I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2001, VOLUME 7, NUMBER 4, PAGES 1047-1080
On numerical solution of large-scale systems of
G. Yu. Kulikov
A. A. Korneva
G. Ya. Benderskaya
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In this paper we study how to integrate numerically large-scale
systems of semi-explicit index 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
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
Numerical examples support theoretical results of the paper.
All articles are
published in Russian.
Last modified: April 17, 2002