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Fitted Fourier-pseudospectral methods for solving a delayed reaction-diffusion partial differential equation in biology

In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynami...

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Bibliographic Details
Main Authors: Adam, A. M. A., Bashier, E. B. M., Hashim, M. H. A., Patidar, K. C.
Format: Conference Proceeding
Language:English
Subjects:
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Summary:In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44 (1963) 651–663]. Seeing that the analytical solution (in closed form) is hard to obtain, we seek for a robust numerical method. The method consists of a Fourier-pseudospectral semi-discretization in space and a fitted operator implicit-explicit scheme in temporal direction. The proposed method is analyzed for convergence and we found that it is unconditionally stable. Illustrative numerical results will be presented at the conference.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.4992716