Runge-Kutta methods for age-structured population models
This paper considers difference schemes based on Runge-Kutta methods for the numerical solution of nonlinear age-structured population models in which the governing equations are first-order hyperbolic initial-boundary value problems. The integral can appear in the boundary condition or in the partial differential equation and the main result here is that it should be approximated by a quadratic scheme of at least the same order as the Runge-Kutta method. The stability, existence and convergence of the solutions are also studied. A number of explicit and implicit methods of orders two to four is implemented on a single test problem. It is concluded that methods based on higher-order schemes are preferable when the data is smooth.
nonlinear age- structured population models
scientific article; zbMATH DE number 758535
scientific article