19 research outputs found
Effect of spatial configuration of an extended nonlinear Kierstead-Slobodkin reaction-transport model with adaptive numerical scheme
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 patternsScopus 201
Clinical risk management of herbâdrug interactions
The concomitant use of conventional and herbal medicines can lead to clinically relevant herbâdrug interactions. Clinical risk management offers a systematic approach to minimize the untoward consequences of these interactions by paying attention to: (i) risk identification and assessment; (ii) development and execution of risk reduction strategies; and (iii) evaluation of risk reduction strategies. This paper reviews which steps should be explored or taken in these domains to improve the clinical risk management of adverse herbâdrug interactions