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.

scholarly journals Application of Homotopy Perturbation Method with an Auxiliary Term for Nonlinear Dropping Equations Arisen in Polymer Packaging System

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Xiang Hong ◽  
Jun Wang ◽  
Li-xin Lu
Keyword(s):  
Numerical Simulation ◽  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Equation Of Motion ◽  
High Accuracy ◽  
Second Order ◽  
Packaging System ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions

The homotopy perturbation method (HPM) with an auxiliary term was applied to obtain approximate analytical solutions of polymer cushioning packaging system. The second-order 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 modified HPM with convenient calculation.

scholarly journals On linear and nonlinear fractional PDEs

2013 ◽  
Vol 40 (4) ◽  
pp. 511-524
Author(s):  
Jamshad Ahmad ◽  
Hassany ul ◽  
Syed Mohyud-Din
Keyword(s):  
Exact Solution ◽  
Fractional Derivative ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Nonlinear Partial Differential Equations ◽  
Variational Iteration Method ◽  
High Accuracy ◽  
New Approach ◽  
Fractional Pdes ◽  
Linear And Nonlinear

In this study, Variational Iteration Method (VIM) has been applied to obtain the analytical solutions of fractional order nonlinear partial differential equations. The iteration procedure is based on a relatively new approach which is called Jumarie?s fractional derivative. Several examples have been solved to elucidate effectiveness of the proposed method and the results are compared with the exact solution, revealing high accuracy and efficiency of the method.

scholarly journals Numerical iteration for nonlinear oscillators by Elzaki transform

2019 ◽  
Vol 39 (4) ◽  
pp. 879-884 ◽  
Author(s):  
Naveed Anjum ◽  
Muhammad Suleman ◽  
Dianchen Lu ◽  
Ji-Huan He ◽  
Muhammad Ramzan
Keyword(s):  
Numerical Simulation ◽  
Laplace Transform ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Nonlinear Oscillators ◽  
High Accuracy ◽  
Numerical Iteration ◽  
The Laplace Transform ◽  
Iteration Methods

Iteration methods are widely used in numerical simulation. This paper suggests the Elzaki transform in the variational iteration method for simple identification of the Lagrange multiplier. The Elzaki transform is a modification of the Laplace transform, and it is extremely useful for treating with nonlinear oscillators as illustrated in this paper, a single iteration leads to a high accuracy of the solution.

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.

Sign in / Sign up

Export Citation Format

Share Document