Power function that is linearized below a user-defined threshold
Function that approximates y=xn where 0 <
n so that
- the function is defined and monotone increasing for all
x.
- dy/dx is bounded and continuous everywhere (for n
< 1).
For x < x0, this function replaces
y=xn by a linear function that is continuously
differentiable everywhere.
A typical use of this function is to replace T =
T4(1/4) in a radiation balance to ensure that the
function is defined everywhere. This can help solving the
initialization problem when a solver may be far from a solution and
hence T4 < 0.
See the package Examples for the graph.
- November 29, 2013, by Marcus Fuchs:
Implementation based on Functions.powerLinearized.
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