Difference Scheme

Finite difference method is a numerical method for approximating the solution to partial differential equations. In this chapter, six commonly used methods for constructing difference schemes are introduced, including Taylor series expansion, method of polynomial interpolation, being-determined coefficient method, integral methods, method of characteristics, and control volume method. We provide an example of a one-dimensional advection equation to illustrate the process. By understanding these methods and concepts, researchers can apply them to other partial differential equations and develop accurate approximate solutions. At the end of this chapter, we give a brief introduction to the difference operator which is a convenient symbol for representing these difference schemes.