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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 1

Chebyshev Wavelet Method for Numerical Solutions of Coupled Burgers’ Equation

Ö. Oruç
F. Bulut
A. Esen
Sayfa
1–16
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Computer simulations show that the proposed method is computationally cheap, fast and quite good even in the case of less number of collocation points.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:This paper deals with the numerical solutions of one dimensional time dependent coupled Burgers’ equation with suitable initial and boundary conditions by using Chebyshev wavelets in collaboration with a collocation method.
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Temel Bulgular & Veri:The feasibility of the proposed method is demonstrated by test problems and indicates that the proposed method gives accurate results in short cpu times.
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Sonuç & Katkı:Computer simulations show that the proposed method is computationally cheap, fast and quite good even in the case of less number of collocation points.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

This paper deals with the numerical solutions of one dimensional time dependent coupled Burgers’ equation with suitable initial and boundary conditions by using Chebyshev wavelets in collaboration with a collocation method. The proposed method converts coupledBurgers’equationsintosystemofalgebraicequationsbyaidoftheChebyshevwavelets andtheirintegralswhichcanbesolvedeasilywithasolver. Benchmarkingoftheproposed method with exact solution and other known methods already exist in the literature is made by three test problems. The feasibility of the proposed method is demonstrated by test problems and indicates that the proposed method gives accurate results in short cpu times. Computer simulations show that the proposed method is computationally cheap, fast and quite good even in the case of less number of collocation points.

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Bu Makaleye Atıf Yap

Oruç, Ö., Bulut, F., Esen, A. (2022). Chebyshev Wavelet Method for Numerical Solutions of Coupled Burgers’ Equation. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 1, 1–16. https://ajindex.com/articles/530538

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Kaynakça (16)

  1. R. Abazari and A. Borhanifar, Numerical study of the solution of the Burgers and coupled Burgers equations by a differential transformation method, Comput. Math. Appl. 59, 2711-2722, 2010
  2. M.A. Abdou and A.A. Soliman, Variational iteration method for solving Burger’s and coupled Burger’s equations, J. Comput. Appl. Math. 181, 245-251, 2005
  3. H. Adibi and P. Assari Chebyshev wavelet method for numerical solution of Fred- holm integral equations of the first kind. Math. Prob. Eng. 2010, 1-17, 2010, doi:10.1155/2010/138408
  4. E. Babolian and F. Fattahzadeh Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration, Appl. Math. Comput. 188, 417- 426, 2007
  5. C. Basdevant, M. Deville, P. Haldenwang and J. M. Lacroix Spectral and finite dif- ference solutions of the Burgers’ equation, Comput. Fluids 14, 23-41, 1986
  6. F. Bulut, Ö. Oruç and A. Esen, Numerical Solutions of Fractional System of Partial Differential Equations By Haar Wavelets, Comput. Model. Eng. Sci. 108 (4), 263-284, 2015
  7. I. Celik, Haar wavelet approximation for magnetohydrodynamic flow equations, Appl. Math. Model. 37, 3894-3902, 2013
  8. I. Celik, Chebyshev Wavelet collocation method for solving generalized Burgers-Huxley equation, Math. Methods. Appl. Sci. 39 (3), 366-377, 2015
  9. C. Chen and C.H. Hsiao, Haar wavelet method for solving lumped and distributed parameter systems, IEE Proc., Control Theory Appl. 144, 87-94, 1997
  10. I. Daubechies, Ten Lectures on Wavelet, SIAM, Philadelphia, 1992
  11. M. Dehghan, A. Hamidi and M. Shakourifar, The solution of coupled Burgers’ equa- tions using Adomian-Pade technique, Appl. Math. Comput. 189, 1034-1047, 2007
  12. S.E. Esipov, Coupled Burgers’ equations: a model of polydispersive sedimentation, Phys. Rev. Lett. 52, 3711-3718, 1995
  13. A.K. Gupta and S. Saha Ray, Travelling wave solution of fractional KdV-Burger- Kuramoto equation describing nonlinear physical phenomena, AIP Adv. 4, 2014, doi: 10.1063/1.4895910.097120-1-11
  14. M.H. Heydari, M.R. Hooshmandasl and F.M. Maalek Ghaini, A new approach of the Chebyshev wavelets method for partial differential equations with boundary conditions of the telegraph type, Appl. Math. Model. 38, 1597-1606, 2014
  15. J. D. Hunter, Matplotlib: A 2D graphics environment, Comput. Sci. Eng. 9 (3), 90-95, 2007
  16. I.E. Inan, D. Kaya and Y. Ugurlu, Auto-Bäcklund transformation and similarity re- ductions for coupled Burger’s equation, Appl.