Iterative procedure for potential distribution of a cylindrical problem?

In summary, the conversation discusses the solution to an electric potential problem for a semi-infinite cylinder. The solution involves using Bessel functions and a parameter λn. The individual is seeking assistance with calculating the various λn values, specifically using a Mathematica procedure. The issue has been resolved.
  • #1
OneMoreName
10
1
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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  • #2
Solved.
 

1. What is an iterative procedure for potential distribution of a cylindrical problem?

An iterative procedure for potential distribution of a cylindrical problem is a mathematical method used to find the potential distribution in a cylindrical system. It involves breaking down the problem into smaller parts and solving them repeatedly until a satisfactory solution is reached.

2. Why is an iterative procedure used for cylindrical problems?

An iterative procedure is often used for cylindrical problems because these types of systems can be complex and difficult to solve using traditional mathematical methods. An iterative approach allows for a more efficient and accurate solution to be obtained.

3. How does an iterative procedure work?

An iterative procedure works by repeatedly solving smaller parts of the problem, known as iterations. Each iteration brings the solution closer to the actual solution, and the process continues until a desired level of accuracy is achieved.

4. What are the advantages of using an iterative procedure for cylindrical problems?

One of the main advantages of using an iterative procedure for cylindrical problems is that it can handle complex and non-linear systems. It also allows for a more accurate solution to be obtained compared to traditional methods. Additionally, an iterative approach can save time and computational resources.

5. Are there any limitations to using an iterative procedure for cylindrical problems?

While an iterative procedure can be effective for solving cylindrical problems, it does have some limitations. It may require a significant amount of computational resources, and the convergence of the solution is not always guaranteed. Additionally, the accuracy of the solution depends on the initial guess and the number of iterations performed.

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