An efficient method for quadratic Riccati differential equation

Communications in Nonlinear Science and Numerical Simulation

Volumn 15, Issue 4, 2010, Pages 835-839

  Aminikhah, Hossein ^a   Hemmatnezhad, Milad ^b  

^a SHAHROOD UNIVERSITY OF TECHNOLOGY   (Iran)

^b UNIVERSITY OF GUILAN   (Iran)

Author keywords

NHPM; Nonlinear equations; Riccati equation; Taylor series expansion

Indexed keywords

PERTURBATION TECHNIQUES; RICCATI EQUATIONS; TAYLOR SERIES;

EXACT SOLUTION; HOMOTOPIES; NEW FORM OF HOMOTOPY PERTURBATION METHOD; NEW FORMS; PERTURBATION METHOD; RICCATI DIFFERENTIAL EQUATION; TAYLOR'S SERIES EXPANSION;

NONLINEAR EQUATIONS;

EID: 70350354972     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.05.009     Document Type: Article

References (31)

1. Liao SJ. The proposed homotopy analysis technique for the solution of nonlinear problems. PhD Thesis. Shanghai Jiao Tong University; 1992.
2. Liao S.J. An explicit, totally analytic approximation of Blasius viscous flow problems. Int J Non-linear Mech 34 (1999) 759-778
3. Liao S.J. On the homotopy analysis method for nonlinear problems. Appl Math Comput 147 (2004) 499-513
4. Liao S.J. Series solutions of unsteady boundary-layer flows over a stretching flat plate. Stud Appl Math 117 (2006) 2529-2539
5. Liao S. Notes on the homotopy analysis method: some definitions and theorems. Commun Nonlinear Sci Numer Simul 14 4 (2009) 983-997
6. Liao S. Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method. Nonlinear Anal Real World Appl 10 4 (2009) 2455-2470
7. He J.H. Homotopy perturbation technique. Comput Meth Appl Mech Eng 178 (1999) 257-262
8. He J.H. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int J Non-linear Mech 35 1 (2000) 37-43
9. He J.H. New interpretation of homotopy perturbation method. Int J Mod Phys B 20 (2006) 2561-2568
10. He J.H. Recent development of homotopy perturbation method. Topol Meth Nonlinear Anal 31 (2008) 205-209
11. He J.H. The homotopy perturbation method for nonlinear oscillators with discontinuities. Appl Math Comput 151 (2004) 287-292
12. He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos Soliton Fract 26 (2005) 695-700
13. He J.H. Limit cycle and bifurcation of nonlinear problems. Chaos Soliton Fract 26 3 (2005) 827-833
14. Rajabi A., and Ganji D.D. Application of homotopy perturbation method in nonlinear heat conduction and convection equations. Phys Lett A 360 (2007) 570-573
15. Ganji D.D., and Sadighi A. Application of homotopy perturbation and variational iteration methods to nonlinear heat transfer and porous media equations. J Comput Appl Math 207 (2007) 24-34
16. Ganji D.D. The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer. Phys Lett A 355 (2006) 337-341
17. Abbasbandy S. A numerical solution of Blasius equation by Adomian's decomposition method and comparison with homotopy perturbation method. Chaos Soliton Fract 31 (2007) 257-260
18. Biazar J., and Ghazvini H. Exact solutions for nonlinear Schrödinger equations by He's homotopy perturbation method. Phys Lett A 366 (2007) 79-84
19. Abbasbandy S. Numerical solutions of the integral equations: homotopy perturbation and Adomian's decomposition method. Appl Math Comput 173 (2006) 493-500
20. He J.H. Homotopy perturbation method for solving boundary value problems. Phys Lett A 350 (2006) 87-88
21. Cveticanin L. Homotopy-perturbation method for pure nonlinear differential equation. Chaos Soliton Fract 30 (2006) 1221-1230
22. Siddiqui A.M., Zeb A., Ghori Q.K., and Benharbit A.M. Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates. Chaos Soliton Fract 36 1 (2008) 182-192
23. Wang Q. Homotopy perturbation method for fractional KdV-Burgers equation. Chaos Soliton Fract 35 5 (2008) 843-850
24. Siddiqui A.M., Zeb A., and Ghori Q.K. Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane. Chaos Soliton Fract 35 1 (2008) 140-147
25. Turgut O., and Ahmet Y. A note on He's homotopy perturbation method for van der Pol oscillator with very strong nonlinearity. Chaos Soliton Fract 34 3 (2007) 989-991
26. Siddiqui A.M., Zeb A., and Ghori Q.K. Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder. Phys Lett A 352 (2006) 404-410
27. Yusufoglu E. Homotopy perturbation method for solving a nonlinear system of second order boundary value problems. Int J Nonlinear Sci Numer Simul 8 (2007) 353-358
28. Abbasbandy S. Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method. Appl Math Comput 172 (2006) 485-490
29. Abbasbandy S. Iterated He's homotopy perturbation method for quadratic Riccati differential equation. Appl Math Comput 175 (2006) 581-589
30. Tan Y., and Abbasbany S. Homotopy analysis method for quadratic Riccati differential equation. Commun Nonlinear Sci Numer Simul 13 (2008) 539-546
31. Abbasbandy S. A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials. J Comput Appl Math 207 1 (2007) 59-163