this paper presents a comparison between variational iteration method (vim) and modfied variational iteration method (mvim) for approximate solution a system of volterra integral equation of the first kind. we convert a system of volterra integral equations to a system of volterra integro-di®erential equations that use vim and mvim to approximate solution of this system and hence obtain an appr...

We continue our investigation of nite element approximations to the system of shallow water equations, based on the generalized wave continuity equation (GWCE) formulation. In previous work, we analyzed this system assuming Dirichlet boundary conditions on both elevation and velocity. Based on physicalgrounds, it is possible to not impose boundaryconditionson elevation. Thus, we examine the for...

In this work, the newly developed optimal perturbation iteration technique with Laplace transform is applied to generalized regularized long wave equations a new fractional operator obtain approximate solutions. We classical differential form by using Atangana-Baleanu derivative which defined Mittag-Leffler function. To show efficiency of proposed method, numerical example given for different v...

We describe a boundary integral method for computing time-dependent, doubly periodic, three-dimensional water waves. This method has been proved to converge to the exact solution. We discuss several analytical issues, including the quadrature of singular integrals, such as single and double layer potentials on surfaces, and stability estimates for discrete versions of operators such as the laye...

In order to investigate corrections to the common KdV approximation for surface water waves in a canal, we derive modulation equations for the evolution of long wavelength initial data. We work in Lagrangian coordinates. The equations which govern corrections to the KdV approximation consist of linearized and inhomogeneous KdV equations plus an inhomogeneous wave equation. These equations are e...

In order to investigate corrections to the common KdV approximation for surface water waves in a canal, we derive modulation equations for the evolution of long wavelength initial data. We work in Lagrangian coordinates. The equations which govern corrections to the KdV approximation consist of linearized and inhomogeneous KdV equations plus an inhomogeneous wave equation. These equations are e...