一致渐近在特征值问题中的应用

Application of uniform asymptotics in the eigenvalue problem

利用由Bassom等提出的一致渐近方法研究了具有简单转折点的大特征值问题,得到了大特征值问题的严格的Airy渐近解,它在Stokes线上一致成立;并得到了大特征值的近似表达式.

The large eigenvalue problem with a simple turning point was studied by virtue of the method of uniform asymptotics introduced by Bassom et al. A rigorous Airy asymptotic solution that holds uniformly on the Stokes lines to the large eigenvalue problem was presented. Besides the asymptotic expressions for the large eigenvalues were also obtained.