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双曲型守恒律方程的小波解法

唐玲艳,宋松和   

  1. 国防科技大学理学院数学与系统科学系;国防科技大学理学院数学与系统科学系 长沙410073;长沙410073
  • 出版日期:2007-01-20 发布日期:2007-01-20

唐玲艳,宋松和. 双曲型守恒律方程的小波解法[J]. 数值计算与计算机应用, 2007, 28(1): 11-17.

WAVELET METHOD FOR HYPERBOLIC CONSERVATION LAWS

  1. Tang Lingyan Song Songhe (Department of Mathematics and System Science,Science school,National University of Defense Technology,Changsha 410073,China)
  • Online:2007-01-20 Published:2007-01-20
本文基于Hamilton-Jacobi方程的小波Galerkin近似和微分算子的小波表示,讨论一维双曲型守恒律方程初值问题的Daubechies小波解.由于小波在空间和时间上的局部性,本方法适用于处理具有奇异解的问题,可以有效的防止数值振荡.数值试验的结果表明,本方法是可行的.
In this paper,the initial problem of one-dimensional hyperbolic conservation law solved by Daubechies wavelets is discussed.The explicit discrete scheme of the above problem is given based on wavelet Galerkin method of Hamilton-Jacobi equation and the wavelet representation of differential operators.Because the wavelets have the time-frequency local property,the new scheme adapt to deal with singularities.Numerical tests are satisfactory.
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[1]I.Daubechies.Ten Lectures on Wavelets.SIAM,1992.
[2]A.Latto,H.Resnikoff and E.Tenenbaum,The Evaluation of Connection coefficients of compactly supported wavelets,in Proceedings of the French-USA Workshop on Wavelets and Turbulence, Princeton,New York,1991,Springer-Verlag.
[3]G.Beylkin,On the Representation of Operators in Base of Compactly Supported Wavelets,SIAM J.Numerical Analysis,Vol.6(1992),1716-1740.
[4]Mats HolmstrSm,Johan Waldén,Adaptive Wavelet Methods for Hyperbolic PDEs,J.Sci.Com- put,13(1998),19-49.
[5]吴勃英,邓中兴,热传导方程的小波解法,应用数学学报,24:1(2001),10-16.
[6]S.Kelly,Gibbs Phenomenon for Wavelets,Applied and Computational Harmonic Analysis,Vol. 3(1996),72-61.
[7]W.Sweldens,R.Piessens,Quadrature formula and asymptotic error expansions for wavelet ap- proximations of smooth functions,SIAM J.Numerical Analysis,Vol.31(1994),1240-1264.
[8]M.G.Crandal,P.L.Lions,Two Approximations of Solutions of Hamilton-Jacobi Equations, Math.Comp.,Vol.43(1984),1-19.
[9]唐玲艳,宋松和,Hamilton-Jacobi方程的小波Galerkin方法,计算数学,28:4(2006),401-408.
[10]Yu Xijun,Fu Hongyuan,Chang Qianshun,the finite element method for hyperbolic conservation laws,计算物理,Vol.16(1999),457-466.
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