1 Numerical Integration

  • Published on
    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>