Numerical Solutions of a Quadratic Integral Equations by Using Variational Iteration and Homotopy Perturbation Methods

Numerical solutions of two-dimensional linear and nonlinear Volterra integral equations: Homotopy perturbation method and differential transform method

New Perturbation Iteration Solutions for Fredholm and Volterra Integral Equations

As one of themost important subjects of mathematics, differential and integral equations are widely used to model a variety of physical problems. Perturbation methods have been used in search of approximate analytical solutions for over a century [1–3]. Algebraic equations, integral-differential equations, and difference equations could be solved by these techniques approximately. However, a ma...

Exact and Numerical Solutions for Nonlinear Higher Order Modified KdV Equations by Using Variational Iteration Method

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...

Numerical Solution of The Parabolic Equations by Variational Iteration Method and Radial Basis Functions

‎In this work‎, ‎we consider the parabolic equation‎: ‎$u_t-u_{xx}=0$‎. ‎The purpose of this paper is to introduce the method of‎ ‎variational iteration method and radial basis functions for‎ ‎solving this equation‎. ‎Also, the method is implemented to three‎ ‎numerical examples‎. ‎The results reveal‎ ‎that the technique is very effective and simple.

Numerical Approximate Solutions of Nonlinear Fredholm Integral Equations of Second Kind Using B-spline Wavelets and Variational Iteration Method

In this paper, nonlinear integral equations have been solved numerically by using B-spline wavelet method and Variational Iteration Method (VIM). Compactly supported semi-orthogonal linear B-spline scaling and wavelet functions together with their dual functions are applied to approximate the solutions of nonlinear Fredholm integral equations of second kind. Comparisons are made between the var...