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Mathematica
8: New and Improved Core Algorithms
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Core Algorithms
Integrate Multidimensional Highly Oscillatory Functions
Mathematica
8 includes the first-ever automatic algorithm for numerical integration of multidimensional oscillatory functions.
In[1]:=
X
ParallelTable[ Plot3D[f, {x, 1, 12}, {y, 1, 12}, PlotLabel -> f, Mesh -> False, PlotPoints -> 60], {f, {Sin[x] Cos[y], Sin[x + y], Re[Exp[I (x + y)]], Re[2^(I x y)]}}]
Out[1]=
In[2]:=
X
NIntegrate[{Sin[x] Cos[y], Sin[x + y]}, {x, 1, 10^4}, {y, 1, 10^4}]
Out[2]=
In[3]:=
X
NIntegrate[{Exp[I (x + y)], 2^(I x y)}, {x, 1, 10^4}, {y, 1, 10^4}]
Out[3]=