Burgers方程的高精度多步显式格式  

Highly Accurate Multistep Explicit Scheme for Burgers Equation

作　　者：唐晨[1] 刘铭[1] 闫海青[1] 

机构地区：[1]天津大学理学院,天津300072

出　　处：《天津大学学报（自然科学与工程技术版）》2004年第10期929-933,共5页Journal of Tianjin University：Science and Technology

基　　金：上海交通大学振动;冲击;噪声国家重点实验室基金资助项目(VSN 2003 03).

摘　　要：为提高Burgers方程的数值计算精度和效率,提出了一种新的高精度多步显式格式.在空间坐标上按差分法离散,在时间方向上将差分改为积分,应用显式指数时程差分法构造出了不同精度的计算格式.对不同初边值Burgers方程进行了数值模拟,并与显式交替分组法、交替Crank Nicolson并行算法和小波法等算法进行了比较.结果表明,当新方法的网格比是参考算法网格比的2.5～20倍时,新方法数值解的绝对误差仍然小于参考算法数值解的绝对误差.该方法为数值求解非线性偏微分方程提供了一族不同精度计算格式,扩大了指数时程差分法的应用领域.A new highly accurate multistep explicit scheme for Burgers equation is proposed in order to improve accuracy and efficiency.The derivatives are discretized with respect to differencing on space coordinate,and integration is used instead of differencing on time direction.Schemes with various precision are constructed based on explicit exponential time differencing. Burgers equations with various initial and boundary conditions are numerically calculated, and compared with other numerical methods such as alternating group explicit method,alternating group Crank-Nicolson parallel algorithm,and wavelet method.Numerical results show that the absolute error of present scheme is smaller than that of other methods when the grid ratio of present scheme is 2.5—20 times bigger than that of reference method.A class of schemes with various precision are presented for nonlinear partial differential equations.The applied scope of exponential time differencing has been extended.

关 键 词：BURGERS方程 任意阶 指数时程差分 显式算法 

分 类 号：O24[理学—计算数学]