Solution of an integro-differential equation arising in oscillating magnetic fields using he's homotopy perturbation method

Progress in Electromagnetics Research

Volumn 78, Issue , 2008, Pages 361-376

  Dehghan, M ^a   Shakeri, F ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

CHARGED PARTICLES; MAGNETIC FIELDS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

HOMOTOPY PERTURBATION METHOD; IMBEDDING PARAMETER;

INTEGRODIFFERENTIAL EQUATIONS;

EID: 38149090283     PISSN: 10704698     EISSN: 15598985     Source Type: Journal    
DOI: 10.2528/PIER07090403     Document Type: Article

References (45)

1. Abbasbandy, S., "A numerical solution of Blasius equation by Adomianís decomposition method and comparison with homotopy perturbation method," Chaos, Solitons and Fractals, Vol. 31, 257-260, 2007.
2. Abbasbandy, S., "Application of He's homotopy perturbation method to functional integral equations," Chaos, Solitons and Fractals, Vol. 31, 1243-1247, 2007.
3. Ariel, P D., "The three-dimensional flow past a stretching sheet and the homotopy perturbation method," Comput Math. Applic., 2006.
4. Beléndez, A., T. Beléndez, A. Márquez, and C. Neipp, "Application of He's homotopy perturbation method to conservative truly nonlinear oscillators," Chaos, Solitons and Fractals, 2006.
5. Cai, X.-C. and M.-S. Li, "Periodic solution of Jacobi elliptic equations by He's perturbation method," Computers and Mathematics with Applications, 2006.
6. Chowdhury, M. S. H. and I. Hashim, "Application of homotopy perturbation method to Klein-Gordon and sine-Gordon equations," Chaos, Solitons and Fractals, 2007.
7. Chowdhury, M. S. H., I. Hashim, and O. Abdulaziz, "Application of homotopy perturbation method to nonlinear population dynamics models," Physics Letters A, Vol. 368, 251-258, 2007.
8. Chowdhury, M. S. H. and I. Hashim, "Solutions of time-dependent Emden-Fowler type equations by homotopy perturbation method," Physics Letters A, Vol. 368, 305-313, 2007.
9. Chun, C. and Y. Ham, "Newton-like iteration methods for solving non-linear equations," Commun. Numer. Meth. Engng., Vol. 22, 475-487, 2006.
10. Chun, C., "Integration using He's homotopy perturbation method," Chaos, Solitons and Fractals, Vol. 34, 1130-1134, 2007.
11. Cveticanin, L., "Homotopy perturbation method for pure nonlinear differential equation," Chaos, Solitons and Fractals, Vol. 30, 1221-1230, 2006.
12. Ganji, D. D. and M. Rafei, "Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method," Physics Letters A, Vol. 356, 131-137, 2006.
13. Ganji, D. D. and A. Sadighi, "Application of homotopyperturbation and variational iteration methods to nonlinear heat transfer and porous media equations," Journal of Computational and Applied Mathematics, Vol. 207, 24-32, 2007.
14. Golbabai, A. and B. Keramati, "Solution of non-linear Fredholm integral equations of the first kind using modified homotopy perturbation method," Chaos, Solitons and Fractals, 2007.
15. Hashim, I. and M. S. H. Chowdhury, "Adaptation of homotopy-perturbation method for numeric analytic solution of system of ODEs," Physics Letters A, 2007.
16. He, J. H., "Homotopy perturbation technique," Comput. Methods Appl. Mech. Eng., Vol. 178, 257-262, 1999.
17. He, J. H., "A coupling method of a homotopy technique and a perturbation technique for non-linear problems," Inter. J. Non-linear Mech., Vol. 35, 37-43, 2000.
18. He, J. H., "Homotopy perturbation method: a new nonlinear analytical technique," Appl. Math. Comput., Vol. 135, 73-79, 2003.
19. He, J. H., "The homotopy perturbation method for nonlinear oscillators with discontinuities," Applied Mathematics and Computation, Vol. 151, 287-292, 2004.
20. He, J. H., "Homotopy perturbatin method for nonlinear bifurcation problems," Int. J. Nonlinear Sei. Numer. Simul., Vol. 6, No. 2, 207-208, 2005.
21. He, J. H., "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons and Fractals, Vol. 26 695-700, 2005.
22. He, J. H., "Homotopy perturbation method for solving boundary value problems," Physics Letters A, Vol. 350, 87-88, 2006.
