Geodesic
Numerical methods based on multipoint Hermite interpolating polynomials for solving the Cauchy problem for stiff systems of ordinary differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 234-244 Cet article a éte moissonné depuis la source Math-Net.Ru

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Families of $A$-, $L$- and $L(\delta)$-stable methods are constructed for solving the Cauchy problem for a system of ordinary differential equations (ODEs). The $L(\delta)$-stability of a method with a parameter $\delta\in(0,1)$ is defined. The methods are based on the representation of the right-hand sides of an ODE system at the step $h$ in terms of two-or three-point Hermite interpolating polynomials. Comparative results are reported for some test problems. The multipoint Hermite interpolating polynomials are used to derive formulas for evaluating definite integrals. Error estimates are given. 
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A. F. Latypov; Yu. V. Nikulichev. Numerical methods based on multipoint Hermite interpolating polynomials for solving the Cauchy problem for stiff systems of ordinary differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 234-244. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a6/

[1] Nikulichev Yu. V., “Chislennyi metod integrirovaniya sistem obyknovennykh differentsialnykh uravnenii na osnove analiticheskogo differentsirovaniya funktsii na EVM”, Chisl. metody mekhan. sploshnoi sredy, 11, no. 1, VTs SO AN SSSR, Novosibirsk, 1980, 133–142 | MR

[2] Dzh. Kholl i Dzh. Uatt (red.), Sovremennye chislennye metody resheniya obyknovennykh differentsialnykh uravnenii, Mir, M., 1979

[3] Beiker Dzh. ml., Greivs-Morris P., Approksimatsii Pade, Mir, M., 1985

[4] Wanner G., Hairer E., Norsett S. P., “Order stars and stability theorems”, BIT, 18 (1978), 475–489 | DOI | MR | Zbl

[5] Shtetter X., Analiz metodov diskretizatsii dlya obyknovennykh differentsialnykh uravnenii, Mir, M., 1978 | MR

[6] Aulchenko S. M., Latypov A. F., Nikulichev Yu. V., “Metod chislennogo integrirovaniya sistem obyknovennykh differentsialnykh uravnenii s ispolzovaniem interpolyatsionnykh polinomov Ermita”, Zh. vychisl. matem. i matem. fiz., 38:10 (1998), 1665–1670 | MR

[7] Gear C. W., “The automatic integration of ordinary differential equations”, Comput. and Structures, 20:6 (1985), 915–920 | DOI

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

[9] Berezin I. S., Zhidkov H. P., Metody vychislenii, Nauka, M., 1970

[10] Kolchanov H. A., Latypov A. F., Likhoshvai V. A. i dr., “Zadachi optimalnogo upravleniya v dinamike gennykh setei i metody ikh resheniya”, Izv. RAN. Teorii i sistemy upravleniya, 2004, no. 6, 36–45 | MR | Zbl