×

A homotopy perturbation algorithm to solve a system of Fredholm-Volterra type integral equations. (English) Zbl 1145.45304

Summary: In this paper, an application of He’s homotopy perturbation (HPM) method is applied to solve the system of Fredholm and Volterra type integral equations, the results revealing that the HPM is very effective and simple.

MSC:

45L05 Theoretical approximation of solutions to integral equations
65R20 Numerical methods for integral equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] He, J.H., Homotopy perturbation technique, Comput. methods appl. mech. engrg., 178, 3-4, 257-262, (1999) · Zbl 0956.70017
[2] He, J.H., A coupling method of homotopy technique and perturbation technique for nonlinear problems, Internat. J. non-linear mech., 35, 1, 37-43, (2000) · Zbl 1068.74618
[3] He, J.H., Homotopy perturbation method: A new nonlinear analytical technique, Appl. math. comput., 135, 73-79, (2003) · Zbl 1030.34013
[4] He, J.H., Comparison of homotopy perturbation method and homotopy analysis method, Appl. math. comput., 156, 527-539, (2004) · Zbl 1062.65074
[5] He, J.H., Variational principles for some nonlinear partial differential equations with variable coefficients, Chaos solitons fractals, 19, 4, 847-851, (2005) · Zbl 1135.35303
[6] Liu, H.M., Variational approach to nonlinear electrochemical system, Chaos solitons fractals, 23, 2, 573-576, (2005)
[7] He, J.H., Variational iteration method: A kind of nonlinear analytical technique: some examples, Internat. J. non-linear mech., 34, 4, 699-708, (1999) · Zbl 1342.34005
[8] He, J.H., Application of homotopy perturbation method to nonlinear wave equations, Chaos solitons fractals, 26, 695-700, (2005) · Zbl 1072.35502
[9] He, J.H., Some asymptotic methods for strongly nonlinear equations, Internat. J. modern phys., B 20, 1141-1199, (2006) · Zbl 1102.34039
[10] He, J.H., A review on some new recently developed nonlinear analytical techniques, Int. J. nonlinear sci. numer. simul., 1, 1, 51-70, (2000) · Zbl 0966.65056
[11] Abbasbandy, S., Numerical solutions of the integral equations: homotopy perturbation method and adomian’s decomposition method, Appl. math. comput., 173, 2-3, 493-500, (2006) · Zbl 1090.65143
[12] Abbasbandy, S., Application of he’s homotopy perturbation method to functional integral equations, Chaos solitons fractals, 31, 5, 1243-1247, (2007) · Zbl 1139.65085
[13] Abbasbandy, S., Application of he’s homotopy perturbation method for Laplace transform, Chaos solitons fractals, 30, 1206-1212, (2006) · Zbl 1142.65417
[14] Ghasemi, M.; Tavassoli Kajani, M.; Babolian, E., Numerical solutions of the nonlinear integro-differential equations: wavelet – galerkin method and homotopy perturbation method, Appl. math. comput., 188, 450-455, (2007) · Zbl 1114.65368
[15] Ghasemi, M.; Tavassoli Kajani, M.; Babolian, E., Numerical solutions of the nonlinear volterra – fredholm integral equations by using homotopy perturbation method, Appl. math. comput., 188, 446-449, (2007) · Zbl 1114.65367
[16] Ghasemi, M.; Tavassoli Kajani, M.; Babolian, E., Application of he’s homotopy perturbation method to nonlinear integro-differential equations, Appl. math. comput., 188, 538-548, (2007) · Zbl 1118.65394
[17] He, J.H., The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl. math. comput., 151, 287-292, (2004) · Zbl 1039.65052
[18] Delves, L.M.; Mohamed, J.L., Computational methods for integral equations, (1985), Cambridge University Press · Zbl 0592.65093
[19] Nayfeh, A.H., Introduction to perturbation technique, (1981), John Wiley and Sons New York
[20] Liao, S.J., An approximate solution technique not depending on small parameter: A special example, Internat. J. non-linear mech., 30, 3, 371-380, (1995) · Zbl 0837.76073
[21] Babolian, E.; Biazar, J.; Vahidi, A.R., The decomposition method applied to systems of Fredholm integral equations of the second kind, Appl. math. comput., 148, 443-452, (2004) · Zbl 1042.65104
[22] Biazar, J.; Babolian, E.; Islam, R., Solution of a system of Volterra integral equations of the first kind by Adomian method, Appl. math. comput., 139, 249-258, (2003) · Zbl 1027.65180
[23] Maleknejad, K.; Shahrezaee, M., Using runge – kutta method for numerical solution of the system of Volterra integral equation, Appl. math. comput., 149, 399-410, (2004) · Zbl 1038.65148
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.