The Optimized White Differential Equation of GM(1,1) Based on the Original Grey Differential Equation

2012 ◽  
Vol 166-169 ◽  
pp. 2971-2975 ◽  
Author(s):  
Rui Zhou ◽  
Jun Jie Li ◽  
Yao Chen
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Prediction Accuracy ◽  
High Growth ◽  
Growth Index ◽  
Simulation Accuracy ◽  
Modeling And Prediction ◽  
Standard Index ◽  
Grey Differential Equation ◽  
The Relationship

This paper starting from the original grey differential equations, through finding the relationship between the raw data and the derivative of its , constructed a new white differential equation which equal to the original grey differential equation, at the same time, getting the new GM(1,1)model which closer to the changes of data. Through the modeling and prediction of the standard index series, this model not only adapts to low growth index series, but also adapts to high-growth index series, and the simulation accuracy and prediction accuracy are high.

scholarly journals Relation between Small Functions with Differential Polynomials Generated by Solutions of Linear Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Zhigang Huang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Entire Functions ◽  
Linear Differential Equations ◽  
Differential Polynomials ◽  
Small Functions ◽  
Linear Differential ◽  
The Relationship ◽  
Growth Of Solutions

This paper is devoted to studying the growth of solutions of second-order nonhomogeneous linear differential equation with meromorphic coefficients. We also discuss the relationship between small functions and differential polynomialsL(f)=d2f″+d1f′+d0fgenerated by solutions of the above equation, whered0(z),d1(z),andd2(z)are entire functions that are not all equal to zero.

G M (1,1) Optimization Model Re-Optimization

2012 ◽  
Vol 538-541 ◽  
pp. 2543-2547
Author(s):  
Yao Chen
Keyword(s):  
Differential Equation ◽  
Optimization Model ◽  
High Growth ◽  
Solution Algorithm ◽  
Grey Model ◽  
Practical Application ◽  
Simulation Accuracy ◽  
Growth Series ◽  
Gray Prediction ◽  
Basic Differential Equation

On the base of the basic differential equation, a new GM (1,1) model applying to non-homogenous index series was established by optimizing the background of original differential equation. Meanwhile, solution algorithm and efficiency of the optimization model was presented and verified in the paper respectively. The results showed that this nonlinear discrete gray prediction model significantly improves the simulation accuracy and is suitable for the non-homogeneous high-growth series. Therefore, our research has certain theory significance and the practical application value for simulation of grey model.

scholarly journals Differential equation model of financial market stability based on Internet big data

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hongling Chen ◽  
Bahjat Fakieh ◽  
Bishr Muhamed Muwafak
Keyword(s):  
Differential Equation ◽  
Big Data ◽  
Differential Equations ◽  
Financial Market ◽  
Equation Model ◽  
Differential Equation Model ◽  
Nonlinear Characteristics ◽  
Differential Equation Models ◽  
Financial Market Stability ◽  
The Relationship

Abstract In the context of Internet big data, the market characteristics of the financial market can be used to feed back its stability with the help of differential equation models. China's financial market is roughly divided into three main markets: stocks, currency and foreign exchange. The interaction of the three has promoted the development of the financial market. With this as a background, the paper aims at these three financial markets and selects relevant indicators that can reflect the indications of the financial market to construct differential equations to analyse the relationship between the three. The paper uses the nonlinear characteristics of ordinary differential equations and related algorithms to solve the three types of market models. It uses an example to demonstrate that the differential equation model proposed in this paper can feed back the evolutionary characteristics of the three, and this model can help investors produce more correct investment decisions.

scholarly journals Generalized Weierstrass Integrability of a Class of Second-order Nonlinear Differential Equations

2021 ◽  
pp. 119-133
Author(s):  
Xin Zhao ◽  
Yanxia Hu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Traveling Wave ◽  
Nonlinear Differential Equations ◽  
Traveling Wave Solutions ◽  
Second Order ◽  
Wave Solutions ◽  
The Relationship ◽  
Integrating Factors

The generalized Weierstrass integrability of a class of second-order nonlinear differential equations is considered. The conditions of existence and the corresponding expressions of generalized Weierstrass inverse integrating factors of the second-order nonlinear differential equation are presented. The relationship between the generalized Weierstrass inverse integrating factors and the Weierstrass inverse integrating factors is given. Finally, as an application of the main results, a Kudryashov-Sinelshchikov equation for obtaining traveling wave solutions is considered.

