A piecewise variational iteration method for Riccati differential equations

Computers and Mathematics with Applications

Volumn 58, Issue 11-12, 2009, Pages 2518-2522

  Geng, Fazhan ^a,b   Lin, Yingzhen ^a   Cui, Minggen ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b CHANGSHU INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Modified variational iteration method; Piecewise variational iteration method; Riccati differential equation

Indexed keywords

INITIAL POSITION; MODIFIED VARIATIONAL ITERATION METHOD; NUMERICAL EXAMPLE; NUMERICAL RESULTS; PIECE-WISE; PIECEWISE VARIATIONAL ITERATION METHOD; RICCATI DIFFERENTIAL EQUATION; VARIATIONAL ITERATION METHOD;

OSCILLATORS (MECHANICAL); RICCATI EQUATIONS;

ITERATIVE METHODS;

EID: 70350566613     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.03.063     Document Type: Article

References (26)

1. Reid W.T. Riccati Differential Equations (1972), Academic Press, New York
2. Carinena J.F., Marmo G., Perelomov A.M., and Ranada M.F. Related operators and exact solutions of Schrodinger equations. International Journal of Modern Physics A 13 (1998) 4913-4929
3. Scott M.R. Invariant Imbedding and its Applications to Ordinary Differential Equations (1973), Addison-Wesley
4. El-Tawil M.A., Bahnasawi A.A., and Abdel-Naby A. Solving Riccati differential equation using Adomians decomposition method. Applied Mathematics and Computation 157 (2004) 503-514
5. Abbasbandy S. Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomians decomposition method. Applied Mathematics and Computation 172 (2006) 485-490
6. Abbasbandy S. A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials. Journal of Computational and Applied Mathematics 207 (2007) 59-63
7. Abbasbandy S. Iterated He's homotopy perturbation method for quadratic Riccati differential equation. Applied Mathematics and Computation 175 (2006) 581-589
8. He J.H. Variational iteration method-A kind of nonlinear analytical technique: Some examples. International Journal of Non-Linear Mechanics 34 (1999) 699-708
9. He J.H. Variational iteration method for autonomous ordinary differential system. Applied Mathematics and Computation 114 (2000) 115-123
10. He J.H. Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B 20 (2006) 1141-1199
11. He J.H., and Wu X.H. Construction of solitary solution and compaction-like solution by variational iteration method. Chaos, Solitons and Fractals 29 (2006) 108-113
12. He J.H., and Wu X.H. Variational iteration method: New development and applications. Computers and Mathematics with Applications 54 (2007) 881-894
13. He J.H. Variational iteration method-Some recent results and new interpretations. Journal of Computational and Applied Mathematics 207 (2007) 3-17
14. Lu J.F. Variational iteration method for solving two-point boundary value problems. Journal of Computational and Applied Mathematics 207 (2007) 92-95
15. Xu L. The variational iteration method for fourth order boundary value problems. Chaos, Solitons and Fractals (2007) 10.1016/j.chaos.2007.06.013
16. Assas L.M.B. Variational iteration method for solving coupled-kdv equations. Chaos, Solitons and Fractals (2007) 10.1016/j.chaos.2007.02.012
17. Soliman A.A., and Abdou M.A. Numerical solutions of nonlinear evolution equations using variational iteration method. Journal of Computational and Applied Mathematics 207 (2007) 111-120
18. Abdou M.A., and Soliman A.A. Variational iteration method for solving Burger's and coupled Burger's equations. Journal of Computational and Applied Mathematics 181 (2005) 245-251
19. Ganji D.D., and Sadighi A. Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations. International Journal of Nonlinear Sciences and Numerical Simulation 7 4 (2006) 411-418
20. Odibat Z.M., and Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. International Journal of Nonlinear Sciences and Numerical Simulation 7 (2006) 27-34
21. Shou D.H., and He J.H. Application of parameter-expanding method to strongly nonlinear oscillators. International Journal of Nonlinear Sciences and Numerical Simulation 8 1 (2007) 121-124
22. Bildik N., and Konuralp A. The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations. International Journal of Nonlinear Sciences and Numerical Simulation 7 1 (2006) 65-70
23. Tatari M., and Dehghan M. On the convergence of He's variational iteration method. Journal of Computational and Applied Mathematics 207 (2007) 121-128
24. J. Biazar, H. Ghazvini, He's variational iteration method for solving hyperbolic differential equations, International Journal of Nonlinear Sciences and Numerical Simulation, 8 (3) 311-314
25. H. Ozer, Application of the variational iteration method to the boundary value problems with jump discontinuities arising in solid mechanics, International Journal of Nonlinear Sciences and Numerical Simulation, 8 (4) 513-518
26. Yusufoglu E. Variational iteration method for construction of some compact and noncompact structures of Klein-Gordon equations. International Journal of Nonlinear Sciences and Numerical Simulation 8 2 (2007) 153-158