modelSphBessel_jzeros
Zeros of Spherical Bessel functions
Extends from Icons.Example (Icon for runnable examples).
Information
Determination of zeros of spherical Bessel functions, j0(xi)=0 and j1(xi)=0, via Modelica/GSL and via direct GSL routines to compare.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 spherical Bessel functions is a crucial element in some boundary value problems involving spherical symmetry and this example shows how the 'Bessel_zeroJnu' block (with nu=n+1/2; 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.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 | ||
| GNU_ScientificLibrary.Blocks.specfunc.SphBessel_jl | sphBessel_j0 | ||
| GNU_ScientificLibrary.Blocks.specfunc.SphBessel_jl | sphBessel_j1 | ||
| GNU_ScientificLibrary.Blocks.specfunc.Bessel_zeroJnu | zeroj0 | ||
| Blocks.specfunc.Bessel_zeroJnu | zeroj1 | ||
| Modelica.Blocks.Sources.Ramp | ramp |