scholarly journals The variational iteration method: A reliable analytic tool for solving linear and nonlinear wave equations

2007 ◽  
Vol 54 (7-8) ◽  
pp. 926-932 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Nonlinear Wave ◽  
Iteration Method ◽  
Wave Equations ◽  
Variational Iteration Method ◽  
Nonlinear Wave Equations ◽  
Analytic Tool ◽  
Variational Iteration ◽  
Linear And Nonlinear

scholarly journals The variational iteration method for solving n-th order fuzzy differential equations

Open Physics ◽  
2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Mohammad Saeidy ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Nonlinear Equations ◽  
Analytical Method ◽  
Iteration Method ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Linear Differential Equations ◽  
Variational Iteration ◽  
Linear And Nonlinear ◽  
Linear Differential

AbstractThe variational iteration method (VIM) proposed by Ji-Huan He is a new analytical method for solving linear and nonlinear equations. In this paper, the variational iteration method has been applied in solving nth-order fuzzy linear differential equations with fuzzy initial conditions. This method is illustrated by solving several examples.

scholarly journals Variational Iteration Method for a Fractional-Order Brusselator System

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Jafari ◽  
Abdelouahab Kadem ◽  
D. Baleanu
Keyword(s):  
Fractional Order ◽  
Fractional Differential Equations ◽  
Iteration Method ◽  
Fractional Derivatives ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Promising Tool ◽  
Approximate Analytical Solutions ◽  
Fractional Differential ◽  
Linear And Nonlinear

This paper presents approximate analytical solutions for the fractional-order Brusselator system using the variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. Two examples are solved as illustrations, using symbolic computation. The numerical results show that the introduced approach is a promising tool for solving system of linear and nonlinear fractional differential equations.

scholarly journals Exact Solution of Linear and Nonlinear Wave Equations by Double Laplace and Iterative Method

2019 ◽  
Vol 11 (5) ◽  
pp. 33
Author(s):  
Adesina K. Adio ◽  
Wumi S. Ajayi ◽  
Olabode O. Bamisile ◽  
Babatunde T. Akanbi
Keyword(s):  
Exact Solution ◽  
Iterative Method ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Iteration Process ◽  
Nonlinear Wave Equations ◽  
Double Laplace Transform ◽  
Linear And Nonlinear

A coupling of double Laplace transform with Iterative method is used to solve linear and nonlinear wave equations subject to initial and boundary conditions. The iteration process leads to disappearance of noise terms and exact solution is obtained at first iteration. Through several examples, the convenience and efficiency of the method is demonstrated, showing its usefulness to overcome difficulties associated with some existing techniques.

Numerical solution of the general Volterra nth-order integro-differential equations via variational iteration method

2018 ◽  
Vol 13 (02) ◽  
pp. 2050042
Author(s):  
Fernane Khaireddine
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Numerical Solution ◽  
General Formula ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Numerical Examples ◽  
Variational Iteration ◽  
Linear And Nonlinear

In this paper, we use the variational iteration method (VIM) to construct approximate solutions for the general [Formula: see text]th-order integro-differential equations. We show that his method can be effectively and easily used to solve some classes of linear and nonlinear Volterra integro-differential equations. Finally, some numerical examples with exact solutions are given.

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