求解Burgers方程的高精度紧致Pade'逼近格式

High-order Compact Pade' Approximation Scheme for Solving Burgers Equation

对一维Burgers方程提出了精度为O(τ3+h4)的紧致Pade'逼近格式,首先利用Hopf-Cole变换,将一维Burgers方程转化为线性扩散方程,然后对空间变量四阶紧致格式进行离散,时间变量利用pade逼近格式得到求解Burgers方程的时间三阶空间四阶精度的隐式差分格式,并对稳定性进行分析,数值结果与Crank-Nicholson格式、Douglass格式和Haar wavelet格式进行比较,数值结果不同时刻和空间,不同雷诺数与准确值进行比较,发现所提格式很好的解决了Burgers方程的数值计算.

In this paper, we propose an accurateO（τ3＋h4 ）high-order compact Pade＇ approximation method for one-di- mensional Burgers＇ equation. Hopf-Cole transformation is used to linearize Burgers＇ equation, the resulting diffusion equation is discretized by using compact finite difference approximation of fourth order for discretizing spatial derivative, pade＇ approxima- tion in time direction derived two level unconditional stable implicit schemes and discussed the stability. Accuracy of the present scheme is demonstrated by solving a test problem and the numerical results is obtained with this method for different time and space. Different values of Reynolds number have been compared with the exact solution and some existing numerical results in- cluding Crank-Nicolson scheme, Douglass scheme and Haar wavelet scheme. Numerical results are shown that the proposed method in good agreement with the exact solutions.