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

TypeNameDefaultDescription
Modelica.Blocks.Sources.Rampramp
GNU_ScientificLibrary.Blocks.specfunc.Bessel_J0bessel_J0
GNU_ScientificLibrary.Blocks.specfunc.Bessel_Jnbessel_J1
GNU_ScientificLibrary.Blocks.specfunc.Bessel_zeroJnuzeroJ0
GNU_ScientificLibrary.Blocks.specfunc.Bessel_zeroJnuzeroJ1
Modelica.Blocks.Logical.ZeroCrossingzeroCrossJ0
Modelica.Blocks.Logical.ZeroCrossingzeroCrossJ1
Modelica.Blocks.MathInteger.TriggeredAddtrigAddJ0
Modelica.Blocks.MathInteger.TriggeredAddtrigAddJ1
Modelica.Blocks.Sources.IntegerConstantintegerConstant
Modelica.Blocks.Sources.BooleanConstantenZJ0
Modelica.Blocks.Sources.BooleanConstantenZJ1