1498.
  • [9] Y. Chen, L. Sun, X. Li, and X. Fu, Numerical solution of nonlinear fractional integral differential equations by using the second kind Chebyshev wavelets, Computer Modeling In Engineering And Sciences, 90 (2013), 359-378.
  • [10] S. Das, Analytical solution of a fractional diffusion equation by variational iteration method, Computers & Mathematics With Applications, 57 (2009), 483-487.
  • [11] S. El-Wakil, A. Elhanbaly, and M. Abdou, Adomian decomposition method for solving fractional nonlinear differential equations, Applied Mathematics And Computation, 182 (2006), 313-324.
  • [12] A. Gupta, and S. Saha Ray, Numerical treatment for the solution of fractional fifth-order Sawada–Kotera equation using second kind Chebyshev wavelet method, Applied Mathematical Modelling, 39 (2015), 5121-5130.
  • [13] I. Hashim, O. Abdulaziz, and S. Momani, Homotopy analysis method for fractional IVPs, Communications In Nonlinear Science And Numerical Simulation, 14 (2009), 674-684.
  • [14] J. He, Nonlinear oscillation with fractional derivative and its applications, International Conference On Vibrating Engineering, 98 (1998), 288-291.
  • [15] M. Heydari, M. Hooshmandasl, and F. Mohammadi, Legendre wavelets method for solving fractional partial differential equations with Dirichlet boundary conditions, Applied Mathematics And Computation, 234 (2014), 267-276.
  • [16] F. Idiz, G. Tanoglu, and N. Aghazadeh,˙ A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type equations, Numerical Algorithms, 95 (2024), 181-206.
  • [17] H. Ismail, K. Raslan, and A. Abd Rabboh, Adomian decomposition method for Burger’s–Huxley and Burger’s–Fisher equations, Applied Mathematics And Computation, 159 (2004), 291-301.
  • [18] R. Jiwari, A Haar wavelet quasilinearization approach for numerical simulation of Burgers’ equation, Computer Physics Communications, 183 (2012), 2413-2423.
  • [19] R. Jiwari, R. Mittal, and K. Sharma, A numerical scheme based on weighted average differential quadrature method for the numerical solution of Burgers’ equation, Applied Mathematics And Computation, 219 (2013), 6680-6691.
  • [20] H. Kheiri and G. Ebadi, Application of the-expansion method for the Burgers, Fisher and Burgers–Fisher equations, Acta Universitatis Apulensis, Mathematics-Informatics, 24 (2010), 35-44.
  • [21] S. Kumar and S. Saha Ray, Numerical treatment for Burgers–Fisher and generalized Burgers–Fisher equations, Mathematical Sciences, 15 (2021), 21-28.
  • [22] Y. Li, N. Sun, B. Zheng, Q. Wang, and Y. Zhang, Wavelet operational matrix method for solving the Riccati differential equation, Communications In Nonlinear Science And Numerical Simulation, 19 (2014), 483-493.
  • [23] R. Mittal and R. Jiwari, Differential quadrature method for two-dimensional Burgers’ equations, International Journal For Computational Methods In Engineering Science And Mechanics, 10 (2009), 450-459.
  • [24] A. Mohammadi, N. Aghazadeh, and S. Rezapour, Haar wavelet collocation method for solving singular and nonlinear fractional time-dependent Emden–Fowler equations with initial and boundary conditions, Mathematical Sciences, 13 (2019), 255-265.
  • [25] A. Mohammadi, N. Aghazadeh, and S. Rezapour, Wavelet-Picard iterative method for solving singular fractional nonlinear partial differential equations with initial and boundary conditions, Computational Methods For Differential Equations, 8 (2020), 610-638.
  • [26] A. Mohammadi, G. Ahmadnezhad, and N. Aghazadeh, Chebyshev-quasilinearization method for solving fractional singular nonlinear Lane-Emden equations, Communications in Mathematics, 30(1) (2022), 201-228.
  • [27] R. Mohammadi, Spline solution of the generalized Burgers’-Fisher equation, Applicable Analysis, J91 (2012), 2189-2215.
  • [28] R. Nawaz, H. Ullah, S. Islam, and M. Idrees, Application of optimal homotopy asymptotic method to Burger equations, Journal Of Applied Mathematics, 2013, Article ID 387478, 8 pages.
  • [29] Z. Odibat and N. Shawagfeh, Generalized Taylor’s formula, Applied Mathematics And Computation, 186 (2007), 286-293.
  • [30] M. Olayiwola, An improved algorithm for the solution of generalized Burger-Fisher equation, Applied Mathematics, 5 (2014), 1609-1614.
  • [31] R. Panda and M. Dash, Fractional generalized splines and signal processing, Signal Processing, 86 (2006), 23402350.
  • [32] I. Podlubny, The Laplace transform method for linear differential equations of the fractional order, ArXiv Preprint Funct-an/9710005, (1997).
  • [33] M. Rashidi, D. Ganji, and S. Dinarvand, Explicit analytical solutions of the generalized Burger and Burger–Fisher equations by homotopy perturbation method, Numerical Methods For Partial Differential Equations, 25 (2009), 409-417.
  • [34] Y. Rossikhin and M. Shitikova, Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids, Applied Mechanics Reviews, 50 (1997), 15-67.
  • [35] U. Saeed and K. Gilani, CAS wavelet quasi-linearization technique for the generalized Burger–Fisher equation, Mathematical Sciences, 12 (2018), 61-69.
  • [36] U. Saeed and M. Rehman, Haar wavelet Picard method for fractional nonlinear partial differential equations, Applied Mathematics And Computation, 264 (2015), 310-322.
  • [37] A. Singh, S. Dahiya, and S. Singh, A fourth-order B-spline collocation method for nonlinear Burgers–Fisher equation, Mathematical Sciences, 14 (2020), 75-85.
  • [38] N. Sweilam, M. Khader, and R. Al-Bar, Numerical studies for a multi-order fractional differential equation, Physics Letters A, 371 (2007), 26-33.
  • [39] Y. Wang and L. Zhu, Solving nonlinear Volterra integro-differential equations of fractional order by using Euler wavelet method, Advances In Difference Equations, 2017 (2017), 1-16.
  • [40] F. Zhou and X. Xu, Numerical solution of the convection diffusion equations by the second kind Chebyshev wavelets, Applied Mathematics And Computation, 247 (2014), 353-367.
  • [41] F. Zhou and X. Xu, Numerical solution of time-fractional diffusion-wave equations via Chebyshev wavelets collocation method, Advances In Mathematical Physics, 2017 (2017), 1-17.
  • [42] C. Zhu and W. Kang, Numerical solution of Burgers–Fisher equation by cubic B-spline quasi-interpolation, Applied Mathematics And Computation, 216 (2010), 2679-2686.
  • [43] L. Zhu and Q. Fan, Solving fractional nonlinear Fredholm integro-differential equations by the second kind Chebyshev wavelet, Communications In Nonlinear Science And Numerical Simulation, 17 (2012), 2333-2341.
آمار
تعداد مشاهده مقاله: 292
تعداد دریافت فایل اصل مقاله: 369


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب