Yusufoğlu, Elcin An efficient algorithm for solving integro-differential equations system. (English) Zbl 1193.65234 Appl. Math. Comput. 192, No. 1, 51-55 (2007). Summary: An application of He’s homotopy perturbation (HPM) method is applied to solve of system of integro-differential equations. The results reveal that the HPM is very effective and simple. Cited in 18 Documents MSC: 65R99 Numerical methods for integral equations, integral transforms 45J05 Integro-ordinary differential equations Keywords:homotopy perturbation method; system of integro-differential equations PDF BibTeX XML Cite \textit{E. Yusufoğlu}, Appl. Math. Comput. 192, No. 1, 51--55 (2007; Zbl 1193.65234) Full Text: DOI References: [1] He, J. H., Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng., 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, Int. 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., Variational principles for some nonlinear partial differential equations with variable coefficients, Chaos Solitons Fract., 19, 4, 847-851 (2005) · Zbl 1135.35303 [5] Liu, H. M., Variational approach to nonlinear electrochemical system, Chaos Solitons Fract., 23, 2, 573-576 (2005) [6] He, J. H., Variational iteration method: a kind of nonlinear analytical technique: some examples, Int. J. Non-linear Mech., 34, 4, 699-708 (1999) · Zbl 1342.34005 [7] He, J. H., Some asymptotic methods for strongly nonlinear equations, Int. J. Moder. Phys. B, 20, 1141-1199 (2006) · Zbl 1102.34039 [8] 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 [9] He, J. H., Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fract., 26, 695-700 (2005) · Zbl 1072.35502 [10] He, J. H., Comparison of homotopy perturbation method and homotopy analysis method, Appl. Math. Comput., 156, 527-539 (2004) · Zbl 1062.65074 [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 for Laplace transform, Chaos Solitons Fract., 30, 1206-1212 (2006) · Zbl 1142.65417 [13] Abbasbandy, S., Application of He’s homotopy perturbation method to functional integral equations, Chaos Solitons Fract., 31, 5, 1243-1247 (2007) · Zbl 1139.65085 [17] Noor, Muhammad Aslam; Mohyud-Din, Syed Tauseef, An efficient algorithm for solving fifth-order boundary value problems, Math. Comput. Model., 45, 7-8, 954-964 (2007) · Zbl 1133.65052 [18] He, J. H., The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl. Math. Comput., 151, 287-292 (2004) · Zbl 1039.65052 [19] Delves, L. M.; Mohamed, J. L., Computational Methods for Integral Equations (1985), Cambridge University Press · Zbl 0592.65093 [20] Nayfeh, A. H., Introduction to Perturbation Technique (1981), John Wiley and Sons: John Wiley and Sons New York [21] Liao, S. J., An approximate solution technique not depending on small parameter: a special example, Int. J. Nonlinear Mech., 30, 3, 371-380 (1995) · Zbl 0837.76073 [22] Biazar, J., Solution of systems of integral-differential equations by Adomian decomposition method, Appl. Math. Comput., 168, 1232-1238 (2005) · Zbl 1082.65594 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.