Backward numerical integration method for nonlinear system

Differential equation is a useful way to describe nonlinear systems. In general, integration is used to solve them, which is a forward method using current information to get the future information. In some special occasions where the system has a fix final condition and a free initial condition, a new kind of integration method with a backward direction is needed. This paper presents a new kind of numerical integration method solving nonlinear system which is called backward numerical integration method and it is analyzed by mathematics deduction. A comparative analysis quantifies the correctness and advantages of this integration method. As concluding remarks, the backward integration method is simple and reliable enough to solve those final condition fixed nonlinear systems.