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MathGroup Archive 2002

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Re: vector integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35083] Re: vector integration
  • From: Mars.bbs at bbs.dartmouth.edu (FangQ)
  • Date: Mon, 24 Jun 2002 03:21:25 -0400 (EDT)
  • Organization: BigGreen BBS
  • Sender: owner-wri-mathgroup at wolfram.com

hi Michael
if u can't get a continuous integration, u can try to evaluate ur object
function at descrete nodes, then, using Intepolation to interpolate them 
into continuous funciton, then, NIntegrate to get numerical solution.
here is an example of evaluate difference, when u try integration, just 
replace D[] into NIntegrate[]:

(*---------------------------------*)
f[x_] := NIntegrate[Sin[Cos[x]], {x, 0, a}];
data = Table[{a, f[x]}, {a, 0, 10}];
expr = Interpolation[data];
Plot[expr[a], {a, 0, 10}];
Plot[Evaluate[D[expr[a], a]], {a, 0, 10}]
(*---------------------------------*)


: hello everybody,

: i am facing a problem in the numerical integration of a vector-valued

: function using Mathematica.

: as the result of some operation on the variable x  defined by  f[x_]=...

: i get a list of numbers {f1,f2,f3,...,fn} each of which depends on the

: variable x.

: the bad point is that the fi can not be evaluated one by one. for some

: chosen value of x i can only calculate the whole list of the fis.

: now i need to integrate each of the fis over x. of course i could

: intgrate each list element separately using NIntegrate:

: 

: Fi=NIntegrate[f[x][[i]],{x,x1,x2}]

: 

: but since the evaluation of the list f[x] is very time consuming i would

: like to somehow integrate the whole list at once which is not possible

: with NIntegrate.

: 

: did anybody encounter this problem, too? does anybody know a useful

: package  or any solution?

: 

: thanks.

: 

: 

: -- 


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