基于Schmidt正交化思想，研究了全直线区域上带渐近边界条件的二阶微分方程的对角化Chebyshev有理谱方法，构造了二阶微分方程的Fourier型Sobolev正交基函数并导出相应的全对角离散代数方程组，在此基础上分别给出了微分方程真解和数值解的Fourier级数展开形式及局部截断形式。数值结果保持了谱精度，且与以往算法相比，新算法优化了计算过程，减少了计算量，并且简单易行。%Based on the idea of Schmidt orthogonalization, a fully diagonalized Chebyshev rational spectral method for solving second order differential equations on the whole line with asymptotic boundary conditions was proposed. Some Fourier-like Sobolev orthogonal basis functions were constructed and fully diagonal discrete algebraic equations were derived. Accordingly, both the exact solutions and the approximate solutions were represented as infinite and truncated Fourier series. The numerical results demonstrate the spectral accuracy. Compared with the existing algorithms, the results of numerical experiment indicate the cost of the computation with the present algorithm is less and the algorithm is easier to be implemented.
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