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

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The discussion focuses on the numerical integration of an oscillatory function over a large interval, specifically the integral of 7π^13*sin(x^4) from 3πe to 73πe. The original poster seeks methods and detailed steps for solving this integral, while also testing their own numerical method against contributions from others. Participants express confusion over the complexity of the constants used and suggest that simplifying the expression may aid in the integration process. Suggestions include using Monte Carlo techniques and examining shorter periods of the function to exploit symmetries. The conversation highlights the challenge of oscillatory integrals and the need for respectful discourse in mathematical discussions.
  • #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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