Newman's numerical technique (1-4) has been used extensively
to solve two-point boundary value problems consisting
of coupled, ordinary differential equations. Unfortunately,
his method does not always yield a solution to a
system of independent equations. Sometimes his algorithm
(BAND) signals incorrectly that the coefficient
matrix is singular (e.g., DETERMINANT = 0 AT J = 2),
and no solution is obtained to the system of equations.
This problem sometimes occurs when one tries to use
BAND to solve a two-point boundary value problem
which consists of a set of mixed order ordinary differential
equations. For example, the battery model equations presented
recently by Evans and White (5) are representative
of this type of equation set. This problem is referred to
here as the "zero determinant problem." The cause of this
problem with BAND is due to the way in which the algorithm
in BAND is used to solve the system of equations.
The problem can be avoided by using alternate difference
expressions or coordinate systems, or by using algorithms
by deBoor (6) or IMSL (7).
Journal of the Electrochemical Society, 1989, pages 3392-3393.
© The Electrochemical Society, Inc. 1989. All rights reserved. Except as provided under U.S. copyright law, this work may not be reproduced, resold, distributed, or modified without the express permission of The Electrochemical Society (ECS). The archival version of this work was published in the Journal of the Electrochemical Society.