Geodesic
On nonlinear algebraic differential systems reducible to non-degenerate systems of ordinary differential equations. Theory and numerical methods of solution
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 1, pp. 15-21.

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

In this paper, we consider algebraic differential systems of the form $$ \frac{dAx}{dt}=Bx+f(x,t) $$ with a regular pair of matrices $(A,В)$. The conditions of reducibility of such systems to non-degenerate systems of ordinary differential equations (ODE) of first order with respect to the derivative $x'(t)$ are given. Methods for the numerical solution of $x(t)$ are proposed. 
@article{SJVM_2010_13_1_a1,
     author = {Yu. E. Boyarintsev},
     title = {On nonlinear algebraic differential systems reducible to non-degenerate systems of ordinary differential equations. {Theory} and numerical methods of solution},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {15--21},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2010_13_1_a1/}
}
TY  - JOUR
AU  - Yu. E. Boyarintsev
TI  - On nonlinear algebraic differential systems reducible to non-degenerate systems of ordinary differential equations. Theory and numerical methods of solution
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2010
SP  - 15
EP  - 21
VL  - 13
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2010_13_1_a1/
LA  - ru
ID  - SJVM_2010_13_1_a1
ER  - 
%0 Journal Article
%A Yu. E. Boyarintsev
%T On nonlinear algebraic differential systems reducible to non-degenerate systems of ordinary differential equations. Theory and numerical methods of solution
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2010
%P 15-21
%V 13
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2010_13_1_a1/
%G ru
%F SJVM_2010_13_1_a1
Yu. E. Boyarintsev. On nonlinear algebraic differential systems reducible to non-degenerate systems of ordinary differential equations. Theory and numerical methods of solution. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 1, pp. 15-21. http://geodesic.mathdoc.fr/item/SJVM_2010_13_1_a1/

[1] Chistyakov V. F., Scheglova A. A., Izbrannye glavy teorii algebro-differentsialnykh sistem, Nauka, Novosibirsk, 2003 | MR | Zbl

[2] Boyarintsev Yu. E., Lineinye i nelineinye algebro-differentsialnye sistemy, Nauka, Novosibirsk, 2000 | Zbl

[3] Boyarintsev Yu. E., Orlova I. V., Puchki matrits i algebro-differentsialnye sistemy, Nauka, Novosibirsk, 2006