Comparison of GSL and Modelica integration routines
Example integral:
I(a) = ∫a1 x-1/2 ln(x)
dx
using the GSL QAGS routine and
Modelica.Math.Nonlinear.quadratureLobatto(). Several values of a
from 0.1 to 10-6 are explored and the integral is
reevaluated for each one. The ratio of the results from the two
methods is also calculated for comparison. As the integrand
contains a singularity at x=0, the integration is stopped at
a=10-6. Only the QAGS result is evaluated for the full
range (qAGS_quad0.y = I(0) = -4). The Lobatto routine will hang or
crash for values of a < 10-6.
IMPORTANT!!!: The integrand-setup model 'CreateIntegrand2' (or a
duplicate) must be run before using GSL integration routines within
a larger Modelica model (like this one). (Alternatively, one could
edit integrand.c directly and then compile "by hand" in a command
window:
gcc -fPIC -c integrand.c integration_mi.c
gcc -shared integration.o integration_mi.o -o
libgsl_integration_MI.so [.dll for windows])
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