An approximate analytic solution of the nonlinear Riccati differential equation

Journal of the Franklin Institute

Volumn 347, Issue 10, 2010, Pages 1850-1862

  Tsai, Pa Yee ^a   Chen, Cha'O Kuang ^a  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ADOMIAN DECOMPOSITION METHODS; APPROXIMANTS; APPROXIMATE ANALYTIC SOLUTIONS; EXACT SOLUTION; FAST CONVERGENCE; HYBRID METHOD; RICCATI DIFFERENTIAL EQUATION; SERIES SOLUTIONS; TRANSFORM ALGORITHM;

LAPLACE TRANSFORMS; RICCATI EQUATIONS;

NONLINEAR EQUATIONS;

EID: 78650034202     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfranklin.2010.10.005     Document Type: Article

References (22)

1. G. Adomian Solving Frontier Problems of Physics: The Decomposition Method 1994 Kluwer Academic Publishers Boston
2. C.H. Chiu, and C.K. Chen A decomposition method for solving the convective longitudinal fins with variable thermal conductivity Int. J. Heat Mass Transfer 45 2002 2067 2075
3. J.H. Kuang, and C.J. Chen Adomian decomposition method used for solving nonlinear pull-in behavior in electrostatic micro-actuators Math. Comput. Model. 41 2005 1479 1491
4. J.C. Hsu, H.Y. Lai, and C.K. Chen Free vibration of non-uniform EulerBernoulli beams with general elastically end constraints using Adomian modified decomposition method J. Sound Vib. 318 2008 965 981
5. Y.T. Yang, S.K. Chien, and C.K. Chen A double decomposition method for solving the periodic base temperature in convective longitudinal fins Energy Convers. Manage. 49 2008 2910 2916
6. W.C. Tien, and C.K. Chen Adomian decomposition method by Legendre polynomials Chaos Solitons Fractals 39 2009 2093 2101
7. S.A. Khuri A Laplace decomposition algorithm applied to a class of nonlinear differential equations J. Appl. Math. 1 2001 141 155
8. E Yusufolu Numerical solution of Duffing equation by the Laplace decomposition algorithm Appl. Math. Comput. 177 2006 572 580
9. S. Bittanti, D.B. Hernandez, and G. Zerbi The simple pendulum and the periodic LQG control problem J. Franklin Inst. 328 1991 299 315
10. C.H. Lee, T.H.S. Li, and F.C. Kung A Riccati equation approach to the robust memoryless stabilization of discrete time-delay systems J. Franklin Inst. 332 1995 107 114
11. E. Hendrickson Synthesis of finite-dimensional Riccati-based feedback controls for problems arising in structural acoustics J. Franklin Inst. 336 1999 565 588
12. V.N. Phat Switched controller design for stabilization of nonlinear hybrid systems with time-varying delays in state and control J. Franklin Inst. 347 2010 195 207
13. Y.H. Ku Solution of the Riccati equation by continued fractions J. Franklin Inst. 293 1972 59 65
14. M.A. El-Tawil, A.A. Bahnasawi, and A. Abdel-Naby Solving Riccati differential equation using Adomian's decomposition method Appl. Math. Comput. 157 2004 503 514
15. B.Q. Tang, and X.F. Li A new method for determining the solution of Riccati differential equations Appl. Math. Comput. 194 2007 431 440
16. Y. Tan, and S. Abbasbandy Homotopy analysis method for quadratic Riccati differential equation Commun. Nonlinear Sci. Numer. Simulat. 13 2008 539 546 (Pubitemid 47497345)
17. F. Geng, Y. Lin, and M. Cui A piecewise variational iteration method for Riccati differential equations Comput. Math. Appl. 58 2009 2518 2522
18. H. Aminikhah, and M. Hemmatnezhad An efficient method for quadratic Riccati differential equation Commun. Nonlinear Sci. Numer. Simulat. 15 2010 835 839
19. S. Abbasbandy Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method Appl. Math. Comput. 172 2006 485 490
20. S. Abbasbandy Iterated He's homotopy perturbation method for quadratic Riccati differential equation Appl. Math. Comput. 175 2006 581 589
21. S. Abbasbandy A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials J. Comput. Appl. Math. 207 2007 59 63
22. G.A. Baker, and P. Graves-Morris Pad Approximants 1996 Cambridge University Press Cambridge