全直线上热传导方程广义Hermite谱方法

Generalized Hermite Spectral Method of Heat Transfer on Whole Line

以带伸缩因子的广义Hermite函数为基函数展开全直线上热传导方程的数值解,逼近热传导方程的正确解。给出算法格式和收敛性分析,数值例子表明所提算法格式具有有效性和高精度。所用方法也可用于求解其他同类问题。

The generalized Hermite functions with scaling factor were used as basis function to expand numerical solution,which approximated the exact solution of heat transfer on the whole line. Algorithms scheme was constructed based on the Hermite spectral method. The convergence of the scheme was proved. Numerical results show that this approach is efficiency and high accuracy. The proposed method is also applicable to other problems.