Finite Difference Methods And Simple Applications To Ordinary Differential Equations

This dissertation is concerned with finite difference methods and applications to ordinary differential equations. In many fields, such as natural science and social science, there are a large number of models which are ordinary differential equations with initial values. For long time, researchers pay attentions to the methods of solving ordinary differential equations. Unfortunately, there are few of ordinary differential equations to be solved, as well as many ordinary differential equations can not be solved. Also, the explicit solutions of ordinary differential equations sometimes are complicated, and not easy to use. Thus, there are needed to study numerical methods of solving ordinary differential equations.In fact, the finite difference method is one of the most useful and powerful methods to obtain approximation solutions of ordinary differential equations. The finite difference method is based on using difference quotient to replace derivative, and constructing difference iteration schemes, and gaining approximation solutions of ordinary differential equations. This method has wide applications to practical problems.This dissertation summarizes various numerical methods solving approximation solutions of ordinary differential equations, such as Euler Method, Runge-Kutta Method, Adams Extrapolation Method etc. The concreted examples are given to illustrate the validity of all kinds of methods.At last, a numerical simulation for Logistic equation modeled simple population with dense restriction is given and related analysis is presented.