×

zbMATH — the first resource for mathematics

Variational iteration method for solving integral equations. (English) Zbl 1141.65400
Summary: Several integral equations are solved by the variational iteration method. Comparison with exact solution shows that the method is very effective and convenient for solving integral equations.

MSC:
65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45B05 Fredholm integral equations
45G10 Other nonlinear integral equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Wazwaz, A.M., Two methods for solving integral equations, Applied mathematics and computation, 77, 79-89, (1996) · Zbl 0846.65077
[2] Wazwaz, A.M., A reliable treatment for mixed volterra – fredholm integral equations, Applied mathematics and computation, 127, 405-414, (2002) · Zbl 1023.65142
[3] He, J.H., Variational iteration method—a kind of nonlinear analytical technique: some examples, International journal of nonlinear mechanics, 34, 4, 699-708, (1999) · Zbl 1342.34005
[4] He, J.H., A review on some new recently developed nonlinear analytical techniques, International journal of nonlinear science numerical simulation, 1, 1, 51-70, (2000) · Zbl 0966.65056
[5] He, J.H., Some asymptotic methods for strongly nonlinear equations, International journal of modern physics B, 20, 10, 1141-1199, (2006) · Zbl 1102.34039
[6] He, J.H., Non-perturbative methods for strongly nonlinear problems, (2006), dissertation. de-Verlag im Internet GmbH Berlin
[7] J.-H. He, Variational iteration method—some recent results and new interpretations, Journal of Computational and Applied Mathematics (in press) · Zbl 1119.65049
[8] He, J.H.; Wu, X.H., Construction of solitary solution and compacton-like solution by variational iteration method, Chaos, solitons and fractals, 29, 1, 108-113, (2006) · Zbl 1147.35338
[9] He, J.H., Variational iteration method for autonomous ordinary differential systems, Applied mathematics and computation, 114, 2-3, 115-123, (2000) · Zbl 1027.34009
[10] Bildik, N.; Konuralp, A., The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations, International journal of nonlinear sciences and numerical simulation, 7, 1, 65-70, (2006) · Zbl 1401.35010
[11] Momani, S.; Abuasad, S., Application of he’s variational iteration method to Helmholtz equation, Chaos, solitons and fractals, 27, 5, 1119-1123, (2006) · Zbl 1086.65113
[12] Odibat, Z.M.; Momani, S., Application of variational iteration method to nonlinear differential equations of fractional order, International journal of nonlinear sciences and numerical simulation, 7, 1, 27-34, (2006) · Zbl 1401.65087
[13] M. Dehghan, M. Tatari, Identifying an unknown function in a parabolic equation with overspecified data via He’s variational iteration method, Chaos, Solitons and Fractals (in press) · Zbl 1152.35390
[14] Mustafa Inc, Numerical simulation of KdV and mKdV equations with initial conditions by the variational iteration method, Chaos, Solitons and Fractals (in press) · Zbl 1142.35572
[15] Soliman, A.A., A numerical simulation and explicit solutions of KdV-burgers’ and lax’s seventh-order KdV equations, Chaos, solitons and fractals, 29, 2, 294-302, (2006) · Zbl 1099.35521
[16] Abulwafa, E.M.; Abdou, M.A.; Mahmoud, A.A., The solution of nonlinear coagulation problem with mass loss, Chaos, solitons and fractals, 29, 2, 313-330, (2006) · Zbl 1101.82018
[17] Moghimi, M.; Hejazi, F.S.A., Variational iteration method for solving generalized burger – fisher and burger equations, Chaos, solitons and fractals, 33, 5, 1756-1761, (2007) · Zbl 1138.35398
[18] Tatari, M.; Dehghan, M., He’s variational iteration method for computing a control parameter in a semi-linear inverse parabolic equation, Chaos, solitons and fractals, 33, 2, 671-677, (2007) · Zbl 1131.65084
[19] Abulwafa, E.M.; Abdou, M.A.; Mahmoud, A.A., Nonlinear fluid flows in pipe-like domain problem using variational-iteration method, Chaos, solitons and fractals, 32, 4, 1384-1397, (2007) · Zbl 1128.76019
[20] Sweilam, N.H.; Khader, M.M., Variational iteration method for one dimensional nonlinear thermoelasticity, Chaos, solitons and fractals, 32, 1, 145-149, (2007) · Zbl 1131.74018
[21] Momani, S.; Odibat, Z., Numerical comparison of methods for solving linear differential equations of fractional order, Chaos, solitons and fractals, 31, 5, 1248-1255, (2007) · Zbl 1137.65450
[22] A.-M. Wazwaz, The variational iteration method for rational solutions for KdV, K(2,2), Burgers, and cubic Boussinesq equations, Journal of Computational and Applied Mathematics (in press)
[23] S. Momani, Z. Odibat, Numerical approach to differential equations of fractional order, Journal of Computational and Applied Mathematics (in press) · Zbl 1119.65127
[24] A.A. Soliman, M.A. Abdou, Numerical solutions of nonlinear evolution equations using variational iteration method, Journal of Computational and Applied Mathematics (in press) · Zbl 1120.65111
[25] M. Tatari, M. Dehghan, On the convergence of He’s variational iteration method, Journal of Computational and Applied Mathematics (in press) · Zbl 1120.65112
[26] N.H. Sweilam, Variational iteration method for solving cubic nonlinear Schrödinger equation, Journal of Computational and Applied Mathematics (in press) · Zbl 1119.65098
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.