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Exponential Euler

The main idea behind the exponential Euler rule is that many biological processes are governed by an exponential decay function. Being the default numerical method in Genesis, it is shortly reviewed for the sake of completeness. For an equation of the form:

$\displaystyle \frac{\mathrm{d}y}{\mathrm{d}t} = A - By$ (1.4)

its scheme is given by:

$\displaystyle y(t+h) = y(t)\mathrm{e}^{-B\Delta t} + \frac{A}{B}(1 - \mathrm{e}^{-B\Delta t})$ (1.5)