Re: Numerical integration inside numerical integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg48824] Re: [mg48811] Numerical integration inside numerical integration*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Fri, 18 Jun 2004 02:12:46 -0400 (EDT)*References*: <200406170807.EAA27751@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 17 Jun 2004, at 17:07, blah12 at mail.com wrote: > Hello all, > > I'm trying to solve numerically an integral like, > > > A=some_value > NIntegrate[f[y,u]*Log[1+NIntegrate[g[y,u,s], {s, A, \[Infinity]}]], > {u, -\[Infinity],\[Infinity]},{y, -\[Infinity],\[Infinity]}] > > I know I am doing this wrong as the inner integration fails because > it doesn't have specific numerical values for y and u. > I guess Mathematica doesn't perform numerical integrations from the > outside to the inside (and so passing each time values of y,u to > the inner integration). > > How can this problem be solved with Mathematica please ? > > Thanks. > > > Just define: h[u_?NumericQ, y_?NumericQ] := f[y, u]*Log[1 + NIntegrate[g[y, u, s], {s, 1, Infinity}]] and then evaluate NIntegrate[h[u, y], {u, -Infinity, Infinity}, {y, -Infinity, Infinity}] It will probably be quite slow since NIntegrate can't compile a function defined in this way. (It may even be slightly better to use the Compiled->False option in the second NIntegrate, though I am not sure if it will make any difference.) Andrzej Kozlowski Chiba, Japan http://www.mimuw.edu.pl/~akoz/

**References**:**Numerical integration inside numerical integration***From:*blah12@mail.com