AGE-TIME DISCONTINUOUS GALERKIN METHOD FOR THE LOTKA-MCKENDRICK EQUATION

- Journal title : Communications of the Korean Mathematical Society
- Volume 18, Issue 3, 2003, pp.569-580
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2003.18.3.569

Title & Authors

AGE-TIME DISCONTINUOUS GALERKIN METHOD FOR THE LOTKA-MCKENDRICK EQUATION

Kim, Mi-Young; Selenge, T.S.;

Kim, Mi-Young; Selenge, T.S.;

Abstract

The Lotka-McKendrick equation which describes the evolution of a single population under the phenomenological conditions is developed from the well-known Malthus’model. In this paper, we introduce the Lotka-McKendrick equation for the description of the dynamics of a population. We apply a discontinuous Galerkin finite element method in age-time domain to approximate the solution of the system. We provide some numerical results. It is experimentally shown that, when the mortality function is bounded, the scheme converges at the rate of in the case of piecewise linear polynomial space. It is also shown that the scheme converges at the rate of when the mortality function is unbounded.

Keywords

age-dependent population dynamics;integro-differential equation;discontinuous Galerkin finite element method;

Language

English

Cited by

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