Double integration of functions involving bessel functions and cosines/sines

In summary, the conversation discusses the difficulty in accurately integrating double integrals involving Bessel functions and sinusoids in Maple. The issue arises with the overlap of sine and cosine over the range of 0 to 2 * Pi, resulting in a value of -129 instead of the expected zero. The person seeking help has tried using other software, such as Matlab, but has not found a solution. The expert suggests that achieving a zero error margin in computer calculations is not always possible and may require writing a custom program.
  • #1
moonkhan
2
0
Can we integrate double integrals involving bessel functions and sinusoids in maple. Also, the overlap of sine and cosine over the range of 0 to 2 * Pi must be exactly zero, but, in maple, it gives some value (of the order of -129). Is there any software, which can compute the exact double integral.
The function i am trying to integrate numerically (please correct me if i am doing rigth by solving numerically):

"((((besselj(const1,const2)./besselk(const1,const2)).*besselk(const1,const1*r/const3).*cos(const*(phi))).*conj((besselj(const2,(kpaa2/a).*(r)).*cos(const2*(phi))))).*r)"
with 0<=phi>=2*Pi, and 0<=r>=125e-6.

I tried with matlab's builtin functions, but the same problem of accuracy.

Thanks in advance.
Moon
 
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  • #2
You cannot expect that you have a zero error margin with a calculation in a computer. ##-129## is already pretty low and you will have to write your own program if you want to do better. In the end it always will be a compromise, since a computer is a discrete machine and you want to use it for calculations with real, i.e. infinitely long numbers.
 

1. What is double integration?

Double integration is a mathematical technique used to find the area under a curve in a two-dimensional space. It involves finding the antiderivative of a function and evaluating it at two different boundaries.

2. What are Bessel functions?

Bessel functions are a family of special functions that arise in mathematical physics and engineering. They are solutions to a type of differential equation known as the Bessel equation and are named after the mathematician Friedrich Bessel.

3. How are Bessel functions and cosines/sines related?

Bessel functions can be expressed in terms of cosines and sines through the use of complex numbers and the Euler formula. This allows for the use of Bessel functions in solving problems involving periodic phenomena, such as sound and electromagnetic waves.

4. When would double integration of functions involving Bessel functions and cosines/sines be used?

Double integration involving Bessel functions and cosines/sines is commonly used in the fields of physics and engineering to solve problems related to heat transfer, vibration analysis, and signal processing.

5. What are some challenges in performing double integration involving Bessel functions and cosines/sines?

One of the major challenges in performing double integration involving Bessel functions and cosines/sines is dealing with complex numbers and the potential for errors in calculations. Additionally, finding the appropriate boundaries for integration can also be challenging and require a deep understanding of the problem at hand.

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