Homotopy perturbation method for the mixed Volterra-Fredholm integral equations

Chaos, Solitons and Fractals

Volumn 42, Issue 5, 2009, Pages 2760-2764

  Yildirim, Ahmet ^a  

^a EGE UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

NONLINEAR EQUATIONS; NUMERICAL METHODS; PERTURBATION TECHNIQUES;

EXACT SOLUTION; HOMOTOPY PERTURBATION METHOD (HPM); MIXED VOLTERRA-FREDHOLM INTEGRAL EQUATIONS; NOISE TERMS; NONLINEAR MIXED VOLTERRA-FREDHOLM INTEGRAL EQUATIONS;

INTEGRAL EQUATIONS;

EID: 67651208845     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2009.03.147     Document Type: Article

References (35)

1. Dickman O. Thresholds and traveling waves for the geographical spread of infection. J Math Biol 6 (1978) 109-130
2. Pachpatta B.G. On mixed Volterra-Fredholm type integral equations. Ind J Pure Appl Math 17 (1986) 488-496
3. Hacia L. On approximate solution for integral equations of mixed type. ZAMM Z Angew Math Mech 76 (1996) 415-416
4. Kauthen P.J. Continuous time collocation methods for Volterra-Fredholm integral equations. Numer Math 56 (1989) 409-424
5. Thieme H.R. A model for the spatio spread of an epidemic. J Math Biol 4 (1977) 337
6. Guoqiang H., and Liqing Z. Asymptotic expansion for the trapezoidal Nystrom method of linear Volterra-Fredholm equations. J Comput Appl Math 51 (1994) 339-348
7. Brunner H. On the numerical solution of nonlinear Volterra-Fredholm integral equation by collocation methods. SIAM J Numer Anal 27 (1990) 987-1000
8. Guoqiang H. Asymptotic error expansion for the Nystrom method for a nonlinear Volterra-Fredholm equations. J Comput Appl Math 59 (1995) 49
9. Maleknejad K., and Hadizadeh M. A new computational method for Volterra-Fredholm integral equations. J Comput Appl Math 37 (1999) 1-8
10. Wazwaz A.M. A reliable treatment for mixed Volterra-Fredholm integral equations. Appl Math Comput 127 (2002) 405-414
11. Banifatemi E., Razzaghi M., and Yousefi S. Two-dimensional Legendre Wavelets Method for the mixed Volterra-Fredholm integral equations. J Vibr Control 13 (2007) 1667-1675
12. He J.H. The homotopy perturbation method for nonlinear oscillators with discontinuities. Appl Math Comput 151 (2004) 287-292
13. He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons & Fractals 26 (2005) 695-700
14. He J.H. Homotopy perturbation method for bifurcation of nonlinear Problems. Int J Nonlin Sci Numer Simul 6 (2005) 207-208
15. He J.H. Homotopy perturbation method for solving boundary value problems. Phys Lett A 350 (2006) 87-88
16. He J.H. Homotopy perturbation technique. Comput Methods Appl Mech Eng 178 (1999) 257-262
17. He J.H. A coupling method of a homotopy technique and a perturbation technique for non-linear problems. Int J Nonlin Mech 35 (2000) 37-43
18. He J.H. Homotopy perturbation method: a new nonlinear analytical technique. Appl Math Comput 135 (2003) 73-79
19. Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m A. A note on He's homotopy perturbation method for van der Pol oscillator with very strong nonlinearity. Chaos, Solitons & Fractals 34 (2007) 989-991
20. Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m 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 Numer Simul 8 (2007) 243-248
21. Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m A. Traveling wave solution of Korteweg-de Vries equation using He's homotopy perturbation method. Int J Nonlin Sci Numer Simul 8 (2007) 239-242
22. Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m A. Determination of periodic solution for a u(1/3) force by He' modified Lindstedt-Poincaré method. J Sound Vibr 301 (2007) 415-419
23. Yi{dotless}ldi{dotless}ri{dotless}m A., and Öziş T. Solutions of singular IVPs of Lane-Emden type by Homotopy Perturbation Method. Phys Lett A 369 (2007) 70-76
24. Shakeri F., and Dehghan M. Solution of delay equations via a homotopy perturbation Method. Math Comput Model 48 (2008) 486-498
25. Abdulaziz O., Hashim I., and Chowdhury M.S.H. Solving variational problems by homotopy-perturbation method. Inter J Numer Methods Eng 75 (2008) 709-721
26. Miansari M., Ganji D.D., and Miansari M. Jacobi elliptic function solutions of the (1+1)-dimensional dispersive long wave equation by Homotopy Perturbation Method. Numer Methods Partial Differ Eq 24 (2008) 1361-1370
27. Beléndez A., Pascual C., Beléndez T., and Hernández A. Solution for an anti-symmetric quadratic nonlinear oscillator by a modified He's homotopy perturbation method. Nonlin Anal: Real World Appl 10 (2009) 416-427
28. Chowdhury M.S.H., and Hashim I. Application of multistage homotopy-perturbation method for the solutions of the Chen system. Nonlin Anal: Real World Appl 10 (2009) 381-391
29. Golbabai A., and Keramati B. Easy computational approach to solution of system of linear Fredholm integral equations. Chaos, Solitons & Fractals 38 2 (2008) 568-574
30. Golbabai A., and Keramati B. Modified homotopy perturbation method for solving Fredholm integral equations. Chaos, Solitons & Fractals 37 5 (2008) 1528-1537
31. Javidi M, Golbabai A. Modified homotopy perturbation method for solving non-linear Fredholm integral equations. Chaos, Solitons & Fractals. doi:10.1016/j.chaos.2007.09.026.
32. Biazar J., and Ghazvini H. He's homotopy perturbation method for solving systems of Volterra integral equations of the second kind. Chaos, Solitons & Fractals 39 (2009) 770-777
33. Golbabai A., and Keramati B. Solution of non-linear Fredholm integral equations of the first kind using modified homotopy perturbation method. Chaos, Solitons & Fractals 39 (2009) 2316-2321
34. Yi{dotless}ldi{dotless}ri{dotless}m A. Solution of BVPs for fourth-order integro-differential equations by using Homotopy Perturbation Method. Comput Math Appl 56 12 (2008) 3175-3180
35. Abdulaziz O., Hashim I., and Momani S. Application of homotopy-perturbation method to fractional IVPs. J Comput Appl Math 216 (2008) 574-584