伪谱法在一类线性常微分方程和Burgers方程中的应用

Application of Pseudo-spectral Method for a Class Linear ODEs and Burgers Equation

在简要介绍谱方法的来源、分类及基本概念并给出谱方法的基本思想的基础上,给出了谱方法中的伪谱法,着重介绍了伪谱法对一类常微分方程的应用,使用切比雪夫多项式作为测试函数来逼近此类方程的解,并给出了伪谱法对Burgers方程的应用,使用离散的Fourier配置法来逼近Burgers方程的解.

On the base of briefly introducing the origin, classification and fundamentals of spectral methods, this paper gave pseudo - spectral methods and emphasized the application of the methods, trying chebyshev polynomials to approximate the solutions of a class of ODEs. Finally, discrete Fourier collocation was used to approximate the solutions of the Burgers equation.