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Re: Nested numerical integral - speed: Is it suppose to be so slow?

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  • Subject: [mg127646] Re: Nested numerical integral - speed: Is it suppose to be so slow?
  • From: Sune <sunenj at gmail.com>
  • Date: Fri, 10 Aug 2012 02:44:01 -0400 (EDT)
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  • References: <jvvqoq$rfp$1@smc.vnet.net>

W Craig Carter and Bob Hanlon made some suggestions that resulted in a speed up of roughly a factor of 20. I include the code here in case anybody else is interested. (further suggestions are of course also welcome!)

Code:

In[17]:= trap[t_, t1_, t2_, a_] := 
 Piecewise[{{a t, 0 < t < t1}, {a t1, t1 < t < t2}, {a (t1 - t + t2), 
    t2 < t < t2 + t1}}, 0]

In[18]:= Ga[t_, t1_, t2_, a_, \[CapitalDelta]_] := 
 trap[t, t1, t2, a] - trap[t - 2 \[CapitalDelta], t1, t2, a]

In[19]:= Fa[t_, g_, a_, \[CapitalDelta]_, \[Delta]_] := 
 Integrate[Ga[u, g/a, \[Delta] - g/a, a, \[CapitalDelta]], {u, 0, t}, 
  Assumptions -> Element[{t, g, a, \[Delta], \[CapitalDelta]}, Reals]]

In[20]:= ba[g_, 
  a_, \[CapitalDelta]_, \[Delta]_] := (2.675222/10)^2 Integrate[
   Fa[x, g, a, \[CapitalDelta], \[Delta]]^2, {x, 
    0, \[Delta] + 2 \[CapitalDelta]}, 
   Assumptions -> Element[{g, a, \[Delta], \[CapitalDelta]}, Reals]]

In[21]:= Timing[ba[5.5, 100000, 12, 0.25]]

Out[21]= {0.702, 3.23471}



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