Numerical simulations of traveling wave solutions in a drift paradox inspired diffusive delay population model

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10 Citations (Scopus)

Abstract

We describe numerical algorithm for the simulation of traveling wave solutions in a newly formulated drift paradox inspired diffusive delay population model. We use method of lines to discretize the boundary value problem for the reaction-diffusion equations and we integrate in time the resulting system of delay differential equations using the embedded pair of continuous Runge-Kutta methods of order four and three. We advance the solution with the method of order four and the approximations of order three are used for local error estimation. Numerical results demonstrate the robustness, efficiency, and accuracy of our approach. Moreover, these numerical results confirm the recent theoretical results on the minimum traveling wave speed for this model.

Original languageEnglish (US)
Pages (from-to)95-103
Number of pages9
JournalMathematics and Computers in Simulation
Volume96
DOIs
StatePublished - 2014

Fingerprint

Population Model
Paradox
Traveling Wave Solutions
Local Error Estimation
Numerical Simulation
Numerical Results
Method of Lines
Runge Kutta methods
Order of Approximation
Wave Speed
Computer simulation
Runge-Kutta Methods
Delay Differential Equations
Reaction-diffusion Equations
Numerical Algorithms
Traveling Wave
Error analysis
Boundary value problems
Differential equations
Boundary Value Problem

Keywords

  • Delay models
  • Drift paradox
  • Numerical simulations
  • Reaction-diffusion equations
  • Traveling wave solutions

ASJC Scopus subject areas

  • Modeling and Simulation
  • Numerical Analysis
  • Applied Mathematics
  • Theoretical Computer Science
  • Computer Science(all)

Cite this

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title = "Numerical simulations of traveling wave solutions in a drift paradox inspired diffusive delay population model",
abstract = "We describe numerical algorithm for the simulation of traveling wave solutions in a newly formulated drift paradox inspired diffusive delay population model. We use method of lines to discretize the boundary value problem for the reaction-diffusion equations and we integrate in time the resulting system of delay differential equations using the embedded pair of continuous Runge-Kutta methods of order four and three. We advance the solution with the method of order four and the approximations of order three are used for local error estimation. Numerical results demonstrate the robustness, efficiency, and accuracy of our approach. Moreover, these numerical results confirm the recent theoretical results on the minimum traveling wave speed for this model.",
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T1 - Numerical simulations of traveling wave solutions in a drift paradox inspired diffusive delay population model

AU - Jackiewicz, Zdzislaw

AU - Liu, H.

AU - Li, B.

AU - Kuang, Yang

PY - 2014

Y1 - 2014

N2 - We describe numerical algorithm for the simulation of traveling wave solutions in a newly formulated drift paradox inspired diffusive delay population model. We use method of lines to discretize the boundary value problem for the reaction-diffusion equations and we integrate in time the resulting system of delay differential equations using the embedded pair of continuous Runge-Kutta methods of order four and three. We advance the solution with the method of order four and the approximations of order three are used for local error estimation. Numerical results demonstrate the robustness, efficiency, and accuracy of our approach. Moreover, these numerical results confirm the recent theoretical results on the minimum traveling wave speed for this model.

AB - We describe numerical algorithm for the simulation of traveling wave solutions in a newly formulated drift paradox inspired diffusive delay population model. We use method of lines to discretize the boundary value problem for the reaction-diffusion equations and we integrate in time the resulting system of delay differential equations using the embedded pair of continuous Runge-Kutta methods of order four and three. We advance the solution with the method of order four and the approximations of order three are used for local error estimation. Numerical results demonstrate the robustness, efficiency, and accuracy of our approach. Moreover, these numerical results confirm the recent theoretical results on the minimum traveling wave speed for this model.

KW - Delay models

KW - Drift paradox

KW - Numerical simulations

KW - Reaction-diffusion equations

KW - Traveling wave solutions

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JO - Mathematics and Computers in Simulation

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