scholarly journals Approximate Analytical Solutions For Time-Dependent Emden-Fowler-Type Equations By Variational Iteration Method

2007 ◽  
Vol 4 (7) ◽  
pp. 439-443 ◽  
Author(s):  
Khaled Batiha
Keyword(s):  
Analytical Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Time Dependent ◽  
Variational Iteration ◽  
Approximate Analytical Solutions

scholarly journals Fractional Black-Scholes model with regularized Prabhakar derivative

2017 ◽  
Vol 102 (116) ◽  
pp. 121-132 ◽  
Author(s):  
Shiva Eshaghi ◽  
Alireza Ansari ◽  
Reza Ghaziani ◽  
Mohammadreza Darani
Keyword(s):  
Analytical Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
European Options ◽  
Variational Iteration ◽  
Black Scholes Model ◽  
Approximate Analytical Solutions ◽  
Black Scholes ◽  
Fractional Type

We introduce a fractional type Black-Scholes model in European options including the regularized Prabhakar derivative. We apply the reconstruction of variational iteration method to get the approximate analytical solutions for some models of generalized fractional Black-Scholes equations in terms of the generalized Mittag-Leffler functions.

scholarly journals APPLICATION OF ABOODH TRANSFORM ON SOME FRACTIONAL ORDER MATHEMATICAL MODELS

2020 ◽  
Vol 20 (3) ◽  
pp. 661-672
Author(s):  
JAWARIA TARIQ ◽  
JAMSHAD AHMAD
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Physical Phenomena ◽  
Convergent Solution

In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.

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.

A NEWLY MODIFIED VARIATIONAL ITERATION METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS

2013 ◽  
Vol 10 (05) ◽  
pp. 1350029
Author(s):  
R. YULITA MOLLIQ ◽  
M. S. M. NOORANI
Keyword(s):  
Iteration Method ◽  
Nonlinear Differential Equations ◽  
Method Comparison ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Accurate Method ◽  
Convergence Region ◽  
Variational Iteration ◽  
Approximate Analytical Solutions ◽  
Modified Variational Iteration Method

This paper presents a new reliable modification of the variational iteration method (MoVIM). An enlarged interval of convergence region of series solutions is obtained by inserting a nonzero auxiliary parameter (ℏ) into the correction functional of variational iteration method. Approximate analytical solutions for some examples of nonlinear problems are obtained using variational iteration method. Comparison with the exact solution, Runge–Kutta method 4, and also another modified variational iteration method has shown that MoVIM is an accurate method for solving nonlinear problems.

scholarly journals Analytical solutions of time-fractional advection problem

2016 ◽  
Vol 12 (6) ◽  
pp. 6286-6289
Author(s):  
Huimin Wang
Keyword(s):  
Analytical Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
The Other ◽  
Variational Iteration

we use variational iteration method (VIM) to solve some nonlinear time-fractional advection problem.Compared to the other method, the VIM is direct and straightforward.

scholarly journals Study of the Nonlinear Dropping Shock Response of Expanded Foam Packaging System

2013 ◽  
Vol 2013 ◽  
pp. 1-3
Author(s):  
Huan-xin Jiang ◽  
Yong Zhu ◽  
Li-xin Lu
Keyword(s):  
Numerical Simulation ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Equation Of Motion ◽  
High Accuracy ◽  
Packaging System ◽  
First Order ◽  
Approximate Analytical Solutions ◽  
Shock Response

The variational iteration method-2 (VIM-2) is applied to obtain approximate analytical solutions of EPS foam cushioning packaging system. The first-order frequency solution of the equation of motion was obtained and compared with the numerical simulation solution solved by the Runge-Kutta algorithm. The results showed the high accuracy of this VIM with convenient calculation.

Identifying a time-dependent heat source with nonlocal boundary and overdetermination conditions by the variational iteration method

2014 ◽  
Vol 24 (7) ◽  
pp. 1545-1552 ◽  
Author(s):  
Guanglu Zhou ◽  
Boying Wu
Keyword(s):  
Exact Solution ◽  
Heat Source ◽  
Iteration Method ◽  
Numerical Technique ◽  
Nonlocal Boundary ◽  
Variational Iteration Method ◽  
Time Dependent ◽  
Successive Approximations ◽  
Content Type ◽  
Variational Iteration

Purpose – The purpose of this paper is to investigate the inverse problem of determining a time-dependent heat source in a parabolic equation with nonlocal boundary and integral overdetermination conditions. Design/methodology/approach – The variational iteration method (VIM) is employed as a numerical technique to develop numerical solution. A numerical example is presented to illustrate the advantages of the method. Findings – Using this method, we obtain the exact solution of this problem. Whether or not there is a noisy overdetermination data, our numerical results are stable. Thus the VIM is suitable for finding the approximation solution of the problem. Originality/value – This method is based on the use of Lagrange multipliers for the identification of optimal values of parameters in a functional and gives rapidly convergent successive approximations of the exact solution if such a solution exists.

The Combined Laplace-Variational Iteration Method for Partial Differential Equations

2013 ◽  
Vol 14 (2) ◽  
Author(s):  
M. Matinfar ◽  
M. Saeidy ◽  
M. Ghasemi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Partial Differential ◽  
Transform Method ◽  
Variational Iteration ◽  
Approximate Analytical Solutions ◽  
The Laplace Transform

AbstractIn this paper, the Laplace transform Variational Iteration Method (LVIM) is employed to obtain approximate analytical solutions of the linear and nonlinear partial differential equations. This method is a combined form of the Laplace transform method and the Variational Iteration Method. The proposed scheme, finds the solutions without any discretization or restrictive assumptions and is free from round-off errors and therefore, reduces the numerical computations to a great extent. Some illustrative examples are presented and the numerical results show that the solutions of the LVIM are in good agreement with the exact solution.

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