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)

本文提出了一种FORTRAN程序，该程序通过有限元方法，运用高阶精度近似解，求解耦合二阶微分方程组中的Sturm-Liouville问题。对微分方程系数的解析和表格表示形式进行了探讨。同时，也考虑了零值（Dirichlet）和零梯度（Neumann）边界条件。程序名称：FESSDE 2.2，目录编号：ACVU_v2_0 [ADIX]。问题性质：求解形式为 d^2Y(x)/dx^2 - [P(x)^(-1)][U(x) - (lambda)R(x)]Y(x) = 0（其中x属于[a,b]区间）的耦合二阶微分方程，并满足边界条件 dY(x)/dx | x=a = 0 或 ∂Y(x)/∂x | x=a = 0，以及 dY(x)/dx | x=b = 0 或 ∂Y(x)/∂x | x=b = 0。在此，(lambda)为特征值，Y(x)为特征向量，P(x)，U(x)，和R(x)为对称矩阵，其中P(x)为对角矩阵，其对角线元素为在给定区间[a,b]上的可微函数，而R(x)为正定矩阵。该程序版本存储于Mendeley Data中，版本信息包括ACVU_v1_0; FESSDE; 10.1016/0010-4655(94)00107-D和ACVU_v2_0; FESSDE 2.2; 10.1016/S0010-4655(98)00099-X。此程序已从贝尔法斯特女王大学（1969-2019）所持有的CPC程序库中导入。