Re: NIntegrate and speed

*To*: mathgroup at smc.vnet.net*Subject*: [mg116792] Re: NIntegrate and speed*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Mon, 28 Feb 2011 05:00:48 -0500 (EST)

On 2/27/11 at 4:35 AM, marco.masi at ymail.com (Marco Masi) wrote: >I have the following problems with NIntegrate. >1) I would like to make the following double numerical integral >converge without errors >R = 8000; Z = 1; rd = 3500; NIntegrate[Exp[-k Abs[Z]]/(1 + (k >rd)^2)^1.5 (NIntegrate[Cos[k R Sin[\[Theta]]], {\[Theta], 0, >\[Pi]}]), {k, 0, \[Infinity]}] >It tells non numerical values present and I don't understand why, >since it evaluates finally a numerical value? 0.000424067 You are getting an error since when the inner integral is initially sampled, k hasn't been assigned a value. You can do the double integral without the error by doing: In[3]:= NIntegrate[ Exp[-k Abs[Z]]/(1 + (k rd)^2)^1.5 Cos[k R Sin[\[Theta]]], {\[Theta], 0, \[Pi]}, {k, 0, \[Infinity]}] Out[3]= 0.000424068 That is, to do a double integral you do not need to type NIntegrate twice. And by using this syntax, the algorithm being used can immediately see k is to be assigned numerical values during the integration.