Geodesic
Method for constructing solutions of linear ordinary differential equations with constant coefficients
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 2, pp. 237-252 Cet article a éte moissonné depuis la source Math-Net.Ru

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For Cauchy problems involving linear differential equations with constant coefficients, a new method for constructing solutions without determining the roots of the characteristic equation is proposed. Formulas for the differentiation of the solution with respect to the equation coefficients are derived, and an approximate analytical solution is found. 
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V. V. Karachik. Method for constructing solutions of linear ordinary differential equations with constant coefficients. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 2, pp. 237-252. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_2_a7/

[1] Petrovskii I.G., Lektsii po teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1970

[2] Bugrov Ya.S., Nikolskii S.M., Differentsialnye uravneniya. Kratnye integraly. Ryady. Funktsii kompleksnogo peremennogo, Nauka, M., 1985

[3] Karachik V.V., “Polynomial solutions to the systems of partial differential equations with constant coefficients”, Yokohama Math. J., 47 (2000), 121–142 | MR | Zbl

[4] Karachik V.V., “Polinomialnye resheniya differentsialnykh uravnenii v chastnykh proizvodnykh s postoyannymi koeffitsientami. I”, Vestn. YuUrGU. Ser. Matematika. Mekhanika. Fizika, 4:10(227) (2011), 4–17

[5] Karachik V.V., “Normalized system of functions with respect to the Laplace operator and its applications”, J. of Math. Analys. and Appl., 287:2 (2003), 577–592 | DOI | MR | Zbl

[6] Gröbner W., Die Lie-Reihen und ihre Anwendungen, VEB. Deutscher Verlag der Wissenschaften, Berlin, 1960 | MR

[7] Cap F.F., Weik J.W., “Applications of Lie series in atomic physics”, Atomic. Energy. Rev., 8:3 (1970), 621–692

[8] Filatov A.N., Obobschennye ryady Li i ikh prilozheniya, Izd-vo AN UzSSR, Tashkent, 1963

[9] Bondarenko B.A., Operatornye algoritmy v differentsialnykh uravneniyakh, Fan, Tashkent, 1984

[10] Maslov V.P., Operatornye metody, Nauka, M., 1973

[11] Bitsadze A.V., “K teorii garmonicheskikh funktsii”, Tr. Tbilisskogo un-ta, 1962, no. 84, 35–37