时空Chebyshev伪谱方法求解Burgers方程

Space-time Pseudospectral Chebyshev Method for Burgers Equation

Burgers方程在数学和物理学的各个领域都有重要的应用,寻求Burgers方程的精确解一直是一个重要的研究课题.提出了使用时空Chebyshev伪谱法求解一维Burgers方程的方法.首先使用Chebyshev伪谱方法对空间导数进行离散,得到一个常微分方程组,然后使用Chebyshev伪谱方法对此常微分方程组进行求解,最后通过数值试验对数值解和精确解进行了比较.数值试验表明:该方法使用简便,稳定性好,有较高的精度.

Burgers equation has important applications in the fields of mathematics and physics,seeking the exact solutions of the Burgers equation has been an important research topic.This paper presents a new method using space-time pseudospectral Chebyshev method for solving the one-dimensional Burgers equations.Firstly,we discretize the Burgers equation in one dimensional space with pseudospectral Chebyshev method,and obtain the system of ordinary differential equations.Secondly,we utilize the pseudospectral Chebyshev method for the numerical integration of the system of ODEs.Finally,the numerical results obtained by this method are compared with the exact results to demonstrate its efficiency.The result of the study shows that this method has a high accuracy and stability.