Finite difference method
Finite difference method (FDM) is a numerical method for solving partial differential (or ordinary differential) equations or systems of equations. (Definite Solution Problems: Solutions to Problems that satisfy Definite Solution Conditions (Initial Value Conditions, Boundary Conditions)
The solution of differential equation in mathematical sense is different from that in physical sense. The solution of physical differential equation has time and space constraints.
Constraints can be subdivided into:
（1）The boundary of space domain and the definite solution conditions satisfied in internal space.
（2）If the problem is time-dependent, the initial solution condition must be satisfied.
The Solution of Finite Difference Method
Firstly, the solution domain is divided by grid (space discretization). Then, the partial differential equation is replaced by difference equation (display or implicit, forward difference, backward difference, center difference). If the equation is time-dependent, the time is also discretized, and the linear algebraic square of unknown function about grid points is obtained.Cheng.
Generally, a two-dimensional structured grid is used to divide the space into a grid of equal size. The increments of the grid in the X and Y directions are equal, and Delta h is used instead.