Solutions of Emden-Fowler equations by homotopy-perturbation method

Nonlinear Analysis: Real World Applications

Volumn 10, Issue 1, 2009, Pages 104-115

  Chowdhury, M S H ^a   Hashim, I ^a  

^a UNIVERSITI KEBANGSAAN MALAYSIA   (Malaysia)

Author keywords

Emden Fowler equations; Homotopy perturbation method; Lane Emden equation

Indexed keywords

DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); PERTURBATION TECHNIQUES;

EMDEN-FOWLER EQUATIONS; HOMOTOPY-PERTURBATION METHOD; LANE-EMDEN EQUATION; PERTURBATION METHODS;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 50349099602     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2007.08.017     Document Type: Article

References (40)

1. Chandrasekhar S. Introduction to the Study of Stellar Structure (1967), Dover, New York
2. Davis H.T. Introduction to Nonlinear Differential and Integral Equations (1962), Dover, New York
3. O.U. Richardson, The Emission of Electricity from Hot Bodies, London, 1921
4. Shawagfeh N.T. Nonperturbative approximate solution for Lane-Emden equation. J. Math. Phys. 34 9 (1993) 4364-4369
5. Wazwaz A.M. A new algorithm for solving differential equations of Lane-Emden type. Appl. Math. Comput. 118 (2001) 287-310
6. Wazwaz A.M. The numerical solution of special fourth-order boundary value problems by the modified decomposition method. Int. J. Comput. Math. 118 (2002) 345-356
7. Wazwaz A.M. The modified decomposition method for analytic treatment of differential equations. Appl. Math. Comput. 173 (2006) 165-176
8. Adomian G. Solution of physical problems by decomposition. Comput. Math. Appl. 27 (1994) 145-154
9. Wazwaz A.M. Adomian decomposition method for a reliable treatment of the Emden-Fowler equation. Appl. Math. Comput. 161 (2005) 543-560
10. Wazwaz A.M. Analytical solution for the time-dependent Emden-Fowler type of equations by Adomian decomposition method. Appl. Math. Comput. 166 (2005) 638-651
11. He J.H. Approximate analytical solution of Blasius' equation. Commum. Nonlinear Sci. Numer. Simul. 3 (1998) 260-263
12. He J.H. Comparison of homotopy perturbation method and homotopy analysis method. Appl. Math. Comput. 156 (2004) 527-539
13. He J.H. Variational iteration method-a kind of non-linear analytical technique: Some examples. Internat. J. Non-Linear Mech. 34 (1999) 699-708
14. He J.H. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Internat. J. Non-Linear Mech. 35 1 (2000) 37-43
15. He J.H. A simple perturbation approach to Blasius equation. Appl. Math. Comput. 140 (2003) 217-222
16. Ablowitz M.J., Herbst B.M., and Schober C. Homotopy perturbation method and axisymmetric flow over a stretching sheet. Int. J. Nonlinear Sci. Numer. Simul. 7 4 (2006) 399-406
17. Cveticanin L. The homotopy-perturbation method applied for solving complex-valued differential equations with strong cubic nonlinearity. J. Sound Vibration 285 (2005) 1171-1179
18. Ganji D.D., and Rajabi A. Assessment of homotopy-perturbation and perturbation methods in heat radiation equations. Int. Commun. Heat Mass Transfer 33 (2006) 391-400
19. Noor M.A., and Mohyud-Din S.T. An efficient algorithm for solving fifth-order boundary value problems. Mathl. Comput. Model. 45 7-8 (2007) 954-964
20. Mo J.Q., and Lin W.T. A variational iteration method for solving El Nino mechanism of atmospheric physics. Acta Phys. Sinica 54 (2005) 1081-1083
21. D.D. Ganji, A. Sadighi, Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations, J. Comput. Appl. Math. doi:10.1016/j.cam.2006.07.030
22. Chowdhury M.S.H., and Hashim I. Solutions of a class of singular second-order IVPs by homotopy-perturbation method. Phys. Lett. A 365 (2007) 439-447
23. Chowdhury M.S.H., Hashim I., and Abdulaziz O. Application of homotopy-perturbation method to nonlinear population dynamics models. Phys. Lett. A 368 (2007) 251-258
24. M.S.H. Chowdhury, I. Hashim, Application of homotopy-perturbation method to Klein-Gordon and sine-Gordon equations, Chaos Solitons Fractals, doi:10.1016/j.chaos.2007.06.091
25. Z. Odibat, S. Momani, Modified homotopy perturbation method: Application to quadratic riccati differential equation of fractional order, Chaos Solitons Fractals, doi:10.1016/j.chaos.2006.06.041
26. S. Momani, Z. Odibat, Homotopy perturbation method for nonlinear partial differential equations of fractional order, Phys. Lett. A, doi:10.1016/j.physleta.2007.01.046
27. Momani S., and Odibat Z. Homotopy perturbation method for nonlinear partial differential equations of fractional order. Phys. Lett. A 365 (2007) 345-350
28. S. Momani, Z. Odibat, Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations, Comput. Math. Appl. (2007), in press (doi:10.1016/j.camwa.2006.12.037)
29. He J.H. Some asymptotic methods for strongly nonlinear equations. Internat. J. Modern Phys. B 20 (2006) 1141-1199
30. El-Shaded M. Application of He's homotopy perturbation method to Volterra's integro-differential equation. Int. J. Non-linear Sci. Numer. Simul. 6 2 (2005) 163-168
31. Siddiqui A., Mahmood R., and Ghori Q. Thin film flow of a third grade fluid on moving a belt by He's homotopy perturbation method. Int. J. Non-linear Sci. Numer. Simul. 7 1 (2006) 15-26
32. He J.H. New interpretation of homotopy perturbation method. Internat. J. Modern Phys. B 20 (2006) 2561-2568
33. Belendez A., Hernandez A., Belendez T., Fernandez E., Alvarez M.L., and Neipp C. Application of He's homotopy perturbation method to the Duffing-Harmonic oscillator. Int. J. Non-linear Sci. Numer. Simul. 8 1 (2007) 79-88
34. Ganji D.D., and Sadighi A. Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations. Int. J. Non-linear Sci. Numer. Simul. 7 4 (2006) 411-418
35. Belendez A., Hernandez A., Belendez T., Neipp C., and Marquez A. Application of the homotopy perturbation method to the nonlinear pendulum. Eur. J. Phys. 28 (2007) 93-104
36. Cveticanin L. Homotopy-perturbation method for pure nonlinear differential equation. Chaos Solitons Fractals 30 (2006) 1221-1230
37. Ozis T., and Yildirum A. A comparative study of He's homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities. Int. J. Non-linear Sci. Numer. Simul. 8 2 (2007) 243-248
38. M.S.H. Chowdhury, I. Hashim, Solutions of time-dependent Emden-Fowler type equations by homotopy-perturbation method,Phys. Lett. A, doi:10.1016/j.physleta.2007.04.020
39. He J.H. Non-Perturbative Methods for Strongly Nonlinear Problems (2006), Die Deutsche bibliothek, Germany
40. Ramos J.I. Linearization techniques for singular initial-value problems of ordinary differential equations. Appl. Math. Comput. 161 (2005) 525-542