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International Journal of Mathematical Research

January 2016, Volume 5, 1, pp 25-39

Riccatis Equation. Asymptotics of Exact Solution

Nikolai Evgenievich Tsapenko

Nikolai Evgenievich Tsapenko 1

  1. National University of Science and Technology “MISiS”, Moscow, Russian Federation 1

Pages: 25-39

DOI: 10.18488/journal.24/2016.5.1/24.1.25.39

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Abstract:

In this article based on a method of approximating equation an asymptotic solution of the general Riccati ‘s equation is obtained. The principal distinctive feature and advantage of the solution is its continuity at turning points. Estimates of accuracy of the approximate solution are derived. Limit values of the asymptotic solution in case of one-sided convergence of argument to turning point of the first order are calculated.

Contribution/ Originality
This study contributes in the existing literature. Thus, the results of that study may be applied for solving problems were set up in works [1], [2], [3]. This study is one of very few studies, which have investigated the asymptotic behavior of solutions of Riccati’s equation in the neighborhood of turning points.

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Reference:

  1. E. F. Kuester, "A lower bound for the length of nonuniform transmission line matching sections," Int. J. Electron. Commun. AEÜ, vol. 66, pp. 1011- 1016, 2012.
  2. N. E. Tsapenko, "Plane electromagnetic waves in heterogeneous medium approximation regarding relative rate of change of wave resistance," Laser and Particle Beams, vol. 11, pp. 679-684, 1993.
  3. S. K. Younis and N. E. Tsapenko, "New solution method of wave problems from the turning points," International Journal of Energy and Power Engineering. Science Publishing Group, USA, vol. 3, pp. 15-20, 2014.
  4. N. E. Tsapenko, "New formulas for an approximate solution of the one-dimensional wave equation," Differential Equations, vol. 25, pp. 1941-1946, 1989.
  5. N. E. Tsapenko, Riccatis's equation and wave processes. Moscow: MSMU-Publisher, Gornaya Kniga, 2008.

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