In this paper, we suggest and analyze a new family of iterative methods for finding zeros of multiplicity of nonlinear equations by using the variational iteration technique. These new methods include the Halley method and its variants forms as special cases. We also give several examples to illustrate the efficiency of these methods. Comparison with modified Newton method is also given. These ...

This paper investigates the implementation of Variational Iteration Method (VIM) to practical and higher order nonlinear equations in kind of Korteweg-de-Vries (KdV) equation. The obtained solutions from thirdand fourth-order modified KdV are compared with the exact and Homotopy Perturbation Method (HPM) solutions. Results illustrate the efficiency and capability of VIM to solve high order nonl...

In this paper, we consider variational iteration method (VIM) to obtain exact solution to the Fisher’s equation. The variational iteration method is based on Lagrange multipliers for identification of optimal value of parameters in a functional. Using this method, it is possible to find the exact solution or an approximate solution of the problem.

This paper presents a novel approach for the problem of generating tiled code for nested for-loops, transformed by a tiling transformation. Tiling or supernode transformation has been widely used to improve locality in multi-level memory hierarchies, as well as to efficiently execute loops onto parallel architectures. However, automatic code generation for tiled loops can be a very complex comp...

A system of nonlinear partial differential equations was solved using a modified variational iteration method (MVIM) combined with genetic algorithm. The introduced an auxiliary parameter (p) in the correction functional to ensure convergence and improve outcomes. Before applying modification, traditional (VIM) used firstly. applied numerically solve Schrödinger-KdV equations. By comparing two ...

This note presents a Laplace transform approach in the determination of the Lagrange multiplier when the variational iteration method is applied to time fractional heat diffusion equation. The presented approach is more straightforward and allows some simplification in application of the variational iteration method to fractional differential equations, thus improving the convergence of the suc...

Two numerical algorithms based on variational iteration and decomposition methods are developed to solve a linear partial integro-differential equation with a weakly singular kernel arising from viscoelasticity. In addition, analytic solution is re-derived by using the variational iteration method and decomposition method.

This paper provides both analytical and numerical solutions of (PDEs) involving time-fractional derivatives. We implemented three powerful techniques, including the modified variational iteration technique, Adomian decomposition homotopy analysis to obtain an approximate solution for bounded space variable ν. The Laplace transformation is used in derivative operator enhance proposed methods’ pe...

In this paper, we apply the variational iteration method (VIM) for solving telegraph equations, which arise in the propagation of electrical signals along a telegraph line. The suggested algorithm is more efficient and easier to handle as compare to the decomposition method. Numerical results show the efficiency and accuracy of the proposed VIM.