@Article{NMTMA-1-321,
author = {Jürgen Geiser},
title = {Fourth-Order Splitting Methods for Time-Dependant Differential Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2008},
volume = {1},
number = {3},
pages = {321--339},
abstract = {<p style="text-align: justify;">This study was suggested by previous work on the simulation of
evolution equations with scale-dependent processes, e.g.,
wave-propagation or heat-transfer, that are modeled by wave
equations or heat equations. Here, we study both parabolic and
hyperbolic equations. We focus on ADI (alternating direction
implicit) methods and LOD (locally one-dimensional) methods, which
are standard splitting methods of lower order, e.g. second-order.
Our aim is to develop higher-order ADI methods, which are performed
by Richardson extrapolation, Crank-Nicolson methods and higher-order
LOD methods, based on locally higher-order methods. We discuss the
new theoretical results of the stability and consistency of the ADI
methods. The main idea is to apply a higher-order time
discretization and combine it with the ADI methods. We also discuss
the discretization and splitting methods for first-order and
second-order evolution equations. The stability analysis is given
for the ADI method for first-order time derivatives and for the LOD
(locally one-dimensional) methods for second-order time derivatives.
The higher-order methods are unconditionally stable. Some numerical
experiments verify our results.</p>},
issn = {2079-7338},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/nmtma/6054.html}
}