Title — Solution of bound state single variable eigenproblems by the extended renormalized Numerov method

Abstract
A Microsoft FORTRAN-77 program is presented which solves second order differential equations of the form [A(x) d^2dx^2+ B(x) d dx]ψ(x) = [V(x) - E]ψ(x) for a variety of boundary conditions. The user specifies A(x), B(x) and V(x) beforehand and choses the appropriate boundary conditions from a menu.

Title of program: NUMROV
Catalogue Id: ABDW_v1_0

Nature of problem
Analysis of models of large amplitude molecular vibration leads to a set of single variable bound state second order differential eigenvalue problems of quite varied form and satisfying a variety of boundary conditions. These equations cannot in general be solved analytically.

Versions of this program held in the CPC repository in Mendeley Data
ABDW_v1_0; NUMROV; 10.1016/0010-4655(88)90073-2

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
本文提出一款微软FORTRAN-77程序，可求解形如[A(x) d²/dx² + B(x) d/dx]ψ(x) = [V(x) - E]ψ(x)的二阶微分方程，支持多种边界条件。用户可预先指定A(x)、B(x)与V(x)，并从菜单中选择合适的边界条件。

程序名称：NUMROV
目录编号：ABDW_v1_0

问题本质
大振幅分子振动模型的分析会导出一系列形式多样、满足多种边界条件的单变量束缚态二阶微分本征值问题。此类方程通常无法通过解析方法求解。

本程序在曼德莱数据（Mendeley Data）的CPC程序库中的版本：
ABDW_v1_0; NUMROV; 10.1016/0010-4655(88)90073-2

本程序源自贝尔法斯特女王大学所维护的CPC程序库（1969-2019）