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Volume 5, Issue 3
An Improved Explicit Scheme for Age-Dependent Population Models with Spatial Diffusion

Galena Pelovska

Int. J. Numer. Anal. Mod., 5 (2008), pp. 466-490.

Published online: 2008-05

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  • Abstract

In this work we present three age-structured models with spatial dependence. We introduce an improved explicit method, namely Super-Time-Stepping (STS) developed for parabolic problems and we use its modification for the numerical treatment of our models. We explain how the acceleration scheme can be adapted to the age-dependent models. We prove convergence of the method in case of Dirichlet boundary conditions and we demonstrate the accuracy and the efficiency of the Modified STS comparing it with other numerical algorithms of same or higher order, namely the explicit, fully implicit and Crank-Nicolson standard schemes.

  • Keywords

population dynamics, age-dependence, linear diffusion, linear and nonlinear models, finite difference method, numerical acceleration, modified super-time-stepping.

  • AMS Subject Headings

35M10, 65N06, 65N12, 92B99

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-5-466, author = {Pelovska , Galena}, title = {An Improved Explicit Scheme for Age-Dependent Population Models with Spatial Diffusion}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {3}, pages = {466--490}, abstract = {

In this work we present three age-structured models with spatial dependence. We introduce an improved explicit method, namely Super-Time-Stepping (STS) developed for parabolic problems and we use its modification for the numerical treatment of our models. We explain how the acceleration scheme can be adapted to the age-dependent models. We prove convergence of the method in case of Dirichlet boundary conditions and we demonstrate the accuracy and the efficiency of the Modified STS comparing it with other numerical algorithms of same or higher order, namely the explicit, fully implicit and Crank-Nicolson standard schemes.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/822.html} }
TY - JOUR T1 - An Improved Explicit Scheme for Age-Dependent Population Models with Spatial Diffusion AU - Pelovska , Galena JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 466 EP - 490 PY - 2008 DA - 2008/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/822.html KW - population dynamics, age-dependence, linear diffusion, linear and nonlinear models, finite difference method, numerical acceleration, modified super-time-stepping. AB -

In this work we present three age-structured models with spatial dependence. We introduce an improved explicit method, namely Super-Time-Stepping (STS) developed for parabolic problems and we use its modification for the numerical treatment of our models. We explain how the acceleration scheme can be adapted to the age-dependent models. We prove convergence of the method in case of Dirichlet boundary conditions and we demonstrate the accuracy and the efficiency of the Modified STS comparing it with other numerical algorithms of same or higher order, namely the explicit, fully implicit and Crank-Nicolson standard schemes.

Pelovska , Galena. (2008). An Improved Explicit Scheme for Age-Dependent Population Models with Spatial Diffusion. International Journal of Numerical Analysis and Modeling. 5 (3). 466-490. doi:
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