... solution of the fractal Lane–Emden equation is obtained by the variational iteration method. The example illustrates that the suggested scheme is efficient and accurate for fractal models. Design/methodology/approach The author establishes the variational principle for fractal Lane–Emden equation...

... calculus have been introduced. Some analytical methods are reviewed, mainly including the variational iteration method, the Ritz method, the homotopy perturbation method, the variational principle and the Taylor series method. An example is given to show the simple solution process and the high accuracy...

...Abdul-Majid Wazwaz Purpose The purpose of this paper is to use the variational iteration method (VIM) for studying boundary value problems (BVPs) characterized with dual solutions. Design/methodology/approach The VIM proved to be practical for solving linear and nonlinear problems arising...

...Mustafa Turkyilmazoglu Purpose – In an earlier paper (Turkyilmazoglu, 2011a), the author introduced a new optimal variational iteration method. The idea was to insert a parameter into the classical variational iteration formula in an aim to prevent divergence or to accelerate the slow convergence...

...G Wu; Eric Wai Ming Lee; Gao Li Purpose – The purpose of this paper is to introduce variational iteration method (VIM) to construct equivalent integral equations for initial-boundary value problems of nonlinear partial differential equations. The Lagrange multipliers become the integral kernels...

...Xiuying Li Purpose – The purpose of this paper is to introduce an effective method for two-dimensional inverse heat conduction problems. Design/methodology/approach – The variational iteration method (VIM) is used to solve two-dimensional inverse heat conduction problems and restore...

...) to particle diffusion in turbulent plasma, and also to heat propagation in a thin rod is mentioned in Ionkin (1977) . In this work, the inverse problem is formulated in Section 2. We extend the use of variational iteration method (VIM) to this inverse source problem. The VIM was first proposed...

... method can be applied to other nonlinear boundary layer flow problems. Originality/value – In this paper, an approximate analytical solution of the MHD Falkner-Skan flow problem is obtained by combining the Lie symmetry method with the variational iteration method and He's polynomials. Dr Buhe...

... differential equations in fractal media. Fractional derivatives are introduced heuristically by the variational iteration method, and fractal derivatives are explained geometrically. Some effective analytical approaches to fractional differential equations, e.g. the variational iteration method, the homotopy...

... expansion method and the variational iteration method (VIM). First a zeroth order asymptotic expansion for the solution of the given singularly perturbed convection-diffusion problem is constructed. Then the reduced terminal value problem is solved by using the VIM. Findings – Two numerical examples...

... differential equation Homotopy analysis method Variational iteration method Caputo fractional derivative Series solution Differential equations Mathematics The homotopy analysis method (HAM) is developed by Liao (1992) . Based on homotopy of topology, the validity of the HAM...

... and efficiency of the proposed method. Hereby we briefly recapitulate the standard solution procedure of the variational iteration method. Consider the following functional equation: Equation 3 where L is the highest order derivative that is assumed to be easily invertible, R is a linear...

... will be tested. Design/methodology/approach Nonlinear heat transfer problems are solved by perturbation iteration method. They are also solved by the well‐known technique variational iteration method in the literature. Findings It is found that perturbation iteration solutions converge faster...

...Mehdi Dehghan; Jalil Manafian Heris Purpose This paper aims to show that the variational iteration method (VIM) and the homotopy perturbation method (HPM) are powerful and suitable methods to solve the Fornberg‐Whitham equation. Design/methodology/approach Using HPM the explicit exact solution...

...Ahmet Yıldırım; Hüseyin Koçak Purpose The purpose of this paper is to implement the variational iteration method and the homotopy perturbation method to give a rational approximation solution of the foam drainage equation with time‐ and space‐fractional derivatives. Design/methodology/approach...

...Said Mohammad Mehdi Hosseini; Syed Tauseef Mohyud‐Din; Husain Ghaneai Purpose The purpose of this paper is to apply He's variational iteration method (VIM) coupled with an auxiliary parameter, which proves very effective to control the convergence region of approximate solution. Design...