@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/}
}
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