FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 4, PAGES 1047-1080

**On numerical solution of large-scale systems of
index $1$ differential-algebraic
equations**

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.

Location: http://mech.math.msu.su/~fpm/eng/k01/k014/k01406h.htm

Last modified: April 17, 2002