scholarly journals Systematic Review of Geometrical Approaches and Analytical Integration for Chen’s System

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1530
Author(s):  
Remus-Daniel Ene ◽  
Camelia Pop ◽  
Camelia Petrişor
Keyword(s):  
Systematic Review ◽  
Approximate Solution ◽  
Numerical Simulations ◽  
Numerical Solution ◽  
Asymptotic Method ◽  
Analytical Integration ◽  
Optimal Homotopy Asymptotic Method ◽  
Special Case

The main goal of this paper is to present an analytical integration in connection with the geometrical frame given by the Hamilton–Poisson formulation of a specific case of Chen’s system. In this special case we construct an analytic approximate solution using the Multistage Optimal Homotopy Asymptotic Method (MOHAM). Numerical simulations are also presented in order to make a comparison between the analytic approximate solution and the corresponding numerical solution.

On two dimensional electrohydrostatic stability

1976 ◽  
Vol 349 (1657) ◽  
pp. 231-243 ◽  
Keyword(s):  
Approximate Solution ◽  
Numerical Solution ◽  
Edge Effects ◽  
Complex Variable ◽  
Equilibrium Configuration ◽  
Quantitative Agreement ◽  
Two Dimensional ◽  
Equilibrium Conditions ◽  
Conducting Membranes ◽  
Special Case

Complex variable techniques are used for the study of the electrohydrostatic stability of two dimensional charged conducting membranes, which are assumed to be fixed along their edges. The formulation of the problem is quite general, but the numerical solution presented refers to the case when the membranes are symmetrical with respect to the plane bisecting their width and carry equal and opposite charges. It is found, as expected, that for a given set of data the equilibrium configuration breaks down if the membranes are sufficiently charged. When the membranes are sufficiently apart the breakdown occurs at their edges and is manifested as inability of the system to satisfy the equilibrium conditions there. When the membranes are sufficiently close together and are charged to a certain level, they touch at their mid-points and the equilibrium breaks down. Our results are compared with an approximate solution of this problem, presented by two other authors. The approximate solution ignores the edge effects of the membranes and overestimates the amount of charge that the membranes can carry before breakdown occurs. In the special case when the gap between the membranes is much less than their width, our results are in quantitative agreement with the approximate solution but as the gap between the membranes increases, the accuracy of the approximate solution decreases.

scholarly journals Approximate Solution of Nonlinear System of BVP Arising in Fluid Flow Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
A. K. Alomari ◽  
N. Ratib Anakira ◽  
A. Sami Bataineh ◽  
I. Hashim
Keyword(s):  
Fluid Flow ◽  
Approximate Solution ◽  
Nonlinear System ◽  
Boundary Value Problems ◽  
Asymptotic Method ◽  
Series Solution ◽  
Flow Problem ◽  
Point Boundary ◽  
Optimal Homotopy Asymptotic Method ◽  
First Time

We extend for the first time the applicability of the Optimal Homotopy Asymptotic Method (OHAM) to find approximate solution of a system of two-point boundary-value problems (BVPs). The OHAM provides us with a very simple way to control and adjust the convergence of the series solution using the auxiliary constants which are optimally determined. Comparisons made show the effectiveness and reliability of the method.

scholarly journals Optimal homotopy asymptotic method to large post-buckling deformation of MEMS

2018 ◽  
Vol 148 ◽  
pp. 13003 ◽  
Author(s):  
Nicolae Herisanu ◽  
Vasile Marinca
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Approximate Method ◽  
Excellent Agreement ◽  
Electrostatic Field ◽  
Asymptotic Method ◽  
Integro Differential Equation ◽  
Analytical Results ◽  
Post Buckling ◽  
Optimal Homotopy Asymptotic Method

In the present paper, the post-buckling response of an axially stressed clamped-clamped actuator, modeled as a beam and subjected to a symmetric electrostatic field is analyzed. An analytical approximate method, namely the Optimal Homotopy Asymptotic Method (OHAM) is applied to the governing nonlinear integro-differential equation. The analytical results obtained through the proposed procedure show excellent agreement with numerical solution, proving the validity of the proposed procedure, which is simple and easy to use.

scholarly journals Applications of OHAM and MOHAM for Fractional Seventh-Order SKI Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Jafar Biazar ◽  
Saghi Safaei
Keyword(s):  
Approximate Solution ◽  
Comparative Study ◽  
Exact Solutions ◽  
Asymptotic Method ◽  
Fractional Derivatives ◽  
Fractional Partial Differential Equations ◽  
Large Interval ◽  
Seventh Order ◽  
Optimal Homotopy Asymptotic Method ◽  
Ito Equation

In this article, a comparative study between optimal homotopy asymptotic method and multistage optimal homotopy asymptotic method is presented. These methods will be applied to obtain an approximate solution to the seventh-order Sawada-Kotera Ito equation. The results of optimal homotopy asymptotic method are compared with those of multistage optimal homotopy asymptotic method as well as with the exact solutions. The multistage optimal homotopy asymptotic method relies on optimal homotopy asymptotic method to obtain an analytic approximate solution. It actually applies optimal homotopy asymptotic method in each subinterval, and we show that it achieves better results than optimal homotopy asymptotic method over a large interval; this is one of the advantages of this method that can be used for long intervals and leads to more accurate results. As far as the authors are aware that multistage optimal homotopy asymptotic method has not been yet used to solve fractional partial differential equations of high order, we have shown that this method can be used to solve these problems. The convergence of the method is also addressed. The fractional derivatives are described in the Caputo sense.

Fractional modeling for prey and predator problem by using optimal homotopy asymptotic method

2020 ◽  
Vol 9 (2) ◽  
pp. 35
Author(s):  
Jafar Biazar ◽  
Saghi Safaei ◽  
Martin Tango
Keyword(s):  
Approximate Solution ◽  
Asymptotic Method ◽  
Population Model ◽  
Fractional Derivatives ◽  
Predator Population ◽  
Fractional Modeling ◽  
Optimal Homotopy Asymptotic Method

In this paper, a fractional-ordered prey and predator population model is introduced and applied to obtain an approximate solution with help of optimal homotopy asymptotic method (OHAM). Some plots for populations of the prey and the predator versus time are presented to show the efficiency and the accuracy of the method and confirm that the method is straightforward as well. The fractional derivatives are described in the Caputo sense. 

Sign in / Sign up

Export Citation Format

Share Document