Browse > Article
http://dx.doi.org/10.4134/CKMS.2007.22.4.623

hp-DISCONTINUOUS GALERKIN METHODS FOR THE LOTKA-MCKENDRICK EQUATION: A NUMERICAL STUDY  

Jeong, Shin-Ja (Department of Mathematics Inha University)
Kim, Mi-Young (Department of Mathematics Inha University)
Selenge, Tsendanysh (Department of Mathematics Inha University)
Publication Information
Communications of the Korean Mathematical Society / v.22, no.4, 2007 , pp. 623-640 More about this Journal
Abstract
The Lotka-McKendrick model which describes the evolution of a single population is developed from the well known Malthus model. In this paper, we introduce the Lotka-McKendrick model. We approximate the solution to the model using hp-discontinuous Galerkin finite element method. The numerical results show that the presented hp-discontinuous Galerkin method is very efficient in case that the solution has a sharp decay.
Keywords
age-dependent population dynamics; integro-differential equation; hp-discontinuous Galerkin finite element method;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By SCOPUS : 1
연도 인용수 순위
1 M. B. Allen and E. L. Isaacson, Numerical Analysis for Applied Science, John Wiley & Sons, 1998
2 M. Iannelli, Mathematical Theory of Age-Structured Population Dynamics, Giardini Editori E Stampatori In Pisa, 1994
3 M.- Y. Kim, A collocation method for the Gurtin-MacCamy equation with finite lifespan, SIAM J. Numer. Anal. 39 (2002), no. 6, 1914-1937   DOI   ScienceOn
4 M.- Y. Kim, Discontinuous Galerkin methods for a model of population dynamics with un- bounded mortality, SIAM J. Sci. Comput. 27 (2006), no. 4, 1371-1393   DOI   ScienceOn
5 M.- Y. Kim, Discontinuous Galerkin methods for the Lotka-Mckendrick equation with finite life-span, Math. Models Methods Appl. Sci. 16 (2006), no. 2, 161-176   DOI   ScienceOn
6 M.-Y. Kim and Ts, Selenge, Age-Time Discontinuous Method for the Lotka-McKendrick Equation, Commun. Korean Math. Soc. 18 (2003), no. 3, 569-580   과학기술학회마을   DOI   ScienceOn
7 J. H. Mathewsm and K. D. Fink, Numerical Methods using Matlab, Prentice-Hall, 1999
8 M. Melenk, hp-Finite Element Methods for Singular Perturbations, Springer, 2002
9 Ch. Schwab, p- and lip-Finite Element Methods: Theory and Applications in Solid and Fluid Mechanics, Oxford University Press Inc., 1998
10 P. E. Lewis and J. P. Ward, The Finite Element Method, Addison-Wesley Publishing Company, 1991
11 V. Thomee, Galerkin Finite Element Methods for Parabolic Problems, Springer Series in Computational Mathematics, Springer, 1997
12 C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, The Cambridge University Press, 1987