Exact solutions of nonlinear diffusion equations by variational iteration method

DOI10.1016/j.camwa.2006.12.077zbMath1145.35311OpenAlexW1991261864MaRDI QIDQ928815

A. Sadighi, Davood Domairry Ganji

Publication date: 11 June 2008

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2006.12.077

zbMATH Keywords

Lagrange multipliersAdomian decomposition methodhomotopy perturbation methodHe's variational iteration method

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Reaction-diffusion equations (35K57) Solutions to PDEs in closed form (35C05) Other special methods applied to PDEs (35A25)

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Cites Work

• Unnamed Item
• Application of He's variational iteration method to Helmholtz equation
• Variational iteration method -- a kind of non-linear analytical technique: Some examples
• Exp-function method for nonlinear wave equations
• The non-classical solution for the inhomogeneous nonlinear diffusion equation
• The homotopy perturbation method for nonlinear oscillators with discontinuities.
• A coupling method of a homotopy technique and a perturbation technique for nonlinear problems
• Homotopy perturbation method for bifurcation of nonlinear problems
• Application of variational iteration method to nonlinear differential equations of fractional order
• The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations
• Approximate analytical solution for seepage flow with fractional derivatives in porous media
• Approximate solution of nonlinear differential equations with convolution product nonlinearities
• Exact solutions to nonlinear diffusion equations obtained by the decomposition method
• Homotopy perturbation method: a new nonlinear analytical technique
• Periodic solutions and bifurcations of delay-differential equations
• Homotopy perturbation method for solving boundary value problems
• Limit cycle and bifurcation of nonlinear problems
• Application of homotopy perturbation method to nonlinear wave equations
• Construction of solitary solution and compacton-like solution by variational iteration method
• New periodic solutions for nonlinear evolution equations using Exp-function method
• Exact solutions to nonlinear diffusion equations obtained by a generalized conditional symmetry method
• New classes of similarity solutions of the inhomogeneous nonlinear diffusion equations
• SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS
• Variational iteration method for autonomous ordinary differential systems