有限谱方法在求解波动问题的数值精确性分析

Accuracy Analysis of Finite Spectral Method for Wave Problems

将高精度的广义有限谱方法的求解格式推广到常规有限谱方法。建立的求解数值系统用于具有分析解的一维Burgers方程的非线性对流扩散问题,KDV方程的单孤独波和双孤独波传播问题。结果表明,适当选取的局地参数l,常规有限谱方法不仅能够准确模拟上述问题,其准确性还可以达到或超过用基于特殊函数展开的广义有限谱方法的求解精度。

Numerical scheme of the generalized finite spectral method is extended to finite spectral method.The method is also of high order accuracy.The established numerical method is validated by applications to the Burgers equation(nonlinear convection-diffusion problem) and KdV equation(single solitary and 2-solitary wave problems),where analytical solutions are available for comparison.Numerical results show that using suitable value of the local parameter,l,the proposed method can be applied to simulate wave propagation problems with even higher accuracy than that of the generalized finite spectral method.