对Logistic方程的非标准有限差分法

Solving Logistic Equation by Nonstandard Finite Difference Method

对Logistic方程运用非标准有限差分法(NSFDM),根据解对初值的单调性和解的单调性两种类型的单调性质讨论了差分方法的稳定性和初等稳定性。并运用数值试验进行了验证。对于离散系统得到了与连续系统相一致的结果。

By Nonstandard Finite Difference Method we study Logistic Equation. According to two types of the monotonous properties of finite difference method, we discuss the stability and primary stability of the difference scheme. Finally, numerical examples are provided to illustrate the theoretical results. The difference equation is dynamically consistent with continuous system.