modelExampleIntegral

Example integration using GSL

Extends from Modelica.Icons.Example (Icon for runnable examples).

Information

Example integral:

I(b) = 2/sqrt(pi) ∫₀^b exp(-x*x) dx

using the GSL QAG routine and a comparison with the known result: erf(b). Several values of b from 0.01 to 1 are explored and the integral is reevaluated for each one. The ratio of I(b)/erf(b) is also calculated and is always consistent with 1.

IMPORTANT!!!: The integrand-setup model 'CreateIntegrand' (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])

For the relevant meanings of the 'rel_err', 'limit', 'key', etc., see the 'qag' function and:

Parameters

Type	Name	Default
Integer	n_par	1
Real	a	0
Real	rel_err	1.e-6
Integer	limit	1000
Integer	key	6

Components

Type	Name	Default	Description
Modelica.Blocks.Sources.Ramp	b_ramp
Modelica.Blocks.Math.Gain	I_qag
Modelica.Blocks.Math.Division	iiratio
Modelica.Blocks.Sources.Constant	a_const
Modelica.Blocks.Sources.Constant[n_par]	p_const
Blocks.integration.QAG_quadrature	qAG_quad
Blocks.specfunc.Erf	erf_gsl