.IDEAS.Utilities.Math.PowerLinearized

Information

• 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.

Revisions

• November 29, 2013, by Marcus Fuchs:
  Implementation based on Functions.powerLinearized.