变系数Burgers方程的一种预处理谱方法  

Spectral Method for Second-order Nonlinear Evolution Equations with Variable Coefficients

作　　者：邓芳芳[1] 马和平[1] 曾凡海[1] 

机构地区：[1]上海大学数学系,上海200444

出　　处：《应用数学与计算数学学报》2010年第1期99-106,共8页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金项目(60874039);上海市教委重点学科建设项目(J50101)

摘　　要：本文用预处理Legendre-Galerkin-Chebyshev配置方法来求解二阶变系数Burgers方程,该方法首先对方程进行预处理,然后在空间方向应用Legendre-Galerkin-Chebyshev配置方法,对时间方向采用leap-frog/Crank-Nicolson格式进行离散,这样可使得变系数项和非线性项能够显式计算.我们对该方法进行了误差估计,并通过数值算例验证了算法的有效性和理论分析的正确性.In this paper,a preconditioning Legendre-Galerkin-Chebyshev collocation method is developed for the second-order Burgers equation with variable coefficient.First, the form of the equation is changed by the idea of the preconditioning method.Then we apply the Legendre-Galerkin-Chebyshev collocation method to the changed equation. For the time discretization,we adopt the leap-frog/Crank-Nicolson scheme such that the nonlinear and variable-coefficient terms can be dealt with explicitly.Error analysis is given to this method.The numerical results are given to confirm the validity of the scheme and the correctness of theoretical analysis.

关 键 词：Legendre-Galerkin-Chebyshev配置方法 预处理 变系数 

分 类 号：O175.2[理学—数学]