Iterative procedure for potential distribution of a cylindrical problem?

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SUMMARY

The discussion focuses on solving an electric potential problem for a semi-infinite cylinder using Bessel functions of the first order. The key solution is presented in equation (1), while equation (2) introduces the parameter λn, which requires calculation through an iterative procedure. The user specifically seeks guidance on implementing this iterative method in Mathematica for determining the λn values.

PREREQUISITES
  • Understanding of Bessel functions of the first order
  • Familiarity with electric potential problems in cylindrical coordinates
  • Knowledge of iterative numerical methods
  • Experience with Mathematica for computational procedures
NEXT STEPS
  • Research the implementation of Bessel functions in Mathematica
  • Learn about iterative methods for solving transcendental equations
  • Explore numerical techniques for calculating eigenvalues in cylindrical geometries
  • Study examples of electric potential problems solved using Mathematica
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Physicists, electrical engineers, and computational scientists working on potential distribution problems in cylindrical geometries, particularly those utilizing Mathematica for numerical solutions.

OneMoreName
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Hi there,

I arrived at the solution for a electric potential problem for a semi-infinite cylinder (there was a potential distribution given for the boundary conditions but that's not important here).

http://i210.photobucket.com/albums/bb283/DidgeFrank/Cylinder_pot.jpg

The solution is equation (1). You have to use the Bessel functions of first order and there is a parameter λn appearing (equation (2)). My problem is how to calculate the various λn values. I know it must work with an iterative procedure. I am especially interested in a Mathematica procedure to do this.

Thanks in advance for some helpful hints,
OMN
 
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