23. Machado, J. M. and M. Tsuchida, "Solutions for a class of integro-differential equations with time periodic coefficients," Appl. Math. E-Notes, Vol. 2, 66-71, 2002.
24. Mei, S. L. and S. W. Zhang, "Coupling technique of variational iteration and homotopy perturbation methods for nonlinear matrix differential equations," Computers and Mathematics with Applications, 2007.
25. Rafei, M., D. D. Ganji, and H. Daniali, "Solution of the epidemic model by homotopy perturbation method," Applied Mathematics and Computation, In press.
26. Rajabi, A., "Homotopy perturbation method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity," Physics Letters A, Vol. 187, 1056-1062, 2007.
27. Ramos, J. I., "Series approach to the Lane-Emden equation and comparison with the homotopy perturbation method," Chaos, Solitons and Fractals, 2006.
28. Shakeri, F. and M. Dehghan, "Inverse problem of diffusion equation by He's homotopy perturbation method," Phys. Scr., Vol. 75, 551-556, 2007.
29. Siddiqui, A. M., A. Zeb, Q. K. Ghori, and A. M. Benharbit, "Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates," Chaos, Solitons and Fractals, 2006.
30. Song, L. and H. Zhang, "Application of the extended homotopy perturbation method to a kind of nonlinear evolution equations," Appl. Maths. and Computation, 2007.
31. Ozis, T. and A. Yildirim, "A note on He's homotopy perturbation method for van der Pol oscillator with very strong nonlinearity," Chaos, Solitons and Fractals, Vol. 34, 989-999, 2007.
32. Wang, Q., "Homotopy perturbation method for fractional KdV-Burgers equation," Chaos, Solitons and Fractals, 2006
33. Yildirim, A. and T. Ozis, "Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method," Physics Letters A, Vol. 369, 70-76, 2007.
34. Yusufoglu, E., "A homotopy perturbation algorithm to solve a system of Fredholm-Volterra type integral equations," Math. Comput. Model., 2007.
35. Chatterjee, K. and J. Poggie, "A parallelized floating random-walk algorithm for the solution of the nonlinear PoissonBoltzman equation," Progress In Electromagnetics Research, PIER 57, 237-252, 2006.
36. Chiang, I. T. and W. C. Chew, "New formulation ans iterative solution for low-frequency volume integral equation," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 3, 289-306, 2005.
37. Çinar, G. and A. Büyükaksoy, "A hybrid method for the solution of plane wave diffraction by an impedance loaded parallel plate waveguide," Progress In Electromagnetics Research, PIER 60, 293-310, 2006.
38. Saadatmandi, A., M. Razzaghi, and M. Dehghan, "Sinccollocation methods for the solution of Hallen's integral equation," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 2, 245-256, 2005.
39. Ojeda, X. and L. Pichon, "Combining the finit element method and a Padé approximation for scattering analysis, application to radiated electromagnetic compatibility problems," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 10, 1375-1390, 2005.
40. Khalaj-Amirhosseini, M., "Analysis of lossy inhomogeneous planar layers using finite difference method," Progress In Electromagnetics Research, PIER 59, 187-198, 2006.
41. Watanabe, K. and K. Kuto, "Numerical analysis of optical waveguides based on periodic fourier transform," Progress In Electromagnetics Research, PIER 64, 1-21, 2006.
42. Shi, Y. and C.-H. Liang, "Analysis of the double-negative materials using multi-domain pseudospectral time-domain algorithm," Progress In Electromagnetics Research, PIER 51, 153-165, 2005.
43. Tong, M. S., Y. Lu, Y. Chen, H. S. Kim, T. G. Chang, K. Kagoshima, and V. Krozer, "Study of stratified dielectric slab medium structures using pseudo-spectral time domain (PSTD) algorithm," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 6, 721-736, 2005.
44. Zhao, J. X., "Numerical and analytical formulizations of the extended Mie theory for solving the sphere scattering problem," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 7, 967-983, 2006.
45. Mouysset, V., P A. Mazet, and P Borderies, "A new approach to evaluate accurately and efficiently electromagnetic fields outside a bounded zone with time-domain volumic methods," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 6, 803-817, 2006.