In this paper, He’s variational iteration method (VIM) is used to obtain approximate analytical solutions of the Abelian differential equation. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of problem. The method is capable of reducing the size of calculation...

In this paper, we apply the local fractional Laplace transform method (or Yang-Laplace transform) on Volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative operators. This approach provides us with a convenient way to find a solution ...

in this work, the blasius equation is studied. homotopy perturbation method (hpm) and homotopy analysis method (ham) are applied to obtain its solution. comparison with variational iteration method (vim) is made to highlight the significant features of employed methods and their capability of handling nonlinear problems. the outcome shows the success of (hpm) and (ham) for solving nonlinear pro...

In this paper, a relatively new method, namely variational iteration method (VIM), is developed for free vibration analysis of a Timoshenko beam with different boundary conditions. In the VIM, an appropriate Lagrange multiplier is first chosen according to order of the governing differential equation of the boundary value problem, and then an iteration process is used till the desired accuracy ...

In this paper, the variational iteration method for solving nth-order fuzzy integro differential equations (nth-FIDE) is proposed. In fact the problem is changed to the system of ordinary fuzzy integro-differential equations and then fuzzy solution of nth-FIDE is obtained. Some examples show the efficiency of the proposed method.

In this paper, nonlinear integral equations have been solved numerically by using B-spline wavelet method and Variational Iteration Method (VIM). Compactly supported semi-orthogonal linear B-spline scaling and wavelet functions together with their dual functions are applied to approximate the solutions of nonlinear Fredholm integral equations of second kind. Comparisons are made between the var...

This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions. Firstly, the problem is reduced to an equivalent problem which is easy to handle using variational iteration method. Secondly, variational iteration method is used to solve the reduced problem. Using this method a rapid convergent sequence can be produced which ten...

In this article, the local fractional variational iteration method is proposed to solve nonlinear partial differential equations within local fractional derivative operators. To illustrate the ability and reliability of the method, some examples are illustrated. A comparison between local fractional variational iteration method with the other numerical methods is given, revealing that the propo...

    In this paper, a variational iteration method (VIM), which is a well-known method for solving nonlinear equations, has been employed to solve an inverse parabolic partial differential equation. Inverse problems in partial differential equations can be used to model many real problems in engineering and other physical sciences. The VIM is to construct correction functional using general Lagr...

In this paper a modification of He's variational iteration method (VIM) has been employed to solve Dung and Riccati equations. Sometimes, it is not easy or even impossible, to obtain the first few iterations of VIM, therefore, we suggest to approximate the integrand by using suitable expansions such as Taylor or Chebyshev expansions.