The experimental kF values were compared with several empirical equations, such as Carberry equation.
Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented.
Analytical isotherm equations such as Langmuir and Freundlich isotherms are widely used for modeling adsorption data.
But the basic definition of linearity holds for much more complicated equations, such as the differential equations used in engineering to describe dynamic systems.
Chemical processes are invariably described by non-linear equations such as chemical reaction kinetics, flow-pressure relationships and physical properties.
Such functions can then be used to discretize high order partial differential equations, such as the biharmonic equation.
Poincaré showed that dynamic systems described by quite simple differential equations, such as the solar system, can nonetheless yield the most random-looking, chaotic behaviour.
A powerful advantage of using analytical groundwater equations such as the WTR is that they allow us to directly assess the spatial sensitivity of the mode of climate-groundwater interactions.
Some systematic errors have been found during the application of the different equations, such as the assumption that students are sitting on chairs with a proper seat height.
These hybrid models consist of a framework of dynamic mass and energy balances, supplemented with fuzzy submodels describing additional equations, such as mass transformation and transfer rates.
Equations such as x t) = (Vx)(t), x′(t) = (Vx)(t), or (Vx)(t) = (Wx)(t), where V and W are causal operators, are dealt with.
