The Variational Iteration Method for a Class of Eighth-Order Boundary-Value Differential Equations

Abstract

The variational iteration method, a well-known method for solving functional equations, is employed to solve a class of eighth-order boundary-value problems, which govern scientific and engineering experimentations. Some special cases of the mentioned equations are solved as examples to illustrate the ability and reliability of the method. The results reveal that the method is very effective and convenient.

The use of homotopy methods for solving nonlinear foam drainage equation

“…In the VIM [28,29,30,31,32,33,34,35], it has been considered the following nonlinear differential equation:…”

Application of the Variational Iteration Method to the Initial Value Problems of Q-difference Equations-Some Examples

“…For the other development of the VIM, readers are referred to the method using the fractional differential equations [21], a new approach to identification of the Lagrange multipliers [22], applications to fuzzy equations [23], new Lagrange multipliers of the VIM in fractional calculus [24][25][26] and applications in the eight-order boundary value problem [27], integrodifferential equation [28] and the wave-diffusion equation [29]. …”

Numerical solution for solving special eighth-order linear boundary value problems using Legendre Galerkin method

“…A selective review for getting the numerical solution of the eighth-order boundary value problems is presented here. Boutayeb and Twizell [18] used finite difference methods, Akram and Siddiqi [19,20] used nonic and non-polynomial spline functions, respectively, Akram and Rehman [21] developed reproducing kernel space, Viswanadham and Ballem [22] used Galerkin method with quintic B-spline, Inc and Evans [23] constructed Adomian decomposition method, Wazwaz [24] developed modified Adomian decomposition method, Siddiqi and Iftikhar [25] used homotopy analysis method, and Ballem and Viswanadham [26] presented the Galerkin method with septic B-splines, whereas Abbasbandy and Shirzadi [27] developed variational iteration method.…”