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Hamilton-Jacobi方程的高分辨率解法
引用本文:汪海滨,封建湖.Hamilton-Jacobi方程的高分辨率解法[J].西南民族学院学报(自然科学版),2006,32(1).
作者姓名:汪海滨  封建湖
作者单位:西北工业大学理学院 陕西西安710072(汪海滨),长安大学理学院 陕西西安710064(封建湖)
摘    要:Ham ilton-Jacob i方程经常应用于控制论和微分对策等方面.它与双曲型守恒律有非常紧密的联系,在一维的情形下,两者几乎完全相同.在多维的空间中,类似的情形依然存在.因此,可以通过这种联系来设计不同的近似算法来求解Ham ilton-Jacob i方程.本文利用CWENO算法成功地求解了包括控制最优化问题在内的许多标量问题,结果表明,这种算法在解的光滑区域具有很高的精度,并能很好地解决具有不连续偏导数的计算问题,数值算例结果也表明这种算法是收敛的.

关 键 词:Hamilton-Jacobi方程  CWENO算法

High-order essentially non- oscillatory schemes for Hamilton- Jacobi equations
WANG Hai-bing,FENG Jian-hu.High-order essentially non- oscillatory schemes for Hamilton- Jacobi equations[J].Journal of Southwest Nationalities College(Natural Science Edition),2006,32(1).
Authors:WANG Hai-bing  FENG Jian-hu
Abstract:Hamilton-Jacobi equations are frequently encountered in applications,e.g.,in control theory and differential games.Hamilton-Jacobi equations are closely related to hyperbolic conservation laws-in one space dimension the former is simply the integrated version of the latter.Similarity also exists for the multidimensional cases,and this is helpful in designing difference approximations.In this paper central weighted essentially non-oscillatory (CWENO) schemes for Hamilton-Jacobi equations are investigated,which yield uniform high-order accuracy in smooth regions and sharply resolve discontinuities in the derivatives.The schemes are numerically tested on a variety of one-dimensional problems,including a problem related to control optimization.High-order accuracy in smooth regions,high resolution of discontinuities in the derivatives,and convergence to viscosity solutions are observed.
Keywords:Hamilton-Jacobi  equation  essentially non-oscillatory scheme  CWENO scheme
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