scholarly journals Lorenz and Lotka-Volterra Equations Using MATLAB Resolution

2021 ◽  
Author(s):  
Aymen Labidi
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Dynamic System ◽  
Volterra Equations ◽  
Explicit Formulas ◽  
Predator Prey ◽  
Rates Of Change ◽  
Engineering Physics ◽  
Physical Quantities

In Mathematics, a differential equation is an equation that relates one or more functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.Mainly the study of differential equations consists of the study of their solutions, and of the properties of their solutions.Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.In our report, we are interested by the resolution of two differential equations, the famous Lorenz dynamic system which was developped to understand the chaotic character of meteorology, and the Predator prey model.In the folowwing report, we are going to resolve these equations in order to understand their meanings using Matlab, but first of all, we should introduce each problem, then develop and explain both mathematical and numerical issues, our main goal is to resolve these systems with an adequate Matlab formulation, using the ode45 function and finally we should discuss the results.

scholarly journals Two-Parametric Conditionally Oscillatory Half-Linear Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Ondřej Došlý ◽  
Simona Fišnarová
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Linear Differential Equations ◽  
Explicit Formulas ◽  
Linear Differential

We study perturbations of the nonoscillatory half-linear differential equation(r(t)Φ(x'))'+c(t)Φ(x)=0,Φ(x):=|x|p-2x,p>1. We find explicit formulas for the functionsr̂,ĉsuch that the equation[(r(t)+λr̂(t))Φ(x')]'+[c(t)+μĉ(t)]Φ(x)=0is conditionally oscillatory, that is, there exists a constantγsuch that the previous equation is oscillatory ifμ-λ>γand nonoscillatory ifμ-λ<γ. The obtained results extend the previous results concerning two-parametric perturbations of the half-linear Euler differential equation.

Discussion on the Complicated Topological Dynamic System of Ordinary Differential Equation (ODE)

2014 ◽  
Vol 696 ◽  
pp. 30-37
Author(s):  
Yun Xia Wang
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Dynamic System ◽  
Closed Form ◽  
Topological Dynamic ◽  
Autonomous Differential Equations

The dynamical system of ODEs is about closed-form researches into the field of ODEs from the perspective of dynamical systems. This paper, starting with the research of path in autonomous differential equations and discussion on Poincaré’s viewpoints, probes into the complicated topological dynamic system of ODEs.

Dengue and Chikungunya simulating model with mosquito periodic mortality rate

2017 ◽  
pp. 2919-2931
Author(s):  
Oscar A. Manrique A. ◽  
Steven Raigosa O. ◽  
Dalia M. Munoz P. ◽  
Mauricio Ropero P. ◽  
Anibal Munoz L. ◽  
...  
Keyword(s):  
Differential Equation ◽  
Mortality Rate ◽  
Differential Equations ◽  
Dynamic System ◽  
Ordinary Differential Equations ◽  
Equation System ◽  
Nonlinear Ordinary Differential Equations ◽  
Differential Equation System ◽  
Infectious Process ◽  
Population Mortality

A dynamic system of nonlinear ordinary differential equations to display the infectious process of Dengue-Chikungunya, is presented. The system including a mosquito periodic mortality rate and simulations of the differential equation system by MATLAB software to determine the effect of climatic variables (temperature, humidity, pluviosity) in the infectious population mortality, is carried out.

scholarly journals Solving Differential Equation by Modified Genetic Algorithms

2018 ◽  
Vol 26 (10) ◽  
pp. 233-241
Author(s):  
Eman Ali Hussain ◽  
Yahya Mourad Abdul – Abbass
Keyword(s):  
Differential Equation ◽  
Genetic Algorithm ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Mathematical Equation ◽  
Individual Solution ◽  
Result Show ◽  
String Representation ◽  
Derivatives Of ◽  
Physical Quantities

   Differential equation is a mathematical equation which contains the derivatives of a variable, such as the equation which represent physical quantities, In this paper  we introduced modified on the method which proposes a polynomial to solve the ordinary differential equation (ODEs) of second order and by using the evolutionary algorithm to find the coefficients of the propose a polynomial [1] . Our method propose a polynomial to solve the ordinary differential equations (ODEs) of nth  order and partial differential equations(PDEs) of order two  by using the Genetic algorithm to find the coefficients of the propose a polynomial ,since Evolution Strategies (ESs) use  a string representation of the solution to some problem and attempt to evolve a good solution through a series of fitness –based evolutionary steps .unlike (GA)  ,an ES will typically not use a population of solution but instead will make a sequence of mutations of an individual solution ,using fitness as a guide[2] . A numerical example with good result show the accuracy of our method compared with some existing methods .and the best error of method it’s not much larger than the error in best of the numerical method solutions.

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.   

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kusano Takaŝi ◽  
Jelena V. Manojlović
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Continuous Function ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Regular Variation ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Positive Continuous Function ◽  
Linear Differential

AbstractWe study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation(p(t)\lvert x^{\prime}\rvert^{\alpha}\operatorname{sgn}x^{\prime})^{\prime}+q(% t)\lvert x\rvert^{\alpha}\operatorname{sgn}x=0,where q is a continuous function which may take both positive and negative values in any neighborhood of infinity and p is a positive continuous function satisfying one of the conditions\int_{a}^{\infty}\frac{ds}{p(s)^{1/\alpha}}=\infty\quad\text{or}\quad\int_{a}^% {\infty}\frac{ds}{p(s)^{1/\alpha}}<\infty.The asymptotic formulas for generalized regularly varying solutions are established using the Karamata theory of regular variation.

scholarly journals Oscillation and non-oscillation of some neutral differential equations of odd order

1992 ◽  
Vol 15 (3) ◽  
pp. 509-515 ◽  
Author(s):  
B. S. Lalli ◽  
B. G. Zhang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solution ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
Neutral Term ◽  
Odd Order ◽  
Existence Criterion ◽  
Oscillation Of Solutions

An existence criterion for nonoscillatory solution for an odd order neutral differential equation is provided. Some sufficient conditions are also given for the oscillation of solutions of somenth order equations with nonlinearity in the neutral term.

scholarly journals Enhancing Accuracy of Runge–Kutta-Type Collocation Methods for Solving ODEs

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 174
Author(s):  
Janez Urevc ◽  
Miroslav Halilovič
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Integration ◽  
Integral Form ◽  
Collocation Methods ◽  
Nonlinear Odes ◽  
New Class ◽  
New Methods ◽  
Runge Kutta

In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration of ordinary differential equations (ODEs) is presented. Its derivation is based on the integral form of the differential equation. The approach enables enhancing the accuracy of the established collocation Runge–Kutta methods while retaining the same number of stages. We demonstrate that, with the proposed approach, the Gauss–Legendre and Lobatto IIIA methods can be derived and that their accuracy can be improved for the same number of method coefficients. We expressed the methods in the form of tables similar to Butcher tableaus. The performance of the new methods is investigated on some well-known stiff, oscillatory, and nonlinear ODEs from the literature.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

Sign in / Sign up

Export Citation Format

Share Document