Ordinary differential equation

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

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

On contrary flexible robot position is not constant and hence partial differential equation is used to represent the distributed nature of position. Further due to sudden change in payload there may be a large variation in manipulator parameters. Thus control with constant gain controllers is difficult and adaptive methods must be

function of a single independent variable. This reduces the partial differential equation to a system of ordinary differential equations, each being a function of a single independent variable. For the transient conduction in a plain wall, the dependent variable is the solution function θ(X, F0), which is expressed in terms of θ(X, F0) = F(X)G(t), and the application of this method results in to the two ordinary differential equations, one in terms of X and the other one in F0. Now we demonstrate

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

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

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

For example, Tartaglia’s formula for a cubic equation x^3=x gives the solution as 1/√3 ((√(-1))^(1/3)+1/(√(-1))^(1/3) ).

In this chapter, we construct stochastic model for energy spot price by using e of Ordinary Least Square Regression Model. At this point, it is imperative to discuss seasonality, which is a commonly observed characteristic in energy markets. In order to assess whether there is actually an underlying pattern prevailing in the return an autocorrelation test can be easily carried out for verification. As explained in [10], the evidence of high autocorrelation manifests an underlying seasonality. On