Volume 17, Issue 3, August 2016, Pages 745–748
Marc E. SONGOLO1
1 Department of Mathematics and Computer Sciences, University of Lubumbashi, RD Congo
Original language: English
Copyright © 2016 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A significant number of ecological phenomena can be modeled using nonlinear reaction-diffusion partial differential equations. This paper considers a system of reaction-diffusion equations with nonlocal initial conditions. Such equations arise as steady-state equations in an age-structured predator-prey model with diffusion. We use the non-standard finite difference method developed by Mickens, which is a scheme that preserves the positivity of solutions. Furthermore, this scheme is explicit and functional relationship is obtained between the time, the space, and age step sizes.
Author Keywords: Predator-prey model, nonlinear diffusion, nonlocal initial conditions, finite difference methods, nonstandard finite difference schemes, positivity of solutions.
Marc E. SONGOLO1
1 Department of Mathematics and Computer Sciences, University of Lubumbashi, RD Congo
Original language: English
Copyright © 2016 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
A significant number of ecological phenomena can be modeled using nonlinear reaction-diffusion partial differential equations. This paper considers a system of reaction-diffusion equations with nonlocal initial conditions. Such equations arise as steady-state equations in an age-structured predator-prey model with diffusion. We use the non-standard finite difference method developed by Mickens, which is a scheme that preserves the positivity of solutions. Furthermore, this scheme is explicit and functional relationship is obtained between the time, the space, and age step sizes.
Author Keywords: Predator-prey model, nonlinear diffusion, nonlocal initial conditions, finite difference methods, nonstandard finite difference schemes, positivity of solutions.
How to Cite this Article
Marc E. SONGOLO, “A positivity-preserving nonstandard finite difference scheme for a system of reaction-diffusion equations with nonlocal initial conditions,” International Journal of Innovation and Applied Studies, vol. 17, no. 3, pp. 745–748, August 2016.
