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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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Main Authors: | , , , |
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Format: | Conference Proceeding |
Language: | English |
Subjects: | |
Online Access: | Get full text |
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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. |
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ISSN: | 0094-243X 1551-7616 |
DOI: | 10.1063/1.4992716 |