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Fil’chakov, P. F.

Use of power series in solving linear and nonlinear ordinary differential equations and systems thereof. (English) Zbl 0206.47105

Ukr. Math. J. 21, 182-197 (1969).
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MSC:

65L99 Numerical methods for ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34A30 Linear ordinary differential equations and systems
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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References:

[1] V. V. Golubev, Lectures on the Analytic Theory of Differential Equations, Second Edition [in Russian], Gostekhizdat, Moscow-Leningrad (1950).
[2] N. P. Erugin, Linear Systems of Ordinary Differential Equations with Periodic and Quasiperiodic Coefficients [in Russian], Izd-vo AN BSSR, Minsk (1963). · Zbl 0119.30102
[3] E. Kamke, Handbook of Ordinary Differential Equations [Russian translation], IL, Moscow (1959).
[4] M. A. Lavrent’ev, On a First-Order Differential Equation [in French], Math. Zeitschrift,23 (1925).
[5] N. M. Matveev, Methods of Integrating Ordinary Differential Equations, Third Edition [in Russian], Vysshaya Shkola, Moscow (1967). · Zbl 0291.65014
[6] V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations [in Russian], Gostekhizdat, Moscow-Leningrad (1949).
[7] I. G. Petrovskii, Lectures on the Theory of Ordinary Differential Equations, Fifth Edition [in Russian], Nauka, Moscow (1964).
[8] L. S. Pontryagin, Ordinary Differential Equations [in Russian], Fizmatgiz, Moscow (1961). · Zbl 0098.05502
[9] J. Sansone, Ordinary Differential Equations, Vols. 1 and 2 [Russian translation], IL, Moscow (1953-1954).
[10] V. I. Smirnov, Course of Higher Mathematics, Fourth Edition, Vol.3, Part 2 [cmin Russian], Gostekhizdat, Moscow-Leningrad (1950).
[11] V. V., Stepanov, Course in Differential Equations [in Russian], Gostekhizdat, Moscow (1953).
[12] S. F. Feshchenko, N. I. Shkil’, and L. D., Nikolenko, Asymptotic Methods in the Theory of Linear Differential Equations [in Russian], Naukova Dumka, Kiev (1966). · Zbl 0141.28004
[13] P. F. Fil’chakov, Approximate Methods of Conformal Mapping [in Russian], Naukova Dumka, Kiev (1964).
[14] P. F. Fil’chakov, ?On an Effective Method of Folding Koshi Problems for Nonlinear Differential Equations,? Dokl. Akad. Nauk UkrSSR, Ser. A, No. 1 (1967); ?On an Effective Method of Folding Boundary Problems for Nonlinear Orderly Differential Equations,? Dokl. Akad. Nauk UkrSSR, Ser. A, No. 2 (1967); ?On the Solution of a System of Nonlinear Differential Equations by Means of Powere Theory,? Dokl. Akad. Nauk UkrSSR, Ser. A, No. 9 (1967); ?On an Effective Method of Allotting Real Values for Ordinary Differential Equations,? Dokl. Akad. Nauk UkrSSR, Ser. A, No. 10 (1967); ?On the Construction of Integrals of Differential Equations not Solved with Reference to a Higher Step,? Dokl. Akad. Nauk, Ser. A, No. 4 (1969).
[15] P. F. Fil’chakov, On One Method of Solving Systems of Algebraic or Transcendental Equations [in Ukrainian], Dokl. Akad. Nauk UkrSSR, Ser. A, No. 1 (1969).
[16] P. F. Fil’chakov and Mi. I. Cinyavskii, On Solving the Fermi-Thomas Equation by Means of Power Series [in Ukrainian], Dokl. Akad. Nauk UkrSSR, Ser. A, No. 2 (1969).
[17] I. Z. Shtokalo, Linear Differential Equations with Variable Coefficients (Asymptotic Methods and Criteria for Stability and Instability of Solutions) [in Russian], Izd-vo Akad. Nauk UkrSSR, Kiev (1960).
[18] I. Z. Shtokalo, Operational Methods and Their Development in the Theory of Linear Differential Equations with Variable Coefficients [in Russian], Izd-vo Akad. Nauk UkrSSR, Kiev (1961).
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