The homotopy perturbation method for solving singular initial value problems

International Journal of Nonlinear Sciences and Numerical Simulation

Volumn 10, Issue 2, 2009, Pages 235-238

  Yildirim, Ahmet ^a   Agirseven, Deniz ^b  

^a EGE UNIVERSITY   (Turkey)

^b TRAKYA UNIVERSITY   (Turkey)

Author keywords

Homotopy perturbation method; Singular initial value problems

Indexed keywords

EID: 65349090342     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2009.10.2.235     Document Type: Article

References (21)

1. S. Chandrasekhar, An Introduction to the Study of Stellar Structure, Dover Publications, New York, 1967.
2. H.T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York, 1967.
3. M. Inc, D.J. Evans, The decomposition method for solving of a class of singular two-point boundary value problems Int. J. Comput. Math. 80 (2003), 869.
4. M. Inc, M. Ergüt, Y, Cherruault, A different approach for solving singular two-point boundary value problems, Kybernetes 34 (2005), 934.
5. A. Aslanov, I.A. Alshaikh, Further developments to the decomposition method for solving singular initial-value problems, Mathematical and Computer Modelling, (2007) (in press)
6. J.H. He, A modified Newton-Raphson method. Communications in Numerical Methods in Engineering, 20(2004), 801-805.
7. J.H. He, Homotopy perturbation technique Computational Methods in Applied Mechanics and Engineering 178( 1999),257-262.
8. J.H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems. Int. J. Nonlin. Mech., 35(2000), 37-43.
9. J.H. He, Homotopy perturbation method: a new nonlinear analytical technique. Appl. Math. Comput., 135(2003), 73-79.
10. J.H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B,20(2006), 1141-1199.
11. J.H. He, New interpretation of homotopy perturbation method, Int. J. Mod. Phys. B 20(2006), 2561-2568.
12. Öziş T, Yildirim A, A note on He's homotopy perturbation method for van der Pol oscillator with very strong nonlinearity. Chaos Soliton. Fract., 34(2007), 989-991.
13. Öziş T, Yildinm A, A comparative study of He's homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities. Int. J. Nonlin. Sci. Num., 8( 2007), 243-248.
14. Öziş T, Yildinm A, Traveling wave solution of Korteweg-de Vries Equation using He's homotopy perturbation method. Int. J. Nonlin. Sci. Num., 8(2007), 239-242.
15. Öziş T, Yildinm A, Determination of periodic solution for a u(l/3) force by He' modified Lindstedt-Poincaré method. J. Sound Vib. 301(2007), 415-419.
16. Yildirim A, Öziş. T, Solutions of Singular IVPs of Lane-Emden type by Homotopy Perturbation Method. Phys.Lett.A 369(2007), 70-76.
17. Yildinm A, Exact Solutions of Nonlinear Differential-difference Equations by He's Homotopy Perturbation Method. Int. J. Nonlin. Sci. Num., 9(2008), 111-114.
18. F. Shakeri, M. Dehghan, Solution of the delay differential equations via homotopy perturbation method, Math.Comput. Model., 48 (2008), 486-498.
19. M. Dehghan, F. Shakeri, Use of He's homotpy perturbation method for solving a partial differential equation arising in modeling of flow in porous media, J.Porous Media, 11 (2008),765-778.
20. M. Tatari, M. Dehghan, The use of the Adomian decomposition method for solving multipoint boundary value problems, Phys. Scripta, 73 (2006), 672-676.
21. A. Saadatmandi, M. Dehghan, A. Eftekhari, Application of He's homotopy perturbation method for non-linear system of second-order boundary value problems, Nonlinear Analysis: Real World Applications, Corrected Proof, Available online 4 March 2008.