WAN De-cheng, WEI Guo-wei. The Study of Quasi-Wavelets Based Numerical Method Applied to Burgers’ Equations[J]. Applied Mathematics and Mechanics, 2000, 21(10): 991-1001.
Citation: WAN De-cheng, WEI Guo-wei. The Study of Quasi-Wavelets Based Numerical Method Applied to Burgers’ Equations[J]. Applied Mathematics and Mechanics, 2000, 21(10): 991-1001.

The Study of Quasi-Wavelets Based Numerical Method Applied to Burgers’ Equations

  • Received Date: 1999-09-06
  • Publish Date: 2000-10-15
  • A quasi-wavelet based numerical method was introduced for solving the evolution of the solutions of nonlinear partial differential Burgers' equations. The quasi wavelet based numerical method was used to discrete the spatial deriatives, while the fourth-order Runge-Kutta method was adopted to deal with the temporal discretization. The calculations were conducted at a variety of Reynolds numbers ranging from 10 to unlimited large. The comparisons of present results with analytical solutions show that the quasi wavelet based numerical method has distinctive local property, and is efficient and robust for numerically solving Burgers' equations.
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  • [1]
    Morlet J,Arens G,Fourgeau E,et al.Wave propagation and sampling theory and complex waves[J].Geophysics,1982,47(2):222-236.
    [2]
    Chui C K.An Introduction to Wavelets[M].San Diego:Academic Press,1992.
    [3]
    Wickerhauser M V.Adapted Wavelet Analysis From Theory to Software[M].Wellesley,MA:A K Peters,1994.
    [4]
    Cohen A,Ryan R D.Wavelets and Multiscales Signal Processing[M].London:Chapman & Hall,1995.
    [5]
    Qian S,Weiss J.Wavelet and the numerical solution of partial differential equations[J].J Comput Phys,1993,106(1):155-175.
    [6]
    Vasilyev O V,Paolucci S.A dynamically adaptive multilevel wavelet collocation method for solving partial differential equations in finite domain[J].J Comput Phys,1996,125(2):498-512.
    [7]
    王诚.低雷诺数下N-S方程的积分方程解法——Gaussian小波分析的应用[D].博士论文.上海:上海交通大学,1997.
    [8]
    Prosser R,Cant R S.On the use of wavelets in computational combustion[J].J Comput Phys,1998,147(2):337-361.
    [9]
    Haar A.Zer theorie der orthogonalen funktionensysteme[J].Math Annal,1910,69(3):331-371.
    [10]
    Mallat S.Multiresolution approximations and wavelet orthonormal bases of L2(R)[J].Transactions of the American Mathematical Society,1989,315(1):68-87.
    [11]
    Wei G W,Zhang D S,Kouri D J.Lagrange distributed approximating functionals[J].Phys Rev Lett,1997,79(5):775-779.
    [12]
    Wei G W,Quasi wavelets and quasi interpolating wavelets[J].Chem Phys Lett,1998,296(3-4):215-222.
    [13]
    Wei G W.Discrete singular convolution for the Fokker-Planck equation[J].J Chem Phys,1999,110(18):8930-8942.
    [14]
    Cole J D.On a quasi-linear parabolic equation occurring in aerodynamics[J].Quart Appl Math,1951,9(2):225-236.
    [15]
    Basdevant C,Deville M,Haldenwang P,et al.Spectral and finite difference solutions of the Burgers equation[J].Comput & Fluids,1986,14(1):23.
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