An accurate eighth order exponentially-fitted method for the efficient solution of the Schrödinger equation

Abstract
An accurate eighth algebraic order exponentially-fitted method is developed for the numerical solution of radial Schrödinger equation and of the coupled differential equations of the Schrödinger type. The free parameters of the new scheme are defined in order to integrate exactly exponential functions. Numerical and theoretical results indicate that the new method is much more efficient than other classical and exponentially fitted methods.

Title of program: MAPLESIM
Catalogue Id: ADLI_v1_0

Nature of problem
With the present program the derivation of the coefficients produced by the equation (14) is obtained. The first part of the proposed program consists of the calculation of the matrix elements which form the coefficients of the system of equations. The second part of the proposed program, as this has been explained in [1], [2] and [3], consists of the iterative application of the L'Hospital's rule (to avoid coefficients of the form 0/0) for the computation of the solution of these equations that ...

Versions of this program held in the CPC repository in Mendeley Data
ADLI_v1_0; MAPLESIM; 10.1016/S0010-4655(99)00459-2

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

摘要
本文针对径向薛定谔方程（radial Schrödinger equation）与薛定谔型耦合微分方程的数值求解问题，提出了一种八阶代数精度指数拟合（exponentially-fitted）方法。通过精确定义新方法的自由参数，使其能够精确积分指数函数。数值与理论结果表明，该方法相较于经典方法及其他指数拟合方法具有更优异的计算效率。

程序名称：MAPLESIM
目录编号：ADLI_v1_0

问题本质
借助本程序可推导由式(14)生成的系数。本程序的第一部分用于计算构成方程组系数的矩阵元；第二部分则如文献[1]、[2]与[3]所述，通过迭代应用洛必达法则（L'Hospital's rule）以规避形如0/0的系数，进而求解上述方程组的解……

本程序在曼德莱数据（Mendeley Data）中的《计算机物理学报》（Computer Physics Communications, CPC）程序库内的收录版本为：ADLI_v1_0; MAPLESIM; 10.1016/S0010-4655(99)00459-2

本程序源自贝尔法斯特女王大学（Queen's University Belfast）所维护的CPC程序库（馆藏周期为1969-2019年）