FDEXTR, a program for the finite-difference solution of the coupled-channel Schrödinger equation using Richardson extrapolation
Description
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 difference method of the second order using the iterative Richardson extrapolation of the difference eigensolutions on a sequence of doubly condensed meshes. The same extrapolational procedure and error estimations are applied to the eigenvalues and eigenfunctions. Zero-value (Dirichlet) or zero-gradient (Neumann) boundary conditions are consider... Title of program: FDEXTR Catalogue Id: ACVG_v1_0 Nature of problem Coupled second-order differential equations of the form <pre> d^2 [-P ---- + Q(x)]Y(x) = lambda Y(x), x in [a,b], dx^2 </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, Q(x) is a symmetric potential matrix and P = cI, where I is the unit matrix and c is a certain constant (usually c = hbar^2/2mu or 1). Such systems of coupled differential equations usua ... Versions of this program held in the CPC repository in Mendeley Data ACVG_v1_0; FDEXTR; 10.1016/0010-4655(94)90169-4 ACVG_v2_0; FDEXTR version 2.1; 10.1016/S0010-4655(98)00033-2 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)