in this paper, we present a comparative study between the modified variational iteration method (mvim) and a hybrid of fourier transform and variational iteration method (ftvim). the study outlines the efficiencyand convergence of the two methods. the analysis is illustrated by investigating four singular partial differential equations with variable coefficients. the solution of singular partia...

In the last few decades, considerable work has been invested in developing new methods for analytical and numerical solutions of differential and integral equations, linear or nonlinear. There has been a great deal of research work done to address the issues of nonlinearity and singularity phenomena that arise in many scientific and engineering problems. Moreover, there has been a great need fo...

In this paper, the Kadomtsev-Petviashvili equation is solved by using the Adomian’s decomposition method , modified Adomian’s decomposition method , variational iteration method , modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The existence and uniqueness of the solution and convergence of the proposed...

Combining the variational iteration method (VIM) with the sparse grid theory, a dynamic sparse grid approach for nonlinear PDEs is proposed in this paper. In this method, a multilevel interpolation operator is constructed based on the sparse grids theory firstly. The operator is based on the linear combination of the basic functions and independent of them. Second, by means of the precise integ...

This paper outlines a comparison of the couplings of He’s and Adomian’s polynomials with correction functional of variational iteration method (VIM) to investigate a solution of Flierl-Petviashivili (FP) equation which plays a very important role in mathematical physics, engineering and applied sciences. These elegant couplings give rise to two modified versions of VIM which are very efficient ...

In this paper, a new analytic iterative technique, called the residual power series method (RPSM), is applied to time fractional Whitham–Broer–Kaup equations. The explicit approximate traveling solutions are obtained by using this method. The efficiency and accuracy of the present method is demonstrated by two aspects. One is analyzing the approximate solutions graphically. The other is compari...

In this paper we develop an efficient method based on the Spectral Collocation Method (SCM) and the Variational Iteration Method (VIM) that can be used for the efficient numerical solution of nonlinear stiff/nonstiff two-point Boundary Value Problems (BVPs). The method derived here has the advantage that it does not require the solution of nonlinear systems of equations. We derive the method wh...

The second-order delay differential equations often appear in the dynamical system, celestial mechanics, kinematics, and so forth. Some numerical methods for solving secondorder delay differential equations have been discussed, which include θ-method [1], trapezoidal method [2], and RungeKutta-Nyströmmethod [3].The variational iteration method (VIM) was first proposed by He [4, 5] and has been ...

F. Shakeri and M. Dehghan in [13] presented the variational iteration method for solving the model describing biological species living together. Here we suggest the differential transform (DT) method for finding the numerical solution of this problem. To this end, we give some preliminary results of the DT and by proving some theorems, we show that the DT method can be easily applied to mentio...

The aim of this paper is to solve numerically the Cauchy problems nonlinear partial differential equation (PDE) in a modified variational iteration approach. standard method (VIM) first studied before modifying it using Adomian polynomials decomposing terms PDE attain new iterative scheme (MVIM). VIM was used iteratively determine parabolic obtain some results. Also, PDEs with aid Maple 18 soft...