Runge-Kutta methods for age-structured population models
type: Item
instance of: scholarly article
title: Runge-Kutta methods for age-structured population models
zbMATH Open document ID: 0822.65070
DOI: 10.1016/0168-9274(95)00010-R
author: J. C. López-Marcos
author: Luis M. Abia
published in: Applied Numerical Mathematics
publication date: 1995-10-18T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 35L60
zbMATH DE Number: 758535
zbMATH Keywords: method of lines
zbMATH Keywords: difference schemes
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: nonlinear age- structured population models
zbMATH Keywords: stability
zbMATH Keywords: convergence
reviewed by: Kevin Burrage
MaRDI profile type: Publication
cites work: Endemic Thresholds and Stability in a Class of Age-Structured Epidemics
cites work: Global Behavior of an Age-Structured Epidemic Model
cites work: A numerical method for nonlinear age dependent population models
cites work: Numerical methods for a model of population dynamics
cites work: A Box Method for a Nonlinear Equation of Population Dynamics
cites work: An explicit extrapolated box scheme for the Gurtin-MacCamy equation
cites work: Non-linear age-dependent population dynamics
cites work: Analytical and Numerical Results for the Age-Structured S-I-S Epidemic Model with Mixed Inter-Intracohort Transmission
cites work: Numerical solutions to equations modelling nonlinearly interacting age- dependent populations
cites work: Second-Order Accurate Difference Methods for a One-Sex Model of Population Dynamics
cites work: An upwind scheme for a nonlinear hyperbolic integro-differential equation with integral boundary condition
cites work: Q4729251
cites work: Rapidly converging numerical algorithms for models of population dynamics
cites work: Q3220397
full work available at URL: 0168-9274(95)00010-r
OpenAlex ID: W4230374657
description: scientific article; zbMATH DE number 758535