Geodesic
On numerical solution of large-scale systems of index~1 differential-algebraic equations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 1047-1080.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{FPM_2001_7_4_a5,
     author = {G. Yu. Kulikov and A. A. Korneva and G. Ya. Benderskaya},
     title = {On numerical solution of large-scale systems of index~1 differential-algebraic equations},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1047--1080},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a5/}
}
TY  - JOUR
AU  - G. Yu. Kulikov
AU  - A. A. Korneva
AU  - G. Ya. Benderskaya
TI  - On numerical solution of large-scale systems of index~1 differential-algebraic equations
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2001
SP  - 1047
EP  - 1080
VL  - 7
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a5/
LA  - ru
ID  - FPM_2001_7_4_a5
ER  - 
%0 Journal Article
%A G. Yu. Kulikov
%A A. A. Korneva
%A G. Ya. Benderskaya
%T On numerical solution of large-scale systems of index~1 differential-algebraic equations
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2001
%P 1047-1080
%V 7
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a5/
%G ru
%F FPM_2001_7_4_a5
G. Yu. Kulikov; A. A. Korneva; G. Ya. Benderskaya. On numerical solution of large-scale systems of index~1 differential-algebraic equations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 1047-1080. http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a5/