Differential equation

they know this to be certain, mathematicians believe that by using math, specifically differential equations, they can predict how things such as population, the stock market, and the weather can be somewhat accurately predicted. In order to decide whether differential equations can predict future events, it is important to know exactly what a differential equation is. A differential equation is an equation involving derivatives of a function or functions.. The functions usually represent some

5.1 Linearization It can be seen clearly by the system’s equation that the model belongs to a nonlinear system. Normal differential equations can be created by the conversion of the system into state space model format. When a control law is designed, Lagrange equations of motion (9) are reformatted. To be able to carry this out, a state vector is introduced which is as follows. x= (θ θ ̇ )^T To be able to apply the LQR technique on the system, linearization is important. Therefore the nonlinear

CHAPTER 1 INTRODUCTION Definition of Differential Equation A differential equation is an equation which consists of derivatives or differentials of one or more dependent variables with respect to one or more independent variables (Abell & Braselton, 1996). Differential equation generally can be classified into two, which are ordinary differential equation and partial differential equation. If a differential equation consists of ordinary derivation of one dependent variable with respect to only one

Balanchard Differential Equation An ODE is an equation that contains ordinary derivatives of a mathematical function. Solutions to ODEs involve determining a function or functions that satisfy the given equation. This can entail performing an anti-derivative i.e. integrating the equation to find the function that best satisfies the differential equation. There are several techniques developed to solve ODEs so as to find the most satisfactory function. This discussion seeks to explore some of these

solving linear differential equations with variable coefficients. The solutions usually take the form of power series; this explains the name Power series method. We review some special second order ordinary differential equations. Power series Method is described at ordinary points as well as at singular points (which can be removed called Frobenius Method) of differential equations. We present a few examples on this method by solving special second order ordinary differential equations. Key words

HPM for Solving the Time-fractional Coupled Burger’s Equations Khadijah M. Abualnaja Department of Mathematics and Statistics, College of Science, Taif University, Taif, KSA dujam@windowslive.com ABSTRACT This paper is devoted to derive the explicit approximate solutions for the time-fractional (Caputo sense) coupled Burger’s equations with implementation of the homotopy perturbation method. The numerical results are compared with the exact solution at special cases of the fractional derivatives

Up to now if I gave you an equation, and asked you to solve it for x you would be, in general, looking for a value of x which solved the equation. Given: x^2+3x+2=0 You can solve this equation to find two values of x. I could also give you an equation which linked x and y explicitly, and you could find a relationship between the two which, given a value of x would give you a value of y. You’ve been doing this now for many years. Now we’re going to add a hugely powerful tool to our mathematical

Duffing Equation computationally. Key features of the chaos theory such as attractors, Poincarè sections and phase-space diagrams have been analysed and discussed. The programing language of choice for this experiment was Fortran 90, which has been written explicitly for the purposes of acquiring a chaotic system and solving the Duffing equation. Introduction The Duffing Oscillator named by the German electrical engineer Georg Duffing is a non-linear, second-order differential equation, periodically

action of the vector fields on $Diff(R^{N})$ is as first order partial differential operators since $V(Y).partial_{Y} f(Y)$ is considered as first order partial differential operators. vspace{0.5cm} The evolution of $fcircphi_{t}$ is given by egin{center} $ frac{d}{dt}(fcircphi_{t})=Vcirc fcircphi_{t}$ end{center} The above equation is an autonomous linear functional differential equation for $fcircphi_{t}$. Such equation has a solution $fcircphi_{t}=exp(tV)circ fcircphi_{t}$ as $phi_{0}=id$ Setting

Solow model is widely considered to be the standard neoclassical economic growth model which serves as the basis for understanding economic growth. I will first introduce the two basic equations that the Solow model is built around, discussing the main assumptions made along the way. I will then present the key equation of the Solow model and discuss its results and implications. I will then address why it is desirable to use log-linearization, and how it can be used to study the dynamics near the steady-state