NIntegrate - bug??
- To: mathgroup at smc.vnet.net
- Subject: [mg85361] NIntegrate - bug??
- From: Costa Bravo <laguna at aol.com>
- Date: Thu, 7 Feb 2008 04:48:04 -0500 (EST)
I have defined the function of Exp with series
expN[x_, p1_] := Module[{min = 10^-20,s, u, j},
s = 1; u = 1; j = 1;
While[u *= N[p1*x/j, 20];
s += u; j++;
u > min*s];
s]
The differences between Exp & expN
tp = 10; tk = 20;
Table[{x, Exp[x/5] - expN[x, 1/5]}, {x, tp, tk, 1}]
(* OK 0*10^-18 *)
(* I have integration Exp[x/5] with 'NIntegrate' *)
NIntegrate[Exp[x/5], {x, tp, tk}]
236.045 (* OK *)
(* and expN[x,1/5] *)
NIntegrate[expN[x, 1/5], {x, tp, tk}]
40. (* Bad !! *)
(* primitive integration expN *)
t1 = Table[expN[x, 1/5], {x, tp, tk, 1/10}];
(Total[t1] - (t1[[1]] + t1[[-1]])/2)/10
236.0533... (* ~OK *)
Why the integration of expN with NIntegrate is bad ?
Tested with Mathematica 5.0 ,5.2 and 6
PS
If defined function expN1 ( without While !!)
expN1[x_, p1_] := Module[{min = 10^-20, s, u, j},
s = 1; u = 1;
Do[u *= N[p1 x/j, 20]; s += u, {j, 30}];
s]
NIntegrate[expN1[x, 1/5], {x, tp, tk}]
236.045 ( OK !!!! )
Thanks in advance.
Costa