@Article{NMTMA-7-1,
author = {},
title = {A Fitted Numerov Method for Singularly Perturbed Parabolic Partial Differential Equation with a Small Negative Shift Arising in Control Theory},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2014},
volume = {7},
number = {1},
pages = {23--40},
abstract = {<p style="text-align: justify;">In this paper, a fitted Numerov method is constructed for a class of singularly
perturbed one-dimensional parabolic partial differential equations with a small
negative shift in the temporal variable. &nbsp;Similar boundary value problems are
associated with a furnace used to process a metal sheet in control theory.
Here, the study focuses on the effect of shift on the boundary layer behavior
of the solution via finite difference approach. &nbsp;When the shift parameter is
smaller than the perturbation parameter, the shifted term is expanded in Taylor
series and an exponentially fitted tridiagonal finite difference scheme is developed.
The proposed finite difference scheme is unconditionally stable. &nbsp;When the shift
parameter is larger than the perturbation parameter, a special type of mesh is
used for the temporal variable so that the shift lies on the nodal points and an
exponentially fitted scheme is developed. &nbsp;This scheme is also unconditionally
stable. &nbsp;The applicability of the proposed methods is demonstrated by means of two examples.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2014.1316nm},
url = {https://global-sci.com/article/90592/a-fitted-numerov-method-for-singularly-perturbed-parabolic-partial-differential-equation-with-a-small-negative-shift-arising-in-control-theory}
}