Re: Problem with nested NIntegrate[]

*To*: mathgroup at smc.vnet.net*Subject*: [mg70235] Re: Problem with nested NIntegrate[]*From*: dimmechan at yahoo.com*Date*: Sun, 8 Oct 2006 02:05:00 -0400 (EDT)*References*: <eg83ok$nc3$1@smc.vnet.net>

First the behavior is not paradoxical; you could say it is feature (at least to me). Second here is the the analytic result Integrate[Integrate[y, {x, -1, 1}], {y, -1, 1}] 0 Third see that despite of the presence of these NIntegrate::inum : messages you got the right answer NIntegrate[NIntegrate[y, {x, -1, 1}], {y, -1, 1}] NIntegrate::inum (...) General::stop: (...) NIntegrate::ploss : (...) 0. I believe when integrating numerically y over {x,-1,1} NIntegrate samples some points where the integrand is not numerically. I can think right now many alternatives in order to avoid the messages. The first is the most desired. NIntegrate[y, {x, -1, 1}, {y, -1, 1}] 0. NIntegrate[NIntegrate[y, {y, -1, 1}], {x, -1, 1}, AccuracyGoal -> 20] 0. Off[NIntegrate::inum] NIntegrate[NIntegrate[y, {x, -1, 1}], {y, -1, 1}, AccuracyGoal -> 20] 0. (*AccuracyGoal ->20 is necessay to supress NIntegrate::ploss : message.*) On[NIntegrate::inum] Block[{Message}, NIntegrate[NIntegrate[y, {x, -1, 1}], {y, -1, 1}]] 0. Block[{$Messages = {}}, NIntegrate[NIntegrate[y, {x, -1, 1}], {y, -1, 1}]] 0. Regards Î?/Î? Eckhard ÎÎ³Ï?Î±Ï?Îµ: > Hello, > > I encountered some strange behaviour of NIntegrate when I use a > somewhat neseted structure of several - in my example of two - > NIntegrate[] functions > > NIntegrate[NIntegrate[y,{x,-1,1}],{y,-1,1}] > > This gives me the error > > NIntegrate::"num Integrand y is not numerical at {x) = 0 > > Why does the inner NIntegrate function not know, what value is > currently assigned to y... > > I hope someone can shed a little light on that seemingly paradoxical > behaviour. > > thanks in advance > > Eckhard