Multistep numerical methods for functional-differential-algebraic equations
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 145-155 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

This paper deals with constructing multistep numerical methods for differential delay equations under additional algebraic constraints. Theorems on the orders of convergence of these methods are proved both for functional-differential equations with algebraic constraints and for singular functional-differential equations.
@article{TIMM_2007_13_2_a13,
     author = {V. G. Pimenov},
     title = {Multistep numerical methods for functional-differential-algebraic equations},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {145--155},
     year = {2007},
     volume = {13},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a13/}
}
TY  - JOUR
AU  - V. G. Pimenov
TI  - Multistep numerical methods for functional-differential-algebraic equations
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2007
SP  - 145
EP  - 155
VL  - 13
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a13/
LA  - ru
ID  - TIMM_2007_13_2_a13
ER  - 
%0 Journal Article
%A V. G. Pimenov
%T Multistep numerical methods for functional-differential-algebraic equations
%J Trudy Instituta matematiki i mehaniki
%D 2007
%P 145-155
%V 13
%N 2
%U http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a13/
%G ru
%F TIMM_2007_13_2_a13
V. G. Pimenov. Multistep numerical methods for functional-differential-algebraic equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 145-155. http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a13/

[1] Khairer E., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Zhestkie i differentsialno-algebraicheskie zadachi, Mir, M., 1999

[2] Kim A. V., Pimenov V. G., $i$-gladkii analiz i chislennye metody resheniya funktsionalno- differentsialnykh uravnenii, NITs “Regulyarnaya i khaoticheskaya dinamika”, M.–Izhevsk, 2004

[3] Krasovskii N. N., Nekotorye zadachi teorii ustoichivosti dvizheniya, Gostekhizdat, M., 1959 | MR

[4] Shimanov S. N., “K teorii lineinykh differentsialnykh uravnenii s posledeistviem”, Differents. uravneniya, 1 (1965), 102–116 | Zbl

[5] Pimenov V. G., “Chislennye metody resheniya FDAU i asimptoticheskoe razlozhenie reshenii singulyarnykh uravnenii s zapazdyvaniem”, Matematika. Mekhanika. Informatika, Mat-ly vseros. nauch. konf., 2006, Chelyab. gos. un-t, Chelyabinsk, 2007, 143–151

[6] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977 | MR

[7] Gear C. T., “Simultaneous numerical solution of diifferential-algebraic equations”, IEEE Trans. Circuit Theory, 18:1 (1971), 89–95 | DOI

[8] Kim A. V., Pimenov V. G., “Multistep numerical methods for functional differential equations”, Math. Computers in Simulation, 45 (1998), 377–384 | DOI | MR | Zbl

[9] Lubich Ch., “On the convergence of multistep methods for nonlinear stiff differential equations applied to differential-algebraic systems”, Numer. Math., 58 (1991), 839–853 | DOI | MR | Zbl