Geodesic
On first- and second-order difference schemes for differential-algebraic equations of index at most two
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1909-1918 
M. V. Bulatov; Lee Ming-Gong; L. S. Solovarova. On first- and second-order difference schemes for differential-algebraic equations of index at most two. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1909-1918. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a3/
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     title = {On first- and second-order difference schemes for differential-algebraic equations of index at most two},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     language = {ru},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Difference schemes of the Euler and trapezoidal types for the numerical solution of the initial-value problem for linear differential-algebraic equations are examined. These schemes are analyzed for model examples, and their superiority over the familiar first- and second-order implicit methods is shown. Conditions for the convergence of the proposed algorithms are formulated.

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

[2] Brenan K. E., Campbell S. L., Petzold L. R., Numerical solution of initial-value problems in differential-algebraic equations, 2nd edition, SIAM Publications, Philadelphia, PA, 1996 | MR | Zbl

[3] Bulatov M. V., Chistyakov V. F., “Ob usloviyakh skhodimosti raznostnykh skhem dlya sistem ODU, ne razreshennykh otnositelno proizvodnykh”, Metody chisl. analiza i optimizatsii, Nauka, Novosibirsk, 1987, 175–187 | MR | Zbl

[4] Bulatov M. V., “Numerical solution of differential-algebraic equations by block methods”, Comput. Sci.-ICCS (2003), v. 2, Springer, 2003, 516–522 | MR | Zbl

[5] Chistyakov V. F., Algebro-differentsialnye operatory s konechnomernym yadrom, Nauka, Novosibirsk, 1996 | MR

[6] Bulatov M. V., Chistyakov V. F., “Ob odnom chislennom metode resheniya differentsialno-algebraicheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz., 42:4 (2002), 459–470 | MR | Zbl

[7] Danilov V. A., Chistyakov V. F., O prepyatstviyakh na puti postroeniya effektivnykh chislennykh metodov resheniya algebro-differentsialnykh sistem, Preprint No 5, IrVTs SO AN SSSR, Irkutsk, 1990 | MR

[8] März R., “Differential-algebraic systems anew”, Appl. Numer. Math., 42 (2002), 315–335 | DOI | MR

[9] Kunkel P., Mehrmann V., “Stability properties of differential-algebraic equations and spin-stabilized diskretizations”, Electr. Trans. Numer. Anal., 26 (2007), 385–420 | MR | Zbl

[10] Gantmakher F. R., Teoriya matrits, Nauka, M., 1966 | MR