Geodesic
The best argument for the parametric continuation of solutions of differential-algebraic equations
Lobachevskii journal of mathematics, Tome 20 (2005), pp. 3-15.

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

New algorithms for numerical continuation of Cauchy problem solution for different forms of DAEs, and results of their implementations are presented.
Keywords: differential-algebraic equations (DAEs), the best argument, Cauchy problem. 
@article{LJM_2005_20_a0,
     author = {V. Alferiev and E. B. Kuznetsov},
     title = {The best argument for the parametric continuation of solutions of differential-algebraic equations},
     journal = {Lobachevskii journal of mathematics},
     pages = {3--15},
     publisher = {mathdoc},
     volume = {20},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2005_20_a0/}
}
TY  - JOUR
AU  - V. Alferiev
AU  - E. B. Kuznetsov
TI  - The best argument for the parametric continuation of solutions of differential-algebraic equations
JO  - Lobachevskii journal of mathematics
PY  - 2005
SP  - 3
EP  - 15
VL  - 20
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2005_20_a0/
LA  - en
ID  - LJM_2005_20_a0
ER  - 
%0 Journal Article
%A V. Alferiev
%A E. B. Kuznetsov
%T The best argument for the parametric continuation of solutions of differential-algebraic equations
%J Lobachevskii journal of mathematics
%D 2005
%P 3-15
%V 20
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2005_20_a0/
%G en
%F LJM_2005_20_a0
V. Alferiev; E. B. Kuznetsov. The best argument for the parametric continuation of solutions of differential-algebraic equations. Lobachevskii journal of mathematics, Tome 20 (2005), pp. 3-15. http://geodesic.mathdoc.fr/item/LJM_2005_20_a0/

[1] V. Chistyakov, Singular systems of ordinary differential equations, Nauka, Novosibirsk, 1982 (Russian)

[2] D. Davidenko, “On a new method for the numerical solution of systems of nonlinear equations”, Dokladi Academii Nauk of Russia, 88, 601–602 | MR | Zbl

[3] D. Davidenko, “On the approximate solution of systems nonlinear equations”, Ukr. Mat. Zh., 5 (1953), 196–206 | MR | Zbl

[4] V. Gorbunov, V. Petrishchev, “Development of the normal spline method for linear differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 43 (2003), 1150–1159 | MR

[5] M. Lahaye, “Une metode de resolution d'une categorie d'equations transcendentes”, Compter Rendus hebdomataires des seances de L'Academie des sciences, 198 (1934), 1840–1842 | Zbl

[6] M. Lahaye, “Solution of system of transcendental equations”, Acad. Roy. Belg. Bull. Cl. Sci., 5 (1948), 805–822

[7] A. Lebedev, L. Chernobrovkin, The dynamics of the flying, Mashinostroenie, 1973 (Russian)

[8] V. Shalashilin, E. Kuznetsov, Paramertic Continuation and Optimal Parametrization in Applied Mathematics and Mechanics, Kluvert Academic Publishers, Dordrecht, Boston, London, 2003 | MR | Zbl