Solution of the Sharpe-Lotka population model via a modified method of characteristics

摘要

The Sharpe-Lotka population model is well known in demography for examining the distribution of a population based on known birth and death rates. An analytical solution has been found for this model only for a portion of the domain of interest. This paper introduces an algorithm for computation of a numerical approximation to Sharpe-Lotka in the region where a known analytical solution does not exist. The algorithm presented will be shown to be of low cost, while retaining high accuracy of the approximate solution.