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As the title suggests, I'm looking for a very accurate algorithm to find the area under an oscillatory function.

For instance, I would like to integrate the following graphenter image description here

I'm currently using simpson's method to integrate this, but I was wondering if there are more accurate methods.

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    $\begingroup$ Your test function looks smooth (infinitely often differentiable), to me. Did you mean to write oscillatory instead? $\endgroup$ – Carl Christian Jun 4 '16 at 19:11
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    $\begingroup$ In what form is the function given? Do you have an analytic or partially analytic form, or is black box or defined by interpolation? $\endgroup$ – Geoffrey Irving Jun 6 '16 at 4:15
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You can look up various quadratures. One method that should fair better is Gauss Quadrature.

I would also recommend looking into any adaptive quadrature schemes. There are many of them out there, so searching up algorithms for adaptive integration would help you.

This wikipedia link should give you some insight into adaptive integration.

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  • $\begingroup$ Thanks for your reply, I'm going to look into it and come back to this answer $\endgroup$ – Hunter Jun 4 '16 at 20:28

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