【摘要】 讨论了二维Burgers方程初边值问题的数值解法.新的方法是基于二维Hopf-Cole变换,将Bur-gers方程的初边值问题相应的变为热传导方程的初边值问题,用修正局部Crank-Nicolson法进行求解,得到了较好的结果,然后再进行逆变换得出原Burgers方程的解.同时也给出了稳定性、相容性及收敛性的理论证明.数值实验结果表明了该方法的正确性和格式的有效性。更多还原

【Abstract】 In this paper,we discuss a numerical method of two dimensional Burgers equation for the initial-boundary value problem.Based on the two-dimensional Hopf-Cole transformation,the new method transforms initial-boundary value problem of Burgers equation to initial-boundary value problem of heat equation by using Hopf-Cole transformation.We use Modified Local Crank-Nicolson Method for heat equation,and obtain a better solution for Burgers equation in inverse transform method.And we give a corresponding theoretical proof for stability,consistence and convergence.The numerical experiment shows the theoretical accuracy and computational effectiveness of proposed method.更多还原