Long-time stability of numerical solutions to Gurtin–MacCamy equations by method of characteristics

摘要

A backward finite difference scheme along the characteristics is considered to approximate the solution of a nonlinear and nonlocal system of integro-differential equations that models the dynamics of a single population. The long-time stability of the numerical solution is proved. The optimal rate of convergence of the scheme is demonstrated in the maximum norm. Results from numerical experiments are presented.