小波分析在人口控制中的应用

The Application by Wavelets for Populations Developing Equation

本文中我们利用小波分析方法来获得人口发展方程的逼近解,首先,我们将非齐次边界条件的连续人口发展方程转化为带齐次边界条件的问题,然后我们关于t将之离散化,同时我们也给出了Daubechie的正交小波的性质以有助于我们获得逼近解。最后我们给出了解决此问题的迭代方法。

In this paper, We discuss the approximate solution of population evolution equation by applying the wavelet analysis. First, we reduce the nonhomogcneous boundary condition of continuous papulation evolution equation to the homogeneous boundary condition, and then, we discrete the problem about the solution to equation of population evolution about the time-variable t using the semi-implicit scheme. At the same time, We discuss the porperties of Daubechies' Orthonormal compactly supported wavelet bases which we will use to obtain the approximate solution. A modified wavelet bases is obtained and the approximation theorem of this modified bases is established. Finally, an interation scheme for obtaining the wavelet approximate solution to our problem is constructed.