1 Numerical Integration
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10-Mar-2015
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<p>NumericalIntegration </p>
<p> LagrangePolynomial </p>
<p>___(1)</p>
<p> (1) Integrate 2 </p>
<p> Error </p>
<p> n = 1 x0 x1 </p>
<p>------ (2) </p>
<p> (2) </p>
<p> n = 2 x0 x1 x2 </p>
<p> Error O(h 4 ) Taylorseries</p>
<p> Integrate 2 </p>
<p> Degreeofaccuracy precision quadratureformula n formula</p>
<p> x k , i = 1, 2,..., n </p>
<p>CompositeNumericalintegrationExample:Simpsonsruleh=2</p>
<p> CompositeSimpsonsruleh=1</p>
<p> CompositeSimpsonsruleh=1/2</p>
<p> Error</p>
<p> CompositeSimpsonsrule</p>
<p>RombergIntegration compositeTrapezoidal</p>
<p> k+1</p>
<p>GaussianQuadrature </p>
<p> x k k 2n1 ( k {1, 2,..., 2n 1} ) n1 n=2 </p>
<p> f(x) 4 4 </p>
<p> GussianQuadrature [1,1]</p>
<p> n 2 n=3 6 6 x k k 2n1 n=3 [a,b]</p>
<p> n=2</p>
<p> n 2 nodes </p>
