Solving Bessel's Equation with Point of Indeterminations

  • Context: Graduate 
  • Thread starter Thread starter Alastor123
  • Start date Start date
Click For Summary
SUMMARY

This discussion focuses on solving Bessel's Equation in the presence of points of indeterminacy, specifically at the origin (r=0) in cylindrical and spherical coordinates. The solution requires the use of Bessel functions of the second kind to address the singularity encountered at this point. Participants emphasize the necessity of a step-by-step approach to effectively develop the solution to the differential equations involved.

PREREQUISITES
  • Understanding of Bessel's Equation and its applications
  • Familiarity with cylindrical and spherical coordinate systems
  • Knowledge of differential equations
  • Basic concepts of singularities in mathematical functions
NEXT STEPS
  • Study the properties and applications of Bessel functions of the second kind
  • Learn techniques for solving differential equations with singularities
  • Explore the derivation of Bessel's Equation in cylindrical coordinates
  • Investigate numerical methods for approximating solutions to Bessel's Equation
USEFUL FOR

Mathematicians, physicists, and engineers dealing with differential equations, particularly those working with cylindrical and spherical models in their research or applications.

Alastor123
Messages
1
Reaction score
0
Hi,

I need help in the development of the soluccion of the differential equations when exist point of indeterminations, like in cylindrical and spheres coordinates in the center of the model, r:=0.

I need a help in how resolve the problem, but step by step, using the Bessel's equation.


thanks.
 
Physics news on Phys.org
You will have to use a bessel function of the second kind if there's a singularity at r=0.
 

Similar threads

Graduate Heat conduction equation in cylindrical coordinates
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Volterra equation of the second kind
  • · Replies 1 ·
Replies
1
Views
961
Graduate Unusual Bessel-like Differential Equation with Negative Sign
  • · Replies 2 ·
Replies
2
Views
2K
MHB Solutions to Bessel's equation with Wolfram
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Bessel vs Modified Bessel Eqn solve PDE
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Second Order Differential equation Bessel-type
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Solving for a steady-state (passive cable equation)
  • · Replies 4 ·
Replies
4
Views
3K
MHB What are Bessel Functions and how can they help solve differential equations?
  • · Replies 1 ·
Replies
1
Views
11K
Graduate Searching for radial part solution of Klein-Gordon type equation
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Solving Special Function Equations Using Lie Symmetries
  • · Replies 6 ·
Replies
6
Views
3K