FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2001, VOLUME 7, NUMBER 4, PAGES 1047-1080
G. Yu. Kulikov
A. A. Korneva
G. Ya. Benderskaya
Abstract
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In this paper we study how to integrate numerically
large-scale systems of semi-explicit index $1$
differential-algebraic
equations by implicit Runge--Kutta methods.
In this case we need to solve
high dimension linear systems with sparse coefficient matrices.
We develop an effective way for packing such matrices
of coefficients. We also derive a special Gaussian
elimination for parallel factorization of nonzero blocks of
the matrix. As a result, we produce a new efficient
procedure to solve linear systems arising
in an application of implicit Runge--Kutta methods to large-scale
differential-algebraic equations of index $1$ . Numerical examples
support theoretical results of the paper.
All articles are published in Russian.
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Last modified: April 17, 2002