scholarly journals The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method

2008 ◽  
Vol 345 (1) ◽  
pp. 476-484 ◽  
Author(s):  
Mustafa Inc
Keyword(s):  
Exact Solutions ◽  
Iteration Method ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Burgers Equations ◽  
Variational Iteration ◽  
Space And Time

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.

Application of Variational Iteration Method for nth-Order Integro-Differential Equations

2009 ◽  
Vol 64 (7-8) ◽  
pp. 439-444 ◽  
Author(s):  
Said Abbasbandy ◽  
Elyas Shivanian
Keyword(s):  
Differential Equations ◽  
Iteration Method ◽  
Initial Conditions ◽  
Initial Approximation ◽  
Variational Iteration Method ◽  
Integrodifferential Equations ◽  
Variational Iteration

AbstractIn this paper, the variational iteration method is proposed to solve Fredholm’s nth-order integrodifferential equations. The initial approximation is selected wisely which satisfies the initial conditions. The results reveal that this method is very effective and convenient in comparison with other methods.

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 Approximate Solution of Linear Fuzzy Initial Value Problems Using Modified Variaional Iteration Method

2021 ◽  
Vol 24 (4) ◽  
pp. 32-39
Author(s):  
Hussein M. Sagban ◽  
◽  
Fadhel S. Fadhel ◽  
Keyword(s):  
Approximate Solution ◽  
Rate Of Convergence ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

The main objective of this paper is to solve fuzzy initial value problems, in which the fuzziness occurs in the initial conditions. The proposed approach, namely the modified variational iteration method, will be used to find the solution of fuzzy initial value problem approximately and to increase the rate of convergence of the variational iteration method. From the obtained results, as it is expected, the approximate results of the proposed method are more accurate than those results obtained without using the modified variational iteration method.

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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