An iteration sequence based on the BLUES (beyond linear use of equation superposition) function method is presented for calculating analytic approximants to solutions nonlinear partial differential equations. This extends previous work using this ordinary equations with an external source term. Now, initial condition plays role source. The tested three examples: a reaction-diffusion-convection ...

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 ...

We introduce and discuss the Homotopy perturbation method, the Adomian decomposition method and the variational iteration method for solving the stefan problem with kinetics. Then, we give an example of the stefan problem with  kinetics and solve it by these methods.

Periodic behavior analysis of nano/microelectromechanical systems (N/MEMS) is an essential field owing to their many promising applications in microinstruments. The interesting and unique properties these systems, particularly, small size, batch fabrication, low power consumption, high reliability, have fascinated researchers industries implement structures for the production different microdev...

The variational iteration method is employed to solve conservative oscillator containing complicated nonlinearities. In order to expand the nonlinear terms into truncated Fourier series, an approach of undetermined coefficient is proposed. Numerical examples shows the feasibility and efficiency of the variational iteration method as well as the presented technique for Fourier series expansion. ...

‎In this work‎, ‎we consider the parabolic equation‎: ‎$u_t-u_{xx}=0$‎. ‎The purpose of this paper is to introduce the method of‎ ‎variational iteration method and radial basis functions for‎ ‎solving this equation‎. ‎Also, the method is implemented to three‎ ‎numerical examples‎. ‎The results reveal‎ ‎that the technique is very effective and simple.

in this paper, the variational iteration method proposed by ji-huan he is applied to solve both linear and nonlinear schrodinger equations. the main property of the method is in its flexibility and ability to solve linear and nonlinear equations accurately and conveniently. in this method, general lagrange multipliers are introduced to construct correction functionals to the problems. the multi...

Motivated by magnetic polymer manufacturing applications, the present research article examines theoretically hydromagnetic boundary layer flow of an electrically conducting non-Newtonian couple stress fluid due to a transient shrinking (contracting) porous sheet. The conservation partial differential equations for mass and momentum are rendered into fifth-order nonlinear ordinary equation via ...