Effect of spatial configuration of an extended nonlinear Kierstead-Slobodkin reaction-transport model with adaptive numerical scheme
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Date
2016
Journal Title
Journal ISSN
Volume Title
Publisher
SpringerOpen
Abstract
In this paper, we consider the numerical simulations of an extended nonlinear form
of Kierstead-Slobodkin reaction-transport system in one and two dimensions. We
employ the popular fourth-order exponential time differencing Runge-Kutta (ETDRK4)
schemes proposed by Cox and Matthew (J Comput Phys 176:430-455,
2002), that was modified by Kassam and Trefethen (SIAM J Sci Comput 26:1214-1233,
2005), for the time integration of spatially discretized partial differential equations. We demonstrate
the supremacy of ETDRK4 over the existing exponential time differencing integrators
that are of standard approaches and provide timings and error comparison. Numerical
results obtained in this paper have granted further insight to the question "What is the
minimal size of the spatial domain so that the population persists?" posed by Kierstead
and Slobodkin (J Mar Res 12:141-147,
1953
), with a conclusive remark that the popula-
tion size increases with the size of the domain. In attempt to examine the biological
wave phenomena of the solutions, we present the numerical results in both one- and
two-dimensional space, which have interesting ecological implications. Initial data and
parameter values were chosen to mimic some existing patterns
Description
Keywords
Exponential time differencing Runge-Kutta method, Diffusion-driven, KiSS model, Spatial pattern formation, Stabilit
Citation
Owolabi K.M., Patidar K.C.(2016). Effect of spatial configuration of an extended nonlinear Kierstead-Slobodkin reaction-transport model with adaptive numerical scheme. SpringerPlus,5:303