Re: Calculate a numerical integral with enough precision

*To*: mathgroup at smc.vnet.net*Subject*: [mg114736] Re: Calculate a numerical integral with enough precision*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Tue, 14 Dec 2010 06:57:56 -0500 (EST)

You want WorkingPrecision to be at least as large as PrecisionGoal. However, the default is to use a WorkingPrecision that is twice the PrecisionGoal. For this particular integral, the oscillations near zero cause problems eventhough the automatic method used appears to be OscillatorySelection (identical results). (tab = Table[{n, NIntegrate[Exp[Sin[1/x]], {x, 0, \[Pi]/2}, WorkingPrecision -> n, PrecisionGoal -> 15, Exclusions -> (x == 0)] // Quiet}, {n, 15, 50, 5}]) // Grid Bob Hanlon ---- Alexei Boulbitch <alexei.boulbitch at iee.lu> wrote: ============= NIntegrate[Exp[Sin[1/x]], {x, 0, \[Pi]/2}, WorkingPrecision -> 12, Exclusions -> (x == 0), PrecisionGoal -> 15] // Quiet 3.09892833696 * /Subject/: [mg114668] Calculate a numerical integral with enough precision * /From/: alphatest <iliurarfwpuap at mailinator.com> * /Date/: Sun, 12 Dec 2010 05:45:17 -0500 (EST) ------------------------------------------------------------------------ How can we calculate the following integral up to 10-12 decimal places? integrate exp(sin(1/x)) , x=0..pi/2 It's as if no integration method or precision option lets you calculate more than 5-6 decimal places. Is it possible? -- Alexei Boulbitch, Dr. habil. Senior Scientist Material Development IEE S.A. ZAE Weiergewan 11, rue Edmond Reuter L-5326 CONTERN Luxembourg Tel: +352 2454 2566 Fax: +352 2454 3566 Mobile: +49 (0) 151 52 40 66 44 e-mail: alexei.boulbitch at iee.lu www.iee.lu