The fuzzy set theory introduced by Zadeh has emerged as an interesting and fascinating branch of pure and applied sciences. The applications of fuzzy set theory can be found in many branches of regional, physical, mathematical, differential equations andengineering sciences. Recently, the authors have made important research results in the theory of fuzzy differentialequations, integrodifferent...

In this paper, we apply the variational iteration method using He’s polynomials for finding the analytical solution of gas dynamic equation. The proposed method is an elegant combination of He’s variational iteration and the homotopy perturbation methods. The suggested algorithm is quite efficient and is practically well suited for use in such problems. The proposed iterative scheme finds the s...

We show that recent applications of the homotopy perturbation method the Adomian decomposition method and the variational iteration method are completely useless for the treatment of nonlinear problems.

In this paper, a new reliable method called the step variational iteration method (SVIM) based on an adaptation of the variational iteration method (VIM) is presented to solve non–chaotic and chaotic systems. The SVIM uses the general Lagrange multipliers for constructing the correction functional for the problems. The SVIM yields a step analytical solution of the form of a rapidly convergent i...

A comparative study is presented about the Adomian’s decomposition method (ADM), variational iteration method (VIM), and fractional variational iteration method (FVIM) in dealing with fractional partial differential equations (FPDEs).The study outlines the significant features of the ADM and FVIMmethods. It is found that FVIM is identical to ADM in certain scenarios. Numerical results from thre...

We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid "noise terms" is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed fo...

We apply the variational iteration method using He’s polynomials VIMHP for solving the fifthorder boundary value problems. The proposedmethod is an elegant combination of variational iteration and the homotopy perturbationmethods and is mainly due to Ghorbani 2007 . The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme...

In this paper we present a primal interior-point hybrid proximal extragradient (HPE) method for solving a monotone variational inequality over a closed convex set endowed with a selfconcordant barrier and whose underlying map has Lipschitz continuous derivative. In contrast to the method of [7] in which each iteration required an approximate solution of a linearized variational inequality over ...

This paper demonstrates a study on some significant latest innovations in the approximated techniques to find the approximate solutions of Caputo fractional Volterra-Fredholm integro-differential equations. To this aim, the study uses the modified Adomian decomposition method (MADM) and the modified variational iteration method (MVIM). A wider applicability of these techniques are based on thei...