scholarly journals Fractional Variational Iteration Method for Fractional Cauchy Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Bao Si-yuan
Keyword(s):  
Cauchy Problem ◽  
Exact Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Solution Procedure ◽  
Iteration Algorithm ◽  
Cauchy Problems ◽  
Variational Iteration ◽  
Fractional Cauchy Problem

The fractional variational iteration method is used to solve the fractional Cauchy problem. Some examples are given to elucidate the solution procedure and reliability of the obtained results. The variational iteration algorithm leads to exact solutions in the present study.

scholarly journals An Aproximation to Solution of Space and Time Fractional Telegraph Equations by the Variational Iteration Method

2012 ◽  
Vol 2012 ◽  
pp. 1-2 ◽  
Author(s):  
Ji-Huan He
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Iteration Algorithm ◽  
Effective Algorithm ◽  
Variational Iteration ◽  
Space And Time ◽  
Telegraph Equations

Sevimlican suggested an effective algorithm for space and time fractional telegraph equations by the variational iteration method. This paper shows that algorithm can be updated by either variational iteration algorithm-II or the fractional variational iteration method.

scholarly journals Variational Iteration Method for Volterra Functional Integrodifferential Equations with Vanishing Linear Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ali Konuralp ◽  
H. Hilmi Sorkun
Keyword(s):  
Exact Solutions ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Integrodifferential Equations ◽  
Test Problems ◽  
Application Process ◽  
Delay Function ◽  
Variational Iteration

Application process of variational iteration method is presented in order to solve the Volterra functional integrodifferential equations which have multi terms and vanishing delays where the delay functionθ(t)vanishes inside the integral limits such thatθ(t)=qtfor0<q<1,t≥0. Either the approximate solutions that are converging to the exact solutions or the exact solutions of three test problems are obtained by using this presented process. The numerical solutions and the absolute errors are shown in figures and tables.

scholarly journals Variational Iteration Method for Solving the Generalized Degasperis-Procesi Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Qian Lijuan ◽  
Tian Lixin ◽  
Ma Kaiping
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Initial Approximation ◽  
Variational Iteration Method ◽  
Original Equation ◽  
Variational Iteration

We introduce the variational iteration method for solving the generalized Degasperis-Procesi equation. Firstly, according to the variational iteration, the Lagrange multiplier is found after making the correction functional. Furthermore, several approximations ofun+1(x,t)which is converged tou(x,t)are obtained, and the exact solutions of Degasperis-Procesi equation will be obtained by using the traditional variational iteration method with a suitable initial approximationu0(x,t). Finally, after giving the perturbation item, the approximate solution for original equation will be expressed specifically.

scholarly journals The local fractional variational iteration method a promising technology for fractional calculus

2020 ◽  
Vol 24 (4) ◽  
pp. 2605-2614 ◽  
Author(s):  
Yong-Ju Yang
Keyword(s):  
Fractional Calculus ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Initial Solution ◽  
Iteration Algorithm ◽  
Promising Technology ◽  
Variational Iteration ◽  
Sumudu Transform

In order to make the local variational iteration algorithm converge faster and more effective, the Sumudu transform is adopted and a proper initial solution is chosen. Some examples are given to show that the presented method is reliable, efficient and easy to implement from a computational viewpoint.

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.

scholarly journals A New Technique of Laplace Variational Iteration Method for Solving Space-Time Fractional Telegraph Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Fatima A. Alawad ◽  
Eltayeb A. Yousif ◽  
Arbab I. Arbab
Keyword(s):  
Laplace Transform ◽  
Exact Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Space Time ◽  
New Techniques ◽  
Variational Iteration ◽  
Telegraph Equations ◽  
A New Technique ◽  
Special Case

In this paper, the exact solutions of space-time fractional telegraph equations are given in terms of Mittage-Leffler functions via a combination of Laplace transform and variational iteration method. New techniques are used to overcome the difficulties arising in identifying the general Lagrange multiplier. As a special case, the obtained solutions reduce to the solutions of standard telegraph equations of the integer orders.

An Alternative Approach to Differential-Difference Equations Using the Variational Iteration Method

2010 ◽  
Vol 65 (12) ◽  
pp. 1055-1059 ◽  
Author(s):  
Naeem Faraz ◽  
Yasir Khan ◽  
Francis Austin
Keyword(s):  
Difference Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Iteration Algorithm ◽  
Mathematical Tool ◽  
Variational Iteration ◽  
Alternative Approach

Although a variational iteration algorithm was proposed by Yildirim (Math. Prob. Eng. 2008 (2008), Article ID 869614) that successfully solves differential-difference equations, the method involves some repeated and unnecessary iterations in each step. An alternative iteration algorithm (variational iteration algorithm-II) is constructed in this paper that overcomes this shortcoming and promises to provide a universal mathematical tool for many differential-difference equations.

scholarly journals On the Numerical Solution of Differential-Algebraic Equations with Hessenberg Index-3

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Melike Karta ◽  
Ercan Çelik
Keyword(s):  
Exact Solutions ◽  
Numerical Solution ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Variational Iteration

Numerical solution of differential-algebraic equations with Hessenberg index-3 is considered by variational iteration method. We applied this method to two examples, and solutions have been compared with those obtained by exact solutions.

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