scholarly journals He’s Max-Min Approach for Coupled Cubic Nonlinear Equations Arising in Packaging System

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Jun Wang
Keyword(s):  
Computer Simulation ◽  
Approximate Solution ◽  
Numerical Solution ◽  
Nonlinear Equations ◽  
High Accuracy ◽  
Packaging System ◽  
Novel Method ◽  
Runge Kutta

He’s inequalities and the Max-Min approach are briefly introduced, and their application to a coupled cubic nonlinear packaging system is elucidated. The approximate solution is obtained and compared with the numerical solution solved by the Runge-Kutta algorithm yielded by computer simulation. The result shows a great high accuracy of this method. The research extends the application of He’s Max-Min approach for coupled nonlinear equations and provides a novel method to solve some essential problems in packaging engineering.

scholarly journals He Chengtian’s Inequalities for a Coupled Tangent Nonlinear System Arisen in Packaging System

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Jun Wang ◽  
Zhi-geng Fan ◽  
Li-xin Lu ◽  
An-jun Chen ◽  
Zhi-wei Wang
Keyword(s):  
Computer Simulation ◽  
Approximate Solution ◽  
Nonlinear System ◽  
High Accuracy ◽  
Packaging System ◽  
Suggested Approach ◽  
Novel Method

He Chengtian’s inequalities from ancient Chinese algorithm are applied to strong tangent nonlinear packaging system. The approximate solution is obtained and compared with the solution yielded by computer simulation, showing a great high accuracy of this method. The suggested approach provides a novel method to solve some essential problems in packaging engineering.

scholarly journals Solutions of the Force-Free Duffing-van der Pol Oscillator Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Muhammad Jamil ◽  
Syed Anwar Ali ◽  
Nadeem Alam Khan
Keyword(s):  
Approximate Solution ◽  
Numerical Solution ◽  
Approximate Method ◽  
Governing Equation ◽  
Laplace Transformation ◽  
Large Time ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Alternative Framework ◽  
Runge Kutta

A new approximate method for solving the nonlinear Duffing-van der pol oscillator equation is proposed. The proposed scheme depends only on the two components of homotopy series, the Laplace transformation and, the Padé approximants. The proposed method introduces an alternative framework designed to overcome the difficulty of capturing the behavior of the solution and give a good approximation to the solution for a large time. The Runge-Kutta algorithm was used to solve the governing equation via numerical solution. Finally, to demonstrate the validity of the proposed method, the response of the oscillator, which was obtained from approximate solution, has been shown graphically and compared with that of numerical solution.

A Novel Method of Spike Detection for Interferograms Based on Two-Step Filtering

2014 ◽  
Vol 599-601 ◽  
pp. 1364-1368
Author(s):  
Yao Pu Zou ◽  
Chang Pei Han ◽  
Lei Zhang ◽  
Wen Gui Pan ◽  
Chao Wang
Keyword(s):  
Computer Simulation ◽  
Theoretical Analysis ◽  
Detection Method ◽  
High Accuracy ◽  
Spike Detection ◽  
Novel Method

According to the characteristics of interferogram, we design a new spike detection method, which firstly filters an interferogram with two different ways and then detects spikes based on both results. Theoretical analysis and computer simulation shows that this algorithm performs well in detecting spikes in any position of an interferogram with high accuracy, and can be easily implemented in hardware.

scholarly journals Phase Fitted And Amplification Fitted Of Runge-Kutta-Fehlberg Method Of Order 4(5) For Solving Oscillatory Problems

2020 ◽  
Vol 17 (2(SI)) ◽  
pp. 0689
Author(s):  
Mohammed Salih ◽  
Fudziah Ismail ◽  
Norazak Senu
Keyword(s):  
Periodic Solution ◽  
Approximate Solution ◽  
Numerical Solution ◽  
Present Method ◽  
Phase Lag ◽  
Real Solution ◽  
Oscillatory Solutions ◽  
Dispersion Error ◽  
Recent Method ◽  
Runge Kutta

In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method.

scholarly journals NUMERICAL SOLUTION FOR IMMUNOLOGY TUBERCULOSIS MODEL USING RUNGE KUTTA FEHLBERG AND ADAMS BASHFORTH MOULTON METHOD

2016 ◽  
Vol 78 (5) ◽  
Author(s):  
Usman Pagalay ◽  
Muhlish Muhlish
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Relative Error ◽  
Nonlinear Differential Equations ◽  
High Accuracy ◽  
First Order ◽  
Tuberculosis Model ◽  
Runge Kutta

The Immunology tuberculosis model that has been formulated by (Ibarguen, E., Esteva, L., & Chavez, L, 2011) in the form of a system of nonlinear differential equations first order. In this study, we used to Runge Kutta Fehlberg method and Adams Bashforth Moulton method. This study has been obtained numerical solution of the model. The results showed that the relative error obtained from the Adams Bashforth Moulton method is smaller when compared with the Runge Kutta Fehlber method. There are two methods has a high accuracy in solving systems of nonlinear differential equations.

scholarly journals A constructive method for an approximate solution to scalar Wiener–Hopf equations

2013 ◽  
Vol 469 (2154) ◽  
pp. 20120721 ◽  
Author(s):  
Anastasia V. Kisil
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Numerical Solution ◽  
Error Bounds ◽  
Real Line ◽  
Unit Interval ◽  
Constructive Method ◽  
Hopf Equation ◽  
Numerical Examples ◽  
Novel Method

This paper presents a novel method of approximating the scalar Wiener–Hopf equation, and therefore constructing an approximate solution. The advantages of this method over the existing methods are reliability and explicit error bounds. Additionally, the degrees of the polynomials in the rational approximation are considerably smaller than in other approaches. The need for a numerical solution is motivated by difficulties in computation of the exact solution. The approximation developed in this paper is with a view of generalization to matrix Wiener–Hopf problems for which the exact solution, in general, is not known. The first part of the paper develops error bounds in L p for . These indicate how accurately the solution is approximated in terms of how accurately the equation is approximated. The second part of the paper describes the approach of approximately solving the Wiener–Hopf equation that employs the rational Carathéodory–Fejér approximation. The method is adapted by constructing a mapping of the real line to the unit interval. Numerical examples to demonstrate the use of the proposed technique are included (performed on C hebfun ), yielding errors as small as 10 −12 on the whole real line.

scholarly journals Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yanqin Liu
Keyword(s):  
Approximate Solution ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Nonlinear Equations ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Transformation Method ◽  
High Accuracy ◽  
Homotopy Perturbation ◽  
He’S Polynomials

A homotopy perturbation transformation method (HPTM) which is based on homotopy perturbation method and Laplace transform is first applied to solve the approximate solution of the fractional nonlinear equations. The nonlinear terms can be easily handled by the use of He's polynomials. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.

Sign in / Sign up

Export Citation Format

Share Document