SYMBOLIC REPRESENTATION OF FORCED OSCILLATIONS OF BRANCHED MECHANICAL SYSTEMS

2021 ◽  
pp. 118-130
Author(s):  
I.P. Popov ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Time Instant ◽  
Forced Oscillations ◽  
Parallel Connections ◽  
Clear Idea ◽  
The Relationship

A calculation of dynamics of a mechanical system with n degrees of freedom, including inert bodies and elastic and damping elements, involves the derivation and integration of a system of n second-order differential equations, which are reduced to a differential equation of 2n order. An increase in the degree of freedom of the mechanical system by one increases the order of the resulting differential equation by two. The solution of higher-order differential equations is rather cumbersome and time-consuming. Integration of equations is proposed to be replaced with rather simpler algebraic methods. A number of relevant theorems that relate both active and reactive parameters of mechanical systems in the series and parallel connection of mechanical power consumers are proved. Using parallel-series and series-parallel connections as an example, the calculation methods for branched mechanical systems with any number of degrees of freedom, based on the use of symbolic or complex representation of forced harmonic oscillations, are shown. The phase relationships determining loading conditions and a possibility of its artificial change are considered. The vector diagrams of the amplitudes of forces, velocities and their components in a complex plane at a zero time instant are presented, which give a complete and clear idea of the relationship between these quantities.

scholarly journals On the Relationship between the Invariance and Conservation Laws of Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
A. H. Kara
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Conservation Laws ◽  
General Setting ◽  
Higher Order ◽  
Point Symmetry ◽  
Formal Procedure ◽  
Symmetry Generators ◽  
The Relationship

In this paper, we highlight the complimentary nature of the results of Anco & Bluman and Ibragimov in the construction of conservation laws that whilst the former establishes the role of multipliers, the latter presents a formal procedure to determine the flows. Secondly, we show that there is an underlying relationship between the symmetries and conservation laws in a general setting, extending the results of Kara & Mahomed. The results take apparently differently forms for point symmetry generators and higher-order symmetries. Similarities exist, to some extent, with a previously established result relating symmetries and multipliers of a differential equation. A number of examples are presented.

Application of Jacobi’s last multiplier for construction of Hamiltonians of certain biological systems

Open Physics ◽  
2012 ◽  
Vol 10 (2) ◽  
Author(s):  
A. Ghose Choudhury ◽  
Partha Guha
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Biological Systems ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Jacobi’S Last Multiplier ◽  
Systems Of Differential Equations ◽  
Hamiltonian Theory ◽  
The Relationship

AbstractThe relationship between Jacobi’s last multiplier and the Lagrangian of a second-order ordinary differential equation is quite well known. In this article we demonstrate the significance of the last multiplier in Hamiltonian theory by explicitly constructing the Hamiltonians of certain well known first-order systems of differential equations arising in biology.

scholarly journals Some Remarks on the Sumudu and Laplace Transforms and Applications to Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Adem Kiliçman ◽  
Hassan Eltayeb
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Laplace Transform ◽  
Laplace Transforms ◽  
Sumudu Transform ◽  
The Relationship

We study the relationship between Sumudu and Laplace transforms and further make some comparison on the solutions. We provide some counterexamples where if the solution of differential equations exists by Laplace transform, the solution does not necessarily exist by using the Sumudu transform; however, the examples indicate that if the solution of differential equation by Sumudu transform exists then the solution necessarily exists by Laplace transform.

Normalization Bernstein Basis For Solving Fractional Fredholm-Integro Differential Equation

2018 ◽  
pp. 491
Author(s):  
Abdul Khaleq O. Al-Jubory ◽  
Shaymaa Hussain Salih
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear System ◽  
Differential Equations ◽  
Bernstein Basis ◽  
Traditional Methods ◽  
Integro Differential Equation

In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations  nonhomogeneous  of the second type (LFFIDEs). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDEs) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDEs) by the assistance of Matlab10.   

Sign in / Sign up

Export Citation Format

Share Document