Finite Difference Methods For Three-order Nonlinear KdV Equation

The thesis as below gives a new nonlinear finite difference formulas for KdV equation, and we design two finite differnce methods using these nonlinear finite differnce formulas and classic explicit scheme and implicit scheme: one is an alternating segment explicit-implicit difference method, and the other is group difference method. And analyzes stability of these methods: which shows these methods are linear stable and have the advantages of parallel computing. We give the numerical examples for alternating segment explicit-implicit difference scheme, and which shows the method is suitable for computing, and can approach the exact solution better.The thesis is composed of three chapters as shown below:Chapter One is the preface, which mainly introduces the characters of some effective numerical methods for KdV equation and two methods given in this thesis.Chpater Two is composed of seven parts.Part One gives the mathematical model as below, which is the initial and boundary problem of the general form of the KdV equation. And makes grid discretization of the domain. In the thesis h and r denote the step length of space and time respectively.initial values:...