Solving Bessel's Equation with Point of Indeterminations

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In summary, Bessel's equation is a second-order linear differential equation used to describe physical phenomena. A point of indeterminacy in the equation is where it becomes undefined or infinite. Solving the equation with these points is important for accurately describing physical systems. Common techniques for solving it include power series solutions and the method of Frobenius. Real-world applications include heat transfer, acoustics, electromagnetic fields, and the design of various devices.
  • #1
Alastor123
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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.
 
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  • #2
You will have to use a bessel function of the second kind if there's a singularity at r=0.
 

1. What is Bessel's equation?

Bessel's equation is a second-order linear differential equation named after the mathematician Friedrich Bessel. It is used to describe the behavior of certain physical phenomena, such as heat conduction, fluid flow, and the oscillations of a circular membrane.

2. What is a point of indeterminacy in Bessel's equation?

A point of indeterminacy in Bessel's equation is a point in the solution where the equation becomes undefined or infinite. This typically occurs when the solution involves a division by zero.

3. Why is solving Bessel's equation with points of indeterminacy important?

Solving Bessel's equation with points of indeterminacy is important because it allows us to find solutions that accurately describe physical phenomena. By understanding the behavior of the equation at these points, we can better understand the behavior of the physical system being modeled.

4. What are some common techniques for solving Bessel's equation with points of indeterminacy?

One common technique for solving Bessel's equation with points of indeterminacy is by using power series solutions. Another method is by using the method of Frobenius, which involves finding a series solution in terms of a power series multiplied by logarithmic terms.

5. What are some real-world applications of solving Bessel's equation with points of indeterminacy?

Bessel's equation with points of indeterminacy has a wide range of applications in physics and engineering. It is used in the study of heat transfer, acoustics, electromagnetic fields, and fluid mechanics, among others. It is also used in the design of antennas, musical instruments, and other devices that involve oscillations or vibrations.

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