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

Title & Authors
AGE-TIME DISCONTINUOUS GALERKIN METHOD FOR THE LOTKA-MCKENDRICK EQUATION
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 $\small{h^2}$ in the case of piecewise linear polynomial space. It is also shown that the scheme converges at the rate of $\small{h^{3/2}}$ when the mortality function is unbounded.
Keywords
age-dependent population dynamics;integro-differential equation;discontinuous Galerkin finite element method;
Language
English
Cited by
1.
hp-DISCONTINUOUS GALERKIN METHODS FOR THE LOTKA-MCKENDRICK EQUATION: A NUMERICAL STUDY,;;;

대한수학회논문집, 2007. vol.22. 4, pp.623-640
1.
Numerical solution of the nonlinear age-structured population models by using the operational matrices of Bernstein polynomials, Applied Mathematical Modelling, 2012, 36, 3, 945
2.
High-order Discontinuous Galerkin Methods for a class of transport equations with structured populations, Computers & Mathematics with Applications, 2016, 72, 3, 768
3.
Discontinuous-continuous Galerkin methods for population diffusion with finite life span, Mathematical Population Studies, 2016, 23, 1, 17
References
1.
Numerical Analysis For Applied Science, 1998.

2.
Finite Elements, 2001.

3.
Elementary Applied Partial Differential Equations with Fourier Series and Boundary Value Problems (Third Edition), 1998.

4.
Mathematical Theory of Age-Structured Population Dynamics, 1994.

5.
numerical Solution of Partial Differential Equations by the Finite Element Method, 1987.

6.
SIAM J. Numer. Anal., 2002. vol.39. 6, pp.1914-1937

7.
The Finite Element Method, 1991.

8.
Springer Series in Computational Mathematics, 1997.