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Science China Technological Sciences

, Volume 57, Issue 7, pp 1285–1292 | Cite as

Wavelet solutions of Burgers’ equation with high Reynolds numbers

  • XiaoJing Liu
  • YouHe Zhou
  • Lei Zhang
  • JiZeng WangEmail author
Article Special Topic: Computational Mechanics

Abstract

A wavelet method is proposed to solve the Burgers’ equation. Following this method, this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified wavelet Galerkin method recently developed by the authors. Then, the classical fourth-order explicit Runge-Kutta method is employed to solve the resulting system of ordinary differential equations. Such a wavelet-based solution procedure has been justified by solving two test examples: results demonstrate that the proposed method has a much better accuracy and efficiency than many other existing numerical methods, and whose order of convergence can go up to 5. Most importantly, our results also indicate that the present wavelet method can readily deal with those fluid dynamics problems with high Reynolds numbers.

Keywords

modified wavelet Galerkin method Runge-Kutta method Burgers’ equation high Reynolds number 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • XiaoJing Liu
    • 1
  • YouHe Zhou
    • 1
  • Lei Zhang
    • 1
  • JiZeng Wang
    • 1
    Email author
  1. 1.Key Laboratory of Mechanics on Disaster and Environment in Western China, the Ministry of Education, and School of Civil Engineering and MechanicsLanzhou UniversityLanzhouChina

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