Publication Details
Multiple Arithmetic in Dynamic System Simulation
stiff systems, Modern Taylor series method, differential equations, continuous
system modelling, multiple arithmetic
A very interesting and promising numerical method of solving systems of ordinary
differential equations based on Taylor series has appeared. The potential of the
Taylor series has been exposed by many practical experiments and a way of
detection and solution of large systems of ordinary differential equations has
been found. Generally speaking, a stiff system contains several components, some
of them are heavily suppressed while the rest remain almost unchanged. This
feature forces the used method to choose an extremely small integration step and
the progress of the computation may become very slow. There are many (implicit)
methods for solving stiff systems of ODE's, from the most simple such as implicit
Euler method to more sophisticated (implicit Runge-Kutta methods) and finally the
general linear methods. Usually a quite complicated auxiliary system of equations
has to be solved in each step. These facts lead to immense amount of work to be
done in each step of the computation. These are the reasons why one has to think
twice before using the stiff solver and to decide between the stiff and non-stiff
solver.
@inproceedings{BUT27764,
author="Jiří {Kunovský} and Jiří {Petřek} and Václav {Šátek}",
title="Multiple Arithmetic in Dynamic System Simulation",
booktitle="Proceedings UKSim 10th International Conference EUROSIM/UKSim2008",
year="2008",
pages="597--598",
publisher="IEEE Computer Society",
address="Cambridge",
isbn="0-7695-3114-8"
}