How Can We Numerically Integrate an Oscillatory Function Over a Large Interval?

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SUMMARY

The forum discussion centers on the numerical integration of the oscillatory function $$\int_{3\cdot\pi\cdot e}^{73\cdot\pi\cdot e}\sin(x^4)\;dx$$. Users debate the complexity of the proposed integral, with suggestions to utilize Monte Carlo techniques and to explore symmetries in the function. The discussion highlights the importance of simplifying constants in the integral expression and emphasizes the need for clarity in numerical methods. Participants express frustration over perceived rudeness and the lack of constructive contributions to the problem-solving process.

PREREQUISITES
  • Understanding of numerical integration techniques, specifically for oscillatory functions.
  • Familiarity with Monte Carlo methods for numerical approximation.
  • Knowledge of integral calculus, including properties of sine functions and periodicity.
  • Experience with computational tools such as MATLAB and Wolfram Alpha for numerical verification.
NEXT STEPS
  • Research "Monte Carlo integration techniques" for oscillatory functions.
  • Explore "symmetry exploitation in numerical integration" to simplify calculations.
  • Learn about "adaptive quadrature methods" for handling oscillatory integrals.
  • Investigate "numerical integration in MATLAB" for practical implementation.
USEFUL FOR

This discussion is beneficial for mathematicians, numerical analysts, and students interested in advanced numerical integration techniques, particularly those dealing with oscillatory functions over large intervals.

  • #31
MarkFL said:
Take a look around the forums again, you will see that the vast majority of people who ask questions show what they have tried so far, and those that don't are encouraged to do so.

Your case is different though...you are (presumably) not asking for help with a homework problem, you are wanting to see how others would approach a problem in elementary numerical analysis.

I am assuming you are perhaps looking for ways to improve your own method. It would make more sense for you to demonstrate your approach so that others might offer you insights into how you might accomplish this.

hello,,,,,,,,,,,,,,,,,

I want to compare my method and style,,,, if I Realize That the numerical method of you is better than mine, I simply do I give up and will not work more,,, so I wanted to know how you solved it, ,,, the question for me is not a homework task is not,,,,,

so far it Appears That the numerical method what i designed and created by me is the only and the best so far yet,,,,,,, since no one else has been Able to make any approximation methods using own or of other mathematicians,,,,,, i will wait to see That goes with This Proposed of exercise,,,,,,,,,,,,att
jefferson alexander vitola(Bigsmile)
 
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  • #32
We are getting nowhere fast here. I am closing this topic. If you wish to discuss this further, send your work via PM to one of the administrators or global moderators, and we will consider reopening the topic for further discussion.

edit: There is a substantial literature on numerical methods for oscillatory integrals, so you might want to try google.
 

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