FESSDE 2.2: A new version of a program for the finite-element solution of the coupled-channel Schrödinger equation using high-order accuracy approximations

Abstract
A FORTRAN 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 2.2
Catalogue Id: ACVU_v2_0 [ADIX]

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 in [a,b], dx dx </PRE> with boundary conditions <PRE> 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 m ...

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)

摘要
本研究提出一款FORTRAN程序，可通过采用高精度近似的有限元法，求解耦合二阶微分方程组的施图姆-刘维尔（Sturm-Liouville）问题。研究中考虑了微分方程系数的解析表达式与表格形式两种定义方式，同时覆盖零值（Dirichlet）与零梯度（Neumann）两类边界条件。

程序名称：FESSDE 2.2
目录编号：ACVU_v2_0 [ADIX]

待求解问题
针对如下形式的耦合二阶微分方程组：
<PRE> -d/dx[P(x)·dY(x)/dx] + [U(x) - λR(x)]Y(x) = 0, x ∈ [a,b] </PRE>
其边界条件为：
<PRE> Y(a) = 0 或 dY(x)/dx|_{x=a} = 0,
Y(b) = 0 或 dY(x)/dx|_{x=b} = 0 </PRE>
其中λ为特征值，Y(x)为特征向量，P(x)、U(x)与R(x)均为对称矩阵；P(x)为对角矩阵，其元素均为给定区间[a,b]上的可微函数，且R(x)为正定m×...

本程序在Mendeley数据平台的CPC库收录的版本包括：
ACVU_v1_0; FESSDE; 10.1016/0010-4655(94)00107-D
ACVU_v2_0; FESSDE 2.2; 10.1016/S0010-4655(98)00099-X

本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2019）

搜集汇总

背景与挑战

背景概述

FESSDE 2.2是一个FORTRAN程序，用于通过有限元方法和高精度近似求解耦合通道薛定谔方程的Sturm-Liouville问题。它支持Dirichlet和Neumann边界条件，以及分析和表格形式的系数输入，适用于科学计算和物理模拟。