Re: Re: Integrate vs Nintegrate for impulsive functions<> got it !!!!
- To: mathgroup at smc.vnet.net
- Subject: [mg61752] Re: [mg61728] Re: Integrate vs Nintegrate for impulsive functions<> got it !!!!
- From: Pratik Desai <pdesai1 at umbc.edu>
- Date: Fri, 28 Oct 2005 03:25:31 -0400 (EDT)
- References: <200510270902.FAA19481@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Bill Rowe wrote: >On 10/26/05 at 2:44 AM, chris.chiasson at gmail.com (Chris Chiasson) >wrote: > > > >>My computer gives the same answer as yours for NIntegrate, but it >>thought for a long while on Integrate and then spit out: >>Complex[-4.4073414839228176`*^145,6.238877585945074`*^146] Bug?? >>Version Number: 5.2.0.0 >>Platform: Windows >> >> > >Using version 5.2 on MacOS 10.4.2, for Integrate I get > >Out[2]= >4.651767835491884*^136 + 1.162941958872971*^136*I > >and for NItegrate, I get the same result reported by Pratik Desai. > >The function being integrated is specified with machine precision coefficients. I strongly suspect this is the root of the problem. > >Integrate will first get a symbolic answer then compute the final answer by substituting the end points into the symbolic answer. > This did the trick!!!! gss[x_] =(-0.24982234345508192767999985675352186955264330379714847631`38.487710383706414 - 0.042973298321580602789058629777534550745591195188598656308`38.14780044850824*I)* Sin[(3.173442724268721537583815006655640900135040283203125`40. + 0.329548078108167386002236298736534081399440765380859375`40.* I)*x]*(Cosh[444.44444444444451391973416320979595184326171875`40.* (-0.40000000000000002220446049250313080847263336181640625`40. + x)^2] - 1.`40.*Sinh[444.44444444444451391973416320979595184326171875`40.* (-0.40000000000000002220446049250313080847263336181640625`40. + x)^2]) s1 = Integrate[gss[x] // TrigToExp // Chop, x] /. {x -> 1} s0 = Integrate[gss[x] // TrigToExp // Chop, x] /. {x -> 0} s1 - s0 >>-0.0199823194185132389104867187573191275 - \ 0.0042568886863634818146396321781608061 \[ImaginaryI] NIntegrate[gss[x], {x, 0, 1}] >>-0.0199823 - 0.00425689 \[ImaginaryI] Cheers!!! Pratik >It is entirely possible this leads to problems even when the orginal function being integrated has reasonable values over the range of integration. > >So, I would be inclined to accept the answer given by NIntegrate as valid and reject the answer given by Integrate. But I would not consider this to be a bug. Instead, I would chalk this up as one of the issues with doing machine precision computations. >-- >To reply via email subtract one hundred and four > > > -- Pratik Desai Graduate Student UMBC Department of Mechanical Engineering Phone: 410 455 8134
- References:
- Re: Integrate vs Nintegrate for impulsive functions
- From: Bill Rowe <readnewsciv@earthlink.net>
- Re: Integrate vs Nintegrate for impulsive functions