Improved homotopy perturbation method for solving Fredholm type integro-differential equations

Chaos, Solitons and Fractals

Volumn 41, Issue 1, 2009, Pages 28-37

 

^a Agadjanov), Elcin   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRODIFFERENTIAL EQUATIONS;

EXACT SOLUTION; FREDHOLM; HOMOTOPY PERTURBATION METHOD (HPM);

PERTURBATION TECHNIQUES;

EID: 67349139225     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.11.005     Document Type: Article

References (39)

1. Liao S. An approximate solution technique not depending on small parameters: a special example. Int J Non-Linear Mech 30 3 (1995) 371-380
2. Liao S., and Tan Y. A general approach to obtain series solutions of nonlinear differential equations. Studies Appl Math 119 (2007) 297-428
3. He J.H. Homotopy perturbation technique. Comput Meth Appl Mech Eng 178 (1999) 257-262
4. He J.H. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int J Non-Linear Mech 35 (2000) 37-43
5. Golbabai A., and Keramati B. Modified homotopy perturbation method for solving Fredholm integral equations. Chaos, Solitons & Fractals 37 (2006) 1528-1537
6. Chun C. Integration using He's homotopy perturbation method. Chaos, Solitons & Fractals 34 (2007) 1130-1134
7. Song Lina, Zhang Hongqing. Application of the extended homotopy perturbation method to a kind of nonlinear evolution equations. Appl Math Comput. doi:10.1016/j.amc.2007.07.035.
8. Feng X., Mei L., and He G. An efficient algorithm for solving Troesch's problem. Appl Math Comput 189 (2007) 500-507
9. Gorji M., Ganji D.D., and Soleimani S. New application of He's Homotopy perturbation method. Int J Nonlinear Sci Numer Simulat 8 (2007) 319-328
10. He J.H. The homtopy perturbation method for nonlinear oscillators with discontinuities. Appl Math Comput 151 (2004) 287-292
11. Cai X.C., Wu W.Y., and Li M.S. Approximate period solution for a kind of non-linear oscillator by He's perturbation method. Int J Nonlinear Sci Numer Simulat 7 (2006) 109-112
12. He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. Int J Nonlinear Sci Numer Simulat 6 (2005) 207-208
13. Cveticanin L. Homotopy-perturbation method for pure nonlinear differential equation. Chaos, Solitons & Fractals 30 (2006) 1221-1230
14. Abbasbandy S. Application of He's homotopy perturbation method for Laplace transform. Chaos, Solitons & Fractals 30 (2006) 1206-1212
15. He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons & Fractals 26 3 (2005) 695-700
16. Wang Q. Homotopy perturbation method for fractional KdV-Burgers equation. Chaos, Solitons & Fractals 35 (2008) 843-847
17. Mei S.-L., Du C.-J., and Zhang S.-W. Asymptotic numerical method for multi-degree-of-freedom nonlinear dynamic systems. Chaos, Solitons & Fractals 35 (2008) 536-542
18. He J.H., Yu Y.P., Yu J.Y., et al. A nonlinear dynamic model for two-strand yarn spinning. Textile Res J 75 (2005) 181-184
19. Mei S.-L., and Zhang S.-W. Coupling technique of variational iteration and homotopy perturbation methods for nonlinear matrix differential equations. Comput Math Appl 54 (2007) 1092-1098
20. He J.H. Homotopy perturbation method for solving boundary value problems. Phys Lett A 350 (2006) 87-88
21. Lan X. He's homotopy perturbation method for a boundary layer equation in unbounded domain. Comput Math Appl 54 (2007) 1067-1070
22. 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 (2007) 770-777
23. Abbasbandy S. Application of He's homotopy perturbation method to functional integral equations. Chaos, Solitons & Fractals 31 (2007) 1243-1247
24. Yusufoǧlu E. A homotopy perturbation algorithm to solve a system of Fredholm-Volterra type integral equations. Math Comput Model, in press. doi:10.1016/j.mcm.2007.06.022.
25. Biazar J., Eslami M., and Ghazvini H. Homotopy perturbation method for systems of partial differential equations. Int J Nonlinear Sci Numer Simulat 8 (2007) 413-418
26. He J.H. Homtopy perturbation method: a new nonlinear analytic technique. Appl Math Comput 135 (2003) 73-79
27. 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
28. 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 Nonlinear Sci Numer Simulat 7 (2006) 7-14
29. Siddiqui A., Ahmed M., and Ghori Q. Couette and Poiseuille flows for non-Newtonian fluids. Int J Nonlinear Sci Numer Simulat 7 (2006) 15-26
30. He J.H. Limit cycle and bifurcation of nonlinear problems. Chaos, Solitons & Fractals 26 (2005) 827-833
31. Feng X., and He Y. High order iterative methods without derivatives for solving nonlinear equations. Appl Math Comput 186 (2007) 1617-1623
32. Yusufoǧlu E. Homotopy perturbation method for solving a nonlinear system of second order boundary value problem. Int J Nonlinear Sci Numer Simulat 8 (2007) 353-358
33. He J.H. Some asymptotic methods for strongly nonlinear equations. Int J Mod Phys B 20 (2006) 1141-1199
34. He JH. Non-perturbative methods for strongly nonlinear problems, Dissertation, de-Verlag im Internet GmbH, Berlin, 2006.
35. Kajani M.T., Ghasemi M., and Babolian E. Comparison between the homotopy perturbation method and the sine-cosine wavelet method for solving linear integro-differential equations. Comput Math Appl 54 (2007) 1162-1166
36. Danfu H., and Xufeng S. Numerical solution of integro-differential equations by using CAS wavelet operational matrix of integration. Appl Math Comput 194 (2007) 460-466
37. Darania P., and Ebadian A. A method for the numerical solution of the integro-differential equations. Appl Math Comput 188 (2007) 657-668
38. Rashidinia J., and Zarebnia M. The numerical solution of integro-differential equation by means of the Sine method. Appl Math Comput 188 (2007) 1124-1130
39. Golbabai A., and Seifollahi S. Radial basis function networks in the numerical solution of linear integro-differential equations. Appl Math Comput 188 (2007) 427-432