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Ingy döt Net 2013-04-10 23:57:08 -07:00
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Task/Numerical-integration-Gauss-Legendre-Quadrature/Mathematica/numerical-integration-gauss-legendre-quadrature.math Normal file
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gaussLegendreQuadrature[func_, {a_, b_}, degree_: 5] :=
Block[{nodes, x, weights},
nodes = Cases[NSolve[LegendreP[degree, x] == 0, x], _?NumericQ, Infinity];
weights = 2 (1 - nodes^2)/(degree LegendreP[degree - 1, nodes])^2;
(b - a)/2 weights.func[(b - a)/2 nodes + (b + a)/2]]
gaussLegendreQuadrature[Exp, {-3, 3}]