TY - JOUR
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
N1 - Funding Information:
We thank the reviewers for their helpful suggestions/comments. This work of YK and HL is supported in part by NSF DMS-0436341 and DMS-0920744 . BL is partially supported by NSF DMS-0616445 .
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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U2 - 10.1016/j.matcom.2012.06.004
DO - 10.1016/j.matcom.2012.06.004
M3 - Article
AN - SCOPUS:84888311240
SN - 0378-4754
VL - 96
SP - 95
EP - 103
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
ER -