Differential operator

methods were first applied to option pricing by Eduardo Schwartz in1977. In general, finite difference methods are used to price options by approximating the differential equation that describes how the option price moves over time by a set of difference equations. This method arises since the option value can be modeled by partial differential equations, such as the Black-Scholes PDE. This approach has the same level of complexity tree methods. The application of Monte Carlo method to option pricing

plane wall of thickness L that is insulated on one side and subject to convection on the other. The conduction is governed by the differential heat equation: u_t=∝u_xx (1) Here, u signifies the temperature of the entire body and ∝ signifies the thermal diffusivity. Furthermore, the differential heat equation above must respect the following boundary conditions: u_x |_(x=0)=0 -ku_x |_(x=L)=h(u|-T_∞) u|_(t=0)=T_i In the above

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

A flat plate solar collector has a dynamic behaviour in response to variations in the intensity of solar radiation at different times of the day and also variations in weather conditions. The characteristics governing the input-output behaviour of a flat plate collector can be described by a mathematical model which serves as a prerequisite for simulation and control. The steady state and transient characteristics of flat plate solar collectors have been studied in \cite{Hilmer1999Solar,Dhariwal2005Solar

with lumped parameter models. Finally, lumped parameter models require modifications in their whole lumped model when changes in any system component occur. As already mentioned, distributed (modularized) models are solved by a set of partial differential equations due to all the dependent variables consist of more than one independent variable. However, these equations can be homogeneous or non-homogenous (inhomogeneous) equations. In practice, the solution of a homogeneous equation with the appropriate

Characterization of one-dimensional VAPEX Figure 1 shows a model of Vapex Process modeled in a vertical thin sandpack (cylindrical), which is saturated with heavy oil. Solvent Injector and oil producer are placed at the bottom of the sandpack. When solvent is injected, it moves upwards due to buoyancy and comes in contact with the heavy oil and heavy oil is extracted and diluted and drained downward by gravity force. We make these following assumptions for our 1D VAPEX Process: 1. We have 2 areas:

My general areas of interest are numerical modeling and tropical meteorology. For example, numerical simulation models of tropical cyclones is the problem that interest me most in atmospheric science. Based on one or two problems in tropical meteorology or related fields, I hope to work based on the existing models, and make unique contributions. My ultimate goal is to develop skills to become a sophisticated researcher and teacher in the field, while pursuing a doctorate degree in atmospheric sciences

a 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

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