scholarly journals The stability analysis of the market price using Lambert function method

2021 ◽  
Vol 61 ◽  
pp. 13-17
Author(s):  
Irma Jankauskienė ◽  
Tomas Miliūnas
Keyword(s):  
Differential Equation ◽  
Function Method ◽  
Market Price ◽  
Transcendental Equation ◽  
Price Stability ◽  
Lambert Function ◽  
Intensity Coefficient ◽  
Delay Argument ◽  
The Stability ◽  
Scalar Differential Equation

In this article we are going to analyze market price stability with different market intensity coefficient and delay argument values. Market price is described as a scalar differential equation with a delay argument. In order to find solutions for the transcendental equation we will use method based on Lambert function. We will present examples of the applications of the method.

τ-D Decomposition to the One Dimensional Delay Differential Equation by Fixed the Coefficient b<0

2013 ◽  
Vol 785-786 ◽  
pp. 1418-1422
Author(s):  
Ai Gao
Keyword(s):  
Differential Equation ◽  
Hopf Bifurcation ◽  
Delay Differential Equation ◽  
Stability Domain ◽  
Transcendental Equation ◽  
One Dimension ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Delay Differential

In this paper, we provide a partition of the roots of a class of transcendental equation by using τ-D decomposition ,where τ>0,a>0,b<0 and the coefficient b is fixed.According to the partition, one can determine the stability domain of the equilibrium and get a Hopf bifurcation diagram that can provide the Hopf bifurcation curves in the-parameter space, for one dimension delay differential equation .

STABILITY AND MULTIPLICITY OF PERIODIC OR ALMOST PERIODIC SOLUTIONS TO SCALAR FIRST-ORDER ODE

2006 ◽  
Vol 04 (03) ◽  
pp. 237-246 ◽  
Author(s):  
ALAIN HARAUX
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Monotonicity Property ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
First Order ◽  
Autonomous Equation ◽  
Stability Pattern ◽  
The Stability ◽  
Scalar Differential Equation

Using a monotonicity property specific to this case, we give a general property of the stability pattern of successive periodic solutions of the first-order scalar differential equation u′ = f(t, u). We also give an optimal smallness condition in order for the quasi-autonomous equation u′+g(u) = f(t) where g ∈ C1(ℝ) and f : ℝ → ℝ is almost periodic to have exactly N almost periodic solutions on the line assuming that we have exactly N equilibria ci and g′(ci) ≠ 0 for all i.

scholarly journals Almost periodic solutions for Abel equations

1997 ◽  
Vol 20 (4) ◽  
pp. 727-735
Author(s):  
Zeng Weiyao ◽  
Shi Jinlin ◽  
Lin Zhensheng ◽  
Lokenath Debnath
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Function Method ◽  
Liapunov Function ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Existence And Stability ◽  
Abel Equations ◽  
Scalar Differential Equation ◽  
Abel Differential Equations

Using the Liapunov function method, the existence of almost periodic solutions of a scalar differential equation is discussed The results for the scalar differential equation are then applied to prove the existence and stability of almost periodic solutions of Abel differential equations We obtain several interesting results which improve the results due to Chongyou [1] and Dongpin [2].

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

scholarly journals Even-order differential equation with continuous delay: nonexistence criteria of Kneser solutions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ali Muhib ◽  
M. Motawi Khashan ◽  
Osama Moaaz
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Delay Argument ◽  
Even Order ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this paper, we study even-order DEs where we deduce new conditions for nonexistence Kneser solutions for this type of DEs. Based on the nonexistence criteria of Kneser solutions, we establish the criteria for oscillation that take into account the effect of the delay argument, where to our knowledge all the previous results neglected the effect of the delay argument, so our results improve the previous results. The effectiveness of our new criteria is illustrated by examples.

Numerical Integration Method for Stability Analysis of Milling With Variable Spindle Speeds

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Ye Ding ◽  
Jinbo Niu ◽  
LiMin Zhu ◽  
Han Ding
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Numerical Integration ◽  
Integration Method ◽  
Transcendental Equation ◽  
Spindle Speed ◽  
Machining Parameters ◽  
Numerical Integration Method ◽  
Stability Diagrams ◽  
Time Period

A semi-analytical method is presented in this paper for stability analysis of milling with a variable spindle speed (VSS), periodically modulated around a nominal spindle speed. Taking the regenerative effect into account, the dynamics of the VSS milling is governed by a delay-differential equation (DDE) with time-periodic coefficients and a time-varying delay. By reformulating the original DDE in an integral-equation form, one time period is divided into a series of subintervals. With the aid of numerical integrations, the transition matrix over one time period is then obtained to determine the milling stability by using Floquet theory. On this basis, the stability lobes consisting of critical machining parameters can be calculated. Unlike the constant spindle speed (CSS) milling, the time delay for the VSS is determined by an integral transcendental equation which is accurately calculated with an ordinary differential equation (ODE) based method instead of the formerly adopted approximation expressions. The proposed numerical integration method is verified with high computational efficiency and accuracy by comparing with other methods via a two-degree-of-freedom milling example. With the proposed method, this paper details the influence of modulation parameters on stability diagrams for the VSS milling.

THE STABILITY ANALYSIS OF HEAT TRANSFER IN SATURATED LIQUID FILM OF THE SPECIAL MATERIALS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1547-1550
Author(s):  
YOULIANG CHENG ◽  
XIN LI ◽  
ZHONGYAO FAN ◽  
BOFEN YING
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Surface Tension ◽  
Stability Analysis ◽  
Liquid Film ◽  
Nonlinear Relationship ◽  
Saturated Liquid ◽  
Nonlinear Surface ◽  
Isothermal Wall ◽  
The Stability

Representing surface tension by nonlinear relationship on temperature, the boundary value problem of linear stability differential equation on small perturbation is derived. Under the condition of the isothermal wall the effects of nonlinear surface tension on stability of heat transfer in saturated liquid film of different liquid low boiling point gases are investigated as wall temperature is varied.

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