×
Ganji, D. D.; Tari, Hafez; Jooybari, M. Bakhshi

Variational iteration method and homotopy perturbation method for nonlinear evolution equations. (English) Zbl 1141.65384

Comput. Math. Appl. 54, No. 7-8, 1018-1027 (2007).
Summary: The variational iteration and homotopy perturbation methods are applied to various evolution equations. To assess the accuracy of the solutions, we compare the results with the exact solutions, revealing that both methods are capable of solving effectively a large number of nonlinear differential equations with high accuracy.

Cited in 1 Review
Cited in 29 Documents

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L75 Higher-order nonlinear hyperbolic equations

Keywords:

variational iteration method; homotopy perturbation method; evolution equations; numerical examples
PDF BibTeX XML Cite
\textit{D. D. Ganji} et al., Comput. Math. Appl. 54, No. 7--8, 1018--1027 (2007; Zbl 1141.65384)
Full Text: DOI

References:

[1] Kaya, D., An explicit and numerical solutions of some fifth-order KdV equation by decomposition method, Applied Mathematics and Computation, 144, 353-363 (2003) · Zbl 1024.65096
[2] Al-Khaled, K., Approximate wave solutions for generalized Benjamin-Bona-Mahony-Burgers equations, Applied Mathematics and Computation, 171, 281-292 (2005) · Zbl 1084.65097
[5] Ganji, D. D., Assessment of homotopy-perturbation and perturbation methods in heat radiation equations, International Communications in Heat and Mass Transfer, 33, 3, 391-400 (2006)
[7] Adomian, G., A review of the decomposition method in applied mathematics, Journal of Mathematical Analysis and Applications, 135, 501-544 (1988) · Zbl 0671.34053
[8] He, J. H., Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B, 20, 1141-1199 (2006) · Zbl 1102.34039
[9] He, J. H., Non-Perturbative Methods for Strongly Nonlinear Problems (2006), Dissertation.de-Verlag im Internet GmbH: Dissertation.de-Verlag im Internet GmbH Berlin
[10] He, J. H., Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178, 3-4, 257-262 (1999) · Zbl 0956.70017
[11] He, J. H., A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International Journal of Non-Linear Mechanics, 35, 1, 37-43 (2000) · Zbl 1068.74618
[12] He, J. H., New interpretation of homotopy perturbation method, International Journal of Modern Physics B, 20, 2561-2568 (2006)
[13] He, J. H., Variational iteration method—a kind of nonlinear analytical technique: Some examples, International Journal of Non-linear Mechanics, 34, 4, 699-708 (1999) · Zbl 1342.34005
[14] He, J. H., Approximate analytical solution for seepage with fractional derivatives in porous media, Computational Methods in Applied Mechanics and Engineering, 167, 57-68 (1998) · Zbl 0942.76077
[15] He, J. H., Approximate solution of nonlinear differential equations with convolution product nonlinearities, Computational Methods in Applied Mechanics and Engineering, 167, 69-73 (1998) · Zbl 0932.65143
[16] He, J. H., Homotopy perturbation method: A new nonlinear analytical technique, Applied Mathematics and Computation, 135, 1, 73-79 (2003) · Zbl 1030.34013
[17] He, J. H., The homotopy perturbation method for nonlinear oscillators with discontinuities, Applied Mathematics and Computation, 151, 1, 287-292 (2004) · Zbl 1039.65052
[18] He, J. H., Periodic solutions and bifurcations of delay-differential equations, Physics Letters A, 347, 4-6, 228-230 (2005) · Zbl 1195.34116
[19] He, J. H., Application of homotopy perturbation method to nonlinear wave equations, Chaos, Solitons and Fractals, 26, 3, 695-700 (2005) · Zbl 1072.35502
[20] He, J. H., Limit cycle and bifurcation of nonlinear problems, Chaos, Solitons and Fractals, 26, 3, 827-833 (2005) · Zbl 1093.34520
[21] He, J. H., Homotopy perturbation method for bifurcation of nonlinear problems, International Journal of Nonlinear Sciences and Numerical Simulation, 6, 2, 207-208 (2005) · Zbl 1401.65085
[22] He, J. H., Homotopy perturbation method for solving boundary value problems, Physics Letters A, 350, 1-2, 87-88 (2006) · Zbl 1195.65207
[23] 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
[24] 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
[25] He, J. H., Variational iteration method for autonomous ordinary differential systems, Applied Mathematics and Computation, 114, 2-3, 115-123 (2000) · Zbl 1027.34009
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.