A high-speed method for eigenvalue problems. II Calculation of the eigenfunction in Milne's method

Abstract A new version of the program MEIGEN is presented for the eigenvalue problem of Sturm-Liouville-type linear equations in Milne's method. Use of the spline function and the WKB approximation provide a high-speed method for calculating eigenvalues and eigenfunctions avoiding divergence problems. Title of program: MEV2 Catalogue Id: ABTN_v2_0 [ACJH] Nature of problem Calculated eigenvalues include necessarily some numerical errors, which often make the eigenfunctions divergent at large distances. An efficient method to avoid this difficulty is necessitated. Versions of this program held in the CPC repository in Mendeley Data ABTN_v1_0; MEIGEN; 10.1016/0010-4655(90)90052-3 ABTN_v2_0; MEV2; 10.1016/0010-4655(92)90006-K ABTN_v3_0; MEV3; 10.1016/0010-4655(94)90088-4 ABTN_v4_0; MEV4; 10.1016/0010-4655(96)00051-3 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)摘要 本文提出程序MEIGEN的新版本，用于求解Milne方法下的Sturm-Liouville型线性方程特征值问题。该方法结合样条函数与WKB近似（WKB approximation），可在计算特征值与本征函数时规避发散问题，实现高速计算。 程序名称：MEV2 目录编号：ABTN_v2_0 [ACJH] 问题本质：计算得到的特征值必然存在一定数值误差，该误差往往会导致本征函数在大距离尺度下出现发散现象，因此亟需一种高效方法解决该难题。 Mendeley数据的CPC库中收录的该程序版本如下： ABTN_v1_0；MEIGEN；10.1016/0010-4655(90)90052-3 ABTN_v2_0；MEV2；10.1016/0010-4655(92)90006-K ABTN_v3_0；MEV3；10.1016/0010-4655(94)90088-4 ABTN_v4_0；MEV4；10.1016/0010-4655(96)00051-3 本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2018）