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

 آمار

تعداد نشریات45
تعداد شماره‌ها1,381
تعداد مقالات16,906
تعداد مشاهده مقاله54,423,595
تعداد دریافت فایل اصل مقاله17,099,392
Heydary, Sahba, Aminataei, Azim. (1401). Numerical solution of Drinfel’d–Sokolov system with the Haar wavelets method. سامانه مدیریت نشریات علمی, 10(4), 1086-1096. doi: 10.22034/cmde.2022.47018.1972
Sahba Heydary; Azim Aminataei. "Numerical solution of Drinfel’d–Sokolov system with the Haar wavelets method". سامانه مدیریت نشریات علمی, 10, 4, 1401, 1086-1096. doi: 10.22034/cmde.2022.47018.1972
Heydary, Sahba, Aminataei, Azim. (1401). 'Numerical solution of Drinfel’d–Sokolov system with the Haar wavelets method', سامانه مدیریت نشریات علمی, 10(4), pp. 1086-1096. doi: 10.22034/cmde.2022.47018.1972
Heydary, Sahba, Aminataei, Azim. Numerical solution of Drinfel’d–Sokolov system with the Haar wavelets method. سامانه مدیریت نشریات علمی, 1401; 10(4): 1086-1096. doi: 10.22034/cmde.2022.47018.1972

Numerical solution of Drinfel’d–Sokolov system with the Haar wavelets method

Computational Methods for Differential Equations
مقاله 17، دوره 10، شماره 4، دی 2022، صفحه 1086-1096    اصل مقاله (721.98 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.47018.1972
نویسندگان
Sahba Heydary؛ Azim Aminataei*
Faculty of Mathematics, K. N. Toosi University of Technology, P. O. Box: 16765–3381, Tehran, Iran.
چکیده
In this article, we use the Haar wavelets (HWs) method to numerically solve the nonlinear Drinfel’d–Sokolov (DS) system. For this purpose, we use an approximation of functions with the help of HWs, and we approximate spatial derivatives using this method. In this regard, to linearize the nonlinear terms of the equations, we use the quasilinearization technique. At the end, to show the effectiveness and accuracy of the method in solving this system one numerical example is provided. 
کلیدواژه‌ها
Drinfel’d–Sokolov system؛ Numerical solution؛ Haar wavelets method؛ Quasilinearization technique
مراجع
  • [1]          G. Ahmadnezhad, N. Aghazadeh, and S. Rezapour, Haar wavelet iteration method for solving time fractional Fisher’s equation, 8 (2020), 505–522.
  • [2]          A. H. Arnous, M. Mirzazadeh, and M. Eslami, Exact solutions of the Drinfel’d–Sokolov–Wilson equation using b¨acklund transformation of riccati equation and trial function approach, Pramana, 86 (2016), 1153–1160.
  • [3]          I. Aziz, S. Islam, and F. Khan, A new method based on Haar wavelet for the numerical solution of two-dimensional nonlinear integral equations, Journal of Computational and Applied Mathematics, 272 (2014), 70–80.
  • [4]          R. E. Bellman and R. E. Kalaba, Quasilinearization And Nonlinear Boundary-Value Problems, 1965.
  • [5]          C. Cattani, T. A. Sulaiman, H. M. Baskonus, and H. Bulut, On the soliton solutions to the Nizhnik-Novikov- Veselov and the Drinfel’d-Sokolov systems, Optical and Quantum Electronics, 50 (2018), 1–11.
  • [6]          I. Daubechies and W. Sweldens, Factoring wavelet transforms into lifting steps, Journal of Fourier analysis and applications, 4 (1998), 247–269.
  • [7]          S. Foadian, R. Pourgholi, S. H. Tabasi, and J. Damirchi, The inverse solution of the coupled nonlinear reaction– diffusion equations by the Haar wavelets, International Journal of Computer Mathematics, 96 (2019), 105–125.
  • [8]          U¨ .  G¨okta¸s  and  W.  Hereman,  Symbolic  computation  of  conserved  densities  for  systems  of  nonlinear  evolution equations Journal of Symbolic Computation, 24 (1997), 591–622.
  • [9]          W.  H¨ardle,  G.  Kerkyacharian,  D.  Picard,  and  A.  Tsybakov,  Wavelets, Approximation, And Statistical Applica- tions, Springer Science & Business Media, 2012.
  • [10]        G. Hariharan and K. Kannan, A comparative study of Haar wavelet method and Homotopy perturbation method for solving one-dimensional reaction-diffusion equations, International Journal of Applied Mathematics and Com- putation, 3 (2011), 21–34.
  • [11]        M. Kumar and S. Pandit, A composite numerical scheme for the numerical simulation of coupled Burgers’ equation, Computer Physics Communications, 185 (2014), 809–817.
  • [12]        U¨ . Lepik, Solving integral and differential equations by the aid of non-uniform Haar wavelets, Applied Mathematics and Computation, 198 (2008), 326–332.
  • [13]        U¨ . Lepik and H. Hein, Haar Wavelets:  With Applications, Springer Science & Business Media, 2014.
  • [14]        E. Misirli and Y. Gurefe, Exact solutions of the Drinfel’d–Sokolov–Wilson equation using the exp-function method, Applied Mathematics and Computation, 216 (2010), 2623–2627.
  • [15]        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 Differ- ential Equations, 8 (2020), 610–638.
  • [16]        R. Pourgholi, N. Tavallaie, and S. Foadian, Applications of Haar basis method for solving some ill-posed inverse problems, Journal of Mathematical Chemistry, 50 (2012), 2317–2337.
  • [17]        S. S. Ray and A. K. Gupta, Comparative analysis of variational iteration method and Haar wavelet method for the numerical solutions of Burgers–Huxley and Huxley equations, Journal of mathematical chemistry, 52 (2014), 1066–1080.
  • [18]        L. Shen, S. Zhu, B. Liu, Z. Zhang, and Y. Cui, Numerical implementation of nonlinear system of fractional Volterra integral–differential equations by Legendre wavelet method and error estimation, Numerical Methods for Partial Differential Equations, 37 (2020), 1344–1360.
  • [19]        P. Sliwinski and Z. Hasiewicz, Computational algorithms for wavelet identification of nonlinearities in hammer- stein systems with random inputs, IEEE Transactions on Signal Processing, 56 (2008), 846–851.
  • [20]        E. Sweet and R. A. V. Gorder, Exponential-type solutions to a generalized Drinfel’d–Sokolov equation, Physica Scripta, 82 (2010), 035006.
  • [21]        A. M. Wazwaz, Exact and explicit travelling wave solutions for the nonlinear Drinfeld–Sokolov system Commu- nications in nonlinear science and numerical simulation, 11 (2006), 311–325.
  • [22]        N. Xiao-Xing and L. Qing-Ping, Darboux transformation for Drinfel’d–Sokolov–Wilson equation, Communications in Theoretical Physics, 64 (2015), 491.
آمار
تعداد مشاهده مقاله: 283
تعداد دریافت فایل اصل مقاله: 343


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب