modelBessel_Jzeros
Zeros of Bessel functions
Extends from Icons.Example (Icon for runnable examples).
Information
Determination of zeros of Bessel functions, J0(xi)=0 and J1(xi)=0, via Modelica/GSL and via direct GSL functions to compare results.Plots of zeroJ0.y and zeroJ1.y should display steps with lower-right corners at ( t , y ) = ( xi,Modelica , xi,GSL ) and such values should be equal at these corners.

The location of the zeros of Bessel functions is a crucial element in some boundary value problems involving cylindrical symmetry and this example shows how the 'Bessel_zeroJnu' block (with nu=n; n integer) provides said info quickly.
As not all special functions' zeros are provided via GSL routines, the displayed use of Modelica's zero-crossing logical blocks could be useful for finding such information for these other functions.
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.Blocks.Sources.Ramp | ramp | ||
| GNU_ScientificLibrary.Blocks.specfunc.Bessel_J0 | bessel_J0 | ||
| GNU_ScientificLibrary.Blocks.specfunc.Bessel_Jn | bessel_J1 | ||
| GNU_ScientificLibrary.Blocks.specfunc.Bessel_zeroJnu | zeroJ0 | ||
| GNU_ScientificLibrary.Blocks.specfunc.Bessel_zeroJnu | zeroJ1 | ||
| Modelica.Blocks.Logical.ZeroCrossing | zeroCrossJ0 | ||
| Modelica.Blocks.Logical.ZeroCrossing | zeroCrossJ1 | ||
| Modelica.Blocks.MathInteger.TriggeredAdd | trigAddJ0 | ||
| Modelica.Blocks.MathInteger.TriggeredAdd | trigAddJ1 | ||
| Modelica.Blocks.Sources.IntegerConstant | integerConstant | ||
| Modelica.Blocks.Sources.BooleanConstant | enZJ0 | ||
| Modelica.Blocks.Sources.BooleanConstant | enZJ1 |