In this letter, He’s Variational iteration method (VIM) is implemented for solving the nonlinear Whitham-Broer-Kaup partial differential equations. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of the problem. The results are compared with those obtained by t...

In this present paper, we solve a two-dimensional nonlinear Volterra-Fredholm integrodifferential equation by using the following powerful, efficient but simple methods: (i) Modified Adomian decomposition method (MADM), (ii) Variational iteration method (VIM), (iii) Homotopy analysis method (HAM) and (iv) Modified homotopy perturbation method (MHPM). The uniqueness of the solution and the conve...

In this paper, we introduced a new generalization method to solve fractional convection–diffusion equations based on the well-known variational iteration method (VIM) improved by an auxiliary parameter. The suggested method was highly effective in controlling the convergence region of the approximate solution. By solving some fractional convection–diffusion equations with a propounded method an...

A generalized Fisher’s equation is solved by using the modified Adomian decomposition method MADM , variational iteration method VIM , homotopy analysis method HAM , and modified homotopy perturbation method MHPM . The approximation solution of this equation is calculated in the form of series whose components are computed easily. The existence, uniqueness, and convergence of the proposed metho...

This article discusses a semi-analytical method for solving modelling equations blood flow through compliant vessels. He's method, also called the variational iteration (VIM), is used to find an approach solution in explicit form. The chosen problem has been handled by asymptotic reduction of associated incompressible Navier–Stokes equations, obtain one-dimensional nonlocal model with source te...

In this work we conceive a method of how the Lagrange multiplier modified Variational Iteration Method can be defined from Laplace transform, And use technique to solve both differential equations and FDEs with initial value conditions, With Illustrative examples by applying VIM Ordinary fractional Differential Equations.

In this paper, we use the optimal homotopy analysis method (OHAM) for approximate solutions of the fractional order Logistic equation. The numerical results obtained are compared with the results obtained by using variational iteration method (VIM) and Adomian decomposition method (ADM). The fractional derivatives are described by Caputo's sense. Exact and/or approximate analytical solutions of...

The variational iterationmethod VIM 1–4 and homotopy perturbationmethod HPM 5– 8 , proposed byHe, are powerful analytical methods for various kinds of linear and nonlinear problems. For example, the variational iteration method has been applied to autonomous ordinary differential equation 9 and delay differential equation 10 . Abdou and Soliman applied this method to Schrodinger-KDV, generalize...

In this article variational iterationmethod (VIM), established by He in (1999), is considered to solve nonlinear Bergur’s equation. This method is a powerful tool for solving a large number of problems. Using variational iteration method, it is possible to find the exact solution or a closed approximate solution of a problem. Comparing the results with those of Adomian’s decomposition and finit...

In this work, the homotopy perturbation method (HPM), variational iteration method (VIM) and Adomian decomposition method (ADM) are applied to solve the Rosenau–Hyman equation. We used the initial condition ( u(x, 0) = −83 cos 2 ( x 4 )) for aforementioned methods. Numerical solutions obtained by these methods are compared with the exact solutions, revealing that the obtained solutions are of h...