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Formulas For Solutions Of The Riccati’s Equation

Year 2017, Volume: 5 Issue: 3, 16 - 24, 01.12.2017

Abstract

In this paper we obtained the formula for the common solution of Riccati equations. Here Riccati equations was solved for common cases. Results obtained have been compared with the conventional ones and a comment has been made on them. The equation provides all necessary conditions of the theorem. The possibility of the application of the obtained results is also considered. The particular solution and the general solutions of the Riccati equations (1) is presented in the common cases and will be written in the forms (3) and (4).

References

  • [1] A.A.L. Bastami, M.R..Belic, N.Z..Petrovic, Special Solutions of the Riccati Equation with Applications to the Gross-Pitaevskii Nolinear PDE, 66, (2010), 1-10.
  • [2]. P.P. Boyle, W. Tian, F. Guan, The Riccati Equation in Mathematical Finance, Journal Symbolic Computation, 33,(2002), 343-355.
  • [3] A.I. Egorov, Riccat Equations, Moskow, Nauka, 2001.
  • [4] E. Kamke, Handbook of Ordinary Differential Equations, Moskow, Nauka, 1976.
  • [5] A.D. Polyanin, V.F. Zaytsev, Handbook of Exact Solutions for Ordinary Differential Equations, Boca Raton-NewYork, CRC Press, 2003.
  • [6] H. Tiberin, S.N. Francisco, M.K.M. Lobo, Analitical Solutions of the Riccati Equation with Coefficients Satisfying Integral or Differential Conditions with Arbitrary Functions, Journal of Applied Mathematics, 2, (2014), 109-118.
  • [7] A. Asanov, M.H. Chelik, R. Asanov, Formulas for Solution of the Linear Differential Equations of the Second Order with the Variable Coefficients, Journal of Mathematics Research, 3, (2011), 32-39.
Year 2017, Volume: 5 Issue: 3, 16 - 24, 01.12.2017

Abstract

References

  • [1] A.A.L. Bastami, M.R..Belic, N.Z..Petrovic, Special Solutions of the Riccati Equation with Applications to the Gross-Pitaevskii Nolinear PDE, 66, (2010), 1-10.
  • [2]. P.P. Boyle, W. Tian, F. Guan, The Riccati Equation in Mathematical Finance, Journal Symbolic Computation, 33,(2002), 343-355.
  • [3] A.I. Egorov, Riccat Equations, Moskow, Nauka, 2001.
  • [4] E. Kamke, Handbook of Ordinary Differential Equations, Moskow, Nauka, 1976.
  • [5] A.D. Polyanin, V.F. Zaytsev, Handbook of Exact Solutions for Ordinary Differential Equations, Boca Raton-NewYork, CRC Press, 2003.
  • [6] H. Tiberin, S.N. Francisco, M.K.M. Lobo, Analitical Solutions of the Riccati Equation with Coefficients Satisfying Integral or Differential Conditions with Arbitrary Functions, Journal of Applied Mathematics, 2, (2014), 109-118.
  • [7] A. Asanov, M.H. Chelik, R. Asanov, Formulas for Solution of the Linear Differential Equations of the Second Order with the Variable Coefficients, Journal of Mathematics Research, 3, (2011), 32-39.
There are 7 citations in total.

Details

Other ID JA45RC37ME
Journal Section Research Article
Authors

A. Asanov This is me

E. Hazar This is me

R. Asanov This is me

Publication Date December 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 3

Cite

APA Asanov, A., Hazar, E., & Asanov, R. (2017). Formulas For Solutions Of The Riccati’s Equation. MANAS Journal of Engineering, 5(3), 16-24.
AMA Asanov A, Hazar E, Asanov R. Formulas For Solutions Of The Riccati’s Equation. MJEN. December 2017;5(3):16-24.
Chicago Asanov, A., E. Hazar, and R. Asanov. “Formulas For Solutions Of The Riccati’s Equation”. MANAS Journal of Engineering 5, no. 3 (December 2017): 16-24.
EndNote Asanov A, Hazar E, Asanov R (December 1, 2017) Formulas For Solutions Of The Riccati’s Equation. MANAS Journal of Engineering 5 3 16–24.
IEEE A. Asanov, E. Hazar, and R. Asanov, “Formulas For Solutions Of The Riccati’s Equation”, MJEN, vol. 5, no. 3, pp. 16–24, 2017.
ISNAD Asanov, A. et al. “Formulas For Solutions Of The Riccati’s Equation”. MANAS Journal of Engineering 5/3 (December 2017), 16-24.
JAMA Asanov A, Hazar E, Asanov R. Formulas For Solutions Of The Riccati’s Equation. MJEN. 2017;5:16–24.
MLA Asanov, A. et al. “Formulas For Solutions Of The Riccati’s Equation”. MANAS Journal of Engineering, vol. 5, no. 3, 2017, pp. 16-24.
Vancouver Asanov A, Hazar E, Asanov R. Formulas For Solutions Of The Riccati’s Equation. MJEN. 2017;5(3):16-24.

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