Convergence of the Semi-implicit Euler Method for Stochastic Age-Dependent Population Equations with Markovian Switching

Abstract

A class of semi-implicit methods is introduced for stochastic age-dependent population equations with Markovian switching. In general, most of stochastic age-dependent population equations do not have explicit solutions. Thus numerical approximation schemes are invaluable tools for exploring their properties. It is proved that the numerical approximation solutions converge to the exact solutions of the equations under the given conditions.