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NUMERICAL DISCRETIZATION OF A POPULATION DIFFUSION EQUATION

  • Cho, Sung-Min (DEPARTMENT OF MATHEMATICS, YONSEI UNIVERSITY) ;
  • Kim, Dong-Ho (UNIVERSITY COLLEGE, YONSEI UNIVERSITY) ;
  • Kim, Mi-Young (DEPARTMENT OF MATHEMATICS, INHA UNIVERSITY) ;
  • Park, Eun-Jae (DEPARTMENT OF COMPUTATIONAL SCIENCE AND ENGINEERING, YONSEI UNIVERSITY)
  • Received : 2010.08.07
  • Accepted : 2010.08.07
  • Published : 2010.09.25

Abstract

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.

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