A DISCONTINUOUS GALERKIN METHOD FOR A MODEL OF POPULATION DYNAMICS

Title & Authors
A DISCONTINUOUS GALERKIN METHOD FOR A MODEL OF POPULATION DYNAMICS
Kim, Mi-Young; Yin, Y.X.;

Abstract
We consider a model of population dynamics whose mortality function is unbounded. We approximate the solution of the model using a discontinuous Galerkin finite element for the age variable and a backward Euler for the time variable. We present several numerical examples. It is experimentally shown that the scheme converges at the rate of $\small{h^{3/2}}$ in the case of piecewise linear polynomial space.
Keywords
age-dependent population dynamics;discontinuous Galerkin method;integro-differential equation;
Language
English
Cited by
1.
Discontinuous Galerkin method for piecewise regular solutions to the nonlinear age-structured population model, Mathematical Biosciences, 2006, 203, 2, 277
References
1.
Numerical Analysis For Applied Science, 1998.

2.
Numerical Analysis, 1997.

3.
Archs Ration. Mech. Analysis, 1974. vol.54. pp.281-300

4.
Elementary Applied Partial Differential Equations with Fourier Series and Boundary Value Problems(Third Edition), 1998.

5.
Mathematical Theory of Age-Structured Population Dynamics, 1994.

6.
Numerical Solution of Partial Differential Equations by the Finite Element Method, 1987.

7.
SIAM J. Number. Anal., 2002. vol.39. 6, pp.1914-1937

8.
Discontinuous Galerkin method for the Lotka-McKendrick equation with finite life-span, 0000.