Geodesic
The numerical solution of the autonomous Cauchy problem with algebraic constraints on the phase variables
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 33 (1993) no. 4, pp. 522-540 
G. Yu. Kulikov. The numerical solution of the autonomous Cauchy problem with algebraic constraints on the phase variables. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 33 (1993) no. 4, pp. 522-540. http://geodesic.mathdoc.fr/item/ZVMMF_1993_33_4_a3/
@article{ZVMMF_1993_33_4_a3,
     author = {G. Yu. Kulikov},
     title = {The numerical solution of the autonomous {Cauchy} problem with algebraic constraints on the phase variables},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {522--540},
     year = {1993},
     volume = {33},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1993_33_4_a3/}
}
TY  - JOUR
AU  - G. Yu. Kulikov
TI  - The numerical solution of the autonomous Cauchy problem with algebraic constraints on the phase variables
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1993
SP  - 522
EP  - 540
VL  - 33
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1993_33_4_a3/
LA  - ru
ID  - ZVMMF_1993_33_4_a3
ER  - 
%0 Journal Article
%A G. Yu. Kulikov
%T The numerical solution of the autonomous Cauchy problem with algebraic constraints on the phase variables
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1993
%P 522-540
%V 33
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_1993_33_4_a3/
%G ru
%F ZVMMF_1993_33_4_a3

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

[1] Ikeda N., Marumo F., Shiratare M., Sato T., “A model of overall regulation of body fiuids”, Ann. Biomed. Engng., 7 (1979), 135–166 | DOI

[2] Guyton A. C., Coleman T. G., Grander H. J., “Circulation: overall regulation”, Ann. Rev. Physiol., 34 (1972), 13–41 | DOI

[3] Boyarintsev Yu. E., Danilov V. A., Loginov A. A., Chistyakov V. F., Chislennye metody resheniya singulyarnykh sistem, Nauka, Novosibirsk, 1989 | Zbl

[4] Hairer E., Wanner G., Solving ordinary differential equations, v. II, Stiff and differential-algebraic problems, Springer, Berlin, 1991 | MR | Zbl

[5] Campbell S. L., Petzoid L. R., “Canonical forms and solvable singular systems of differential equations”, SIAM J. Algorithm and Discrete Methods, 1983, no. 4, 517–521 | DOI | MR | Zbl

[6] Gear C. W., “The simultaneous numerical solution of differential-algebraic equations”, IEEE Trans. Circuit Theory TC, 18 (1971), 89–95 | DOI

[7] Gear C. W., Petzoid L. R., “ODE methods for the solution of differential-algebraic systems”, SIAM J. Numer. Analys., 21 (1984), 716–728 | DOI | MR | Zbl

[8] Marz R., Multistep methods for initial value problems in implicit differential-algebraic equations, Preprint No 22, Humboldt Univ. Sekt. Math., Berlin, 1981 | MR

[9] Lotstedt P., Petzoid L. R., “Numerical solution of nonlinear differential equations with algebraic constrains. I: Convergence results for backward differentiation formulas”, Math. Comput., 46 (1986), 491–516 | MR

[10] Brenan K. E., Engquist B. E., Backward differentiation approximations of nonlinear differential-algebraic equations, Rept. No 101, Dept. Comput. Sci. Uppsala Univ., Uppsala, Sweden, 1985

[11] Brenan K. E., Petzoid L. R., “The numerical solution of higher index differential-algebraic equations by implicit Runge-Kutta methods”, SIAM J. Numer. Analys., 26 (1986), 976–996 | DOI | MR

[12] Tikhonov A. N., Vasileva A. B., Sveshnikov A. G., Differentsialnye uravneniya, Nauka, M., 1985 | MR

[13] Ortega Dzh., Reinboldt V., Iteratsionnye metody resheniya nelineinykh sistem uravnenii so mnogimi neizvestnymi, Mir, M., 1975 | MR

[14] Ortega Dzh., Pul U., Vvedenie v chislennye metody resheniya differentsialnykh uravnenii, Nauka, M., 1986 | MR | Zbl

[15] Kulikov G. Yu., “Ob odnom sposobe chislennogo resheniya avtonomnoi zadachi Koshi s algebraicheskoi svyazyu na fazovye peremennye”, Vestn. MGU. Ser. matem., mekhan., 1992, no. 1, 14–19 | MR