FESSDE, a program for the finite-element solution of the coupled-channel Schrödinger equation using high-order accuracy approximations

Abstract
A FORTRAN 77 program is presented which solves the Sturm-Liouville problem for a system of coupled second-order differential equations by the finite element method using high-order accuracy approximations. The analytical and tabular forms of giving the coefficients of differential equations are considered. Zero-value (Dirichlet) and zero-gradient (Neumann) boundary conditions are also considered.

Title of program: FESSDE
Catalogue Id: ACVU_v1_0

Nature of problem
Coupled second-order differential equations of the form <PRE> d dY(x) - -- [P(x)-----] + [U(x) - lambdaR(x)]Y(x) = 0, x contained in [a,b], dx dx with boundary conditions dY(x)| Y(a) = 0 or -----| = 0, dx |x=a dY(x)| Y(b) = 0 or -----| = 0, dx |x=b </PRE> are solved. Here lambda is an eigenvalue, Y(x) is an eigenvector, P(x), U(x) and R(x) are symmetrical matrices, P(x) is a diagonal matrix, elements of which are the differentiable functions on a given interval [a,b], and R(x) is a positive matr ...

Versions of this program held in the CPC repository in Mendeley Data
ACVU_v1_0; FESSDE; 10.1016/0010-4655(94)00107-D
ACVU_v2_0; FESSDE 2.2; 10.1016/S0010-4655(98)00099-X

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

本文提出了一种基于有限元素法，采用高阶精度近似解法求解耦合二阶微分方程组Sturm-Liouville问题的FORTRAN 77程序。本文详细探讨了微分方程系数的解析和表格表示形式，并考虑了零值（Dirichlet）和零梯度（Neumann）边界条件。程序名称：FESSDE，目录编号：ACVU_v1_0。问题描述涉及形式如下的耦合二阶微分方程组：

<PRE> d^2Y(x) / dx^2 - [P(x) dY(x) / dx + U(x) - u03bbR(x)]Y(x) = 0, x in [a,b],

其中，u03bb为特征值，Y(x)为特征向量，P(x)、U(x)和R(x)均为对称矩阵，P(x)为对角矩阵，其对角元素是在区间[a,b]上的可微函数，而R(x)为正矩阵...

该程序版本存储于Mendeley数据中CPC程序库，包括以下版本：

ACVU_v1_0; FESSDE; 10.1016/0010-4655(94)00107-D
ACVU_v2_0; FESSDE 2.2; 10.1016/S0010-4655(98)00099-X

本程序已从贝尔法斯特女王大学（1969-2019）的CPC程序库中导入。