This paper outlines a detailed study of some relatively new techniques which are originated by He for solving diversified nonlinear problems of physical nature. In particular, we will focus on the variational iteration method VIM and its modifications, the homotopy perturbation method HPM , the parameter expansion method, and exp-function method. These relatively new but very reliable technique...

In this article, we apply the Daftardar-Gejji and Jafari method (DJM) to solve multispecies Lotka–Volterra equation. A comparison between DJM, differential transformation (DTM), variational iteration (VIM), Adomian decomposition (ADM) shows that DJM is a reliable powerful for solving nonlinear equations. The efficiency applicability of are confirmed by considering some examples. proposed proced...

this paper presents an efficient modification of the variational iteration method for solvingboundary value problems using the chebyshev polynomials. the proposed method can be applied to linearand nonlinear models. the scheme is tested for some examples and the obtained results demonstrate thereliability and efficiency of the proposed method.

In this paper, we apply the homotopy perturbation method (HPM), modified method(MHPM), variational iteration (VIM), Adomian decomposition (ADM), and (MADM) to solve nonlinear mixed Volterra-Fredholm integral equations itssystem. We investigate approximate solution of equation its system via proposed methods. Thevalidity efficiency these methods are demonstrated through various numerical example...

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.

In this paper, we have introduced a fractional-ordered predator-prey population model which has been successfully solved with the help of two powerful analytical methods, namely, Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM). The fractional derivatives are described in the Caputo sense. Using initial values, we have derived the explicit solutions of predator-prey pop...

*Correspondence: [email protected]; [email protected] 1College of Mathematics and Information Science, Neijiang Normal University, Neijiang, 641112, China 3Department of Mathematics and Computer Sciences, Cankaya University, Balgat, Ankara 06530, Turkey Full list of author information is available at the end of the article Abstract A novel modification of the variational iteratio...

In this paper, the approximate analytic solutions of the mathematical model of time fractional diffusion equation (FDE) with a moving boundary condition are obtained with the help of variational iteration method (VIM) and Adomian decomposition method (ADM). By using boundary conditions, the explicit solutions of the diffusion front and fractional releases in the dimensionless form have been der...

Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of application. This paper presents the analytical solutions of the space fractional diffusion equations by variational iteration method (VIM). By using initial conditions, the expli...