Numerical integration methods

08012022, 03:43 AM
Post: #24




RE: Numerical integration methods
(07312022 04:59 PM)parisse Wrote: "order" may mean max degree of polynomial where the method is exact, or the exponent in the step of the error, up to the author choice... I see. The order of the error, not the order of the polynomial, in this case. Thank you. (07312022 04:59 PM)parisse Wrote: Yes, it is important not to reevaluate the function for efficiency reasons. The idea is to estimate the error of the order 30 method in h^30 by This method works beautifully, but I am fuzzy about some of the details. For instance, why *(err1/err2)^2 ? Why not *(err1/err2) or *(err1/err2)^3 ? Was ^2 derived mathematically, or experimentally? I'm guessing it was experimentally determined to give a reasonable error approximation. And why does the 3rd calculation use 6 nodes? Why not 5 or 7? I realize you want the 3rd calculation to be different enough (but not too different) from the 2nd calculation to determine the error. Was 6 determined experimentally to produce an optimal error estimate? Or is there something mathematical that makes 6 the best choice? Using 6 leaves the entire middle third of the interval unevaluated. Seems like including the center node would have been advantageous. 

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