Year of Graduation
Numerical Modeling of Soliton Dynamics in the Frame of the Schrödinger Equation
This paper explorers the process of numerical simulation by the example of the extended nonlinear Schrödinger equation. The aim is numerical simulation of soliton dynamics of the extended nonlinear Schrödinger equation. As part of this goal were formulated following tasks: learning the basic principles of numerical modeling, selection of methods for the solution of the physical problem, the numerical results obtained by using special mathematical environments, displaying the data in the form of graphs and their subsequent testing and analysis.In this paper, there are three chapters. The first chapter describes in detail each of the stages of mathematical modeling. Are examples of mathematical models. The second chapter discusses the various means to implement the numerical model. Describes their advantages and disadvantages. We study the problem of selection of numerical methods depending on the type of mathematical problems. The third chapter discusses the above equation finite difference method using the Runge-Kutta method and its modifications - Merson. Performed a numerical solution of the problem with the help of mathematical environments Maple and MATLAB. The results are compared with analytical. Held description numerical methods for solving the nonlinear Schrödinger equation used in various scientific papers.In the course of work demonstrates some features such mathematical environments such as MATLAB and Maple. Studied and applied in practice their basic tools for solving differential equations. Identifies the main positive and negative characteristics of each of these environments.The result of this work is settled numerically extended nonlinear Schrodinger equation in different mathematical environments. Provided visualization of numerical and analytical solutions. Revealed that the obtained numerical results agree with the analytical solution. Also investigated ways of solving the nonlinear Schrödinger equation used in various scientific papers.