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MathGroup Archive 2007

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NAntiDerivative function for using NDSolve to compute antiderivatives

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83380] NAntiDerivative function for using NDSolve to compute antiderivatives
  • From: "Andrew Moylan" <andrew.j.moylan at gmail.com>
  • Date: Sun, 18 Nov 2007 06:10:03 -0500 (EST)

Pretty often on this newsgroup I notice users computing antiderivatives
numerically like this:

g[x_?NumericQ] := NIntegrate[f[t], {t, 0, x}].

This is slow when g needs to be evaluated many times. The usual remedies are
to call FunctionInterpolation on g, or, what is usually better, replace the
calls to NIntegrate with a call to NDSolve.

I encounter this a lot so I have a function, NAntiDerivative, that solves it
using the NDSolve method. The definition of g, above, is replaced by

g = NAntiDerivative[f].

NAntiDerivative automatically calls NDSolve as required, and remembers the
results of previous calls to make future evaluations faster. I thought other
people might find it useful. It's at
http://andrew.j.moylan.googlepages.com/mathematica.



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