Power function y = xn for n < 1
Hypothesis and equations
Let f be the real function f(x) = xn with 0 < n < 1.
To avoid a derivative that tends to infinity near 0, f is replaced by the function g such that g (x) = bx + ax² for 0 < x < xc and g(x) = f(x) for x > xc.
The coefficients a and b are selected so as to keep the continuity of g and its derivative at xc, real chosen close to 0 and depending on the applications. It is shown that a = (n-1) xcn-2 and b = (2-n) xcn-1.
Bibliography
none
Instructions for use
Example of calling of the function for n = 0.66, xc = 2.5
model Unnamed Real f "Function f"; Real g "Function g"; Real g1 "Derivative function of g"; parameter Real n=0.66 "Exponent of f(x)=x^n"; parameter Real xc=2.5 "Abscissa of the junction point "; equation f=time^n; (g,g1)=f_Pow(x=time,xc=xc,n=n); end Unnamed; |
Known limits / Use precautions
none
Validations
Validated function - Hassan Bouia 12/2010
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Licensed by EDF under a 3-clause BSD-license
Copyright © EDF 2009 - 2023
BuildSysPro version 3.6.0
Author : Hassan BOUIA, EDF (2010)
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function f_Pow input Real x "X-axis"; input Real xc "Junction X-axis"; input Real n "Exponent of the function"; output Real g "Value of the function g at x"; output Real g1 "Value of the derivative function of g at x"; end f_Pow;