Majid Bani-Yaghoub, Ph.D.Associate Professor &
Associate Director
Office: Manheim 205
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Numerical Simulations of a Nonlocal Delayed Reaction-Diffusion Model
1. Convergence of PDE solution to stationary wavefront
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To illustrate the formation and stability of wave solutions we turn our attention to a
class of nonlocal delayed RD equation proposed by So et al (2001, Proc. R. Soc.
Lond. A, 457, 1841–1853). In particular, the
authors adopted Smith-Thieme’s approach to obtain the following model of single
species population.
where x ∈ R, 0 < ε≤ 1, w(x, t) represents the total mature population u(x, a, t) at age a, time t and position x that is given by
The kernel function is given by
Formation of the traveling waves of the model with constant delay (τ = 12)
Formation of traveling waves with Gibbs phenomenon due to increasing delay
PDE solution for τ = 11
Formation of a wavefront in a 2-dimensional domain for the reduced model
where x ∈ R, 0 < ε≤ 1, w(x, t) represents the total mature population u(x, a, t) at age a, time t and position x that is given by
The kernel function is given by
Formation of the traveling waves of the model with constant delay (τ = 12)
Formation of traveling waves with Gibbs phenomenon due to increasing delay
PDE solution for τ = 11
Formation of a wavefront in a 2-dimensional domain for the reduced model