单物种人口模型指数隐式Euler方法的振动性

本文研究了用以描述单物种人口模型的延迟Logistic方程的数值振动性.对方程应用隐式Euler方法进行求解,针对离散格式定义了指数隐式Euler方法,证明了该方法的收敛阶为1.根据线性振动性理论获得了数值解振动的充分条件.进而还对非振动数值解的性质作了讨论.最后用数值算例对理论结果进行了验证.

OSCILLATIONS OF EXPONENTIAL IMPLICIT EULER METHOD FOR A SINGLE SPECIES POPULATION MODEL

In this paper, we consider the oscillations of numerical solutions for the delay logistic equation which is used to describe the single species population model. Applying the implicit Euler method to this model, exponential implicit Euler method is defined according to the corresponding discrete scheme. It is proven that the exponential implicit Euler method is of order 1. The sufficient conditions under which the numerical solutions oscillate are obtained by the linearized oscillation theory. Furthermore, the property of every non-oscillatory numerical solution is studied. Finally, some numerical examples are given to test the theoretical results.