Effect of spatial configuration of an extended nonlinear Kierstead-Slobodkin reaction-transport model with adaptive numerical scheme

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dc.contributor.authorOwolabi, Kolade M.
dc.contributor.authorPatidar, Kailash C.
dc.date.accessioned2017-06-09T14:11:09Z
dc.date.available2017-06-09T14:11:09Z
dc.date.issued2016
dc.description.abstractIn 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 patternsen_US
dc.description.accreditationScopus 2017
dc.identifier.citationOwolabi K.M., Patidar K.C.(2016). Effect of spatial configuration of an extended nonlinear Kierstead-Slobodkin reaction-transport model with adaptive numerical scheme. SpringerPlus,5:303en_US
dc.identifier.issn21931801
dc.identifier.urihttp://dx.doi.org/10.1186/s40064-016-1941-y
dc.identifier.urihttp://hdl.handle.net/10566/2951
dc.language.isoenen_US
dc.publisherSpringerOpen
dc.rightsAll the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License
dc.subjectExponential time differencing Runge-Kutta methoden_US
dc.subjectDiffusion-drivenen_US
dc.subjectKiSS modelen_US
dc.subjectSpatial pattern formationen_US
dc.subjectStabiliten_US
dc.titleEffect of spatial configuration of an extended nonlinear Kierstead-Slobodkin reaction-transport model with adaptive numerical schemeen_US
dc.typeArticleen_US

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