Gauss-Laguerre Integration Method - Keystone Mining Post

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Numerical Integration

"Numerical Integration Solutions"

Gauss-Laguerre Method

N RESULT

(Actually after 6 is a repetition)

Results from Gauss-Laguerre method

IMPLEMENTATION
Gauss-Laguerre Integration

To compute the following integral using the Gauss-Laguerre method:

I = ∫₀^∞ e^-x sin x dx

The delegate function is simply a sine function, since the weighting function w(x) = e^-x for the Gauss-Laguerre integration.

Running this example creates the results shown above. The exact result of this integral is equal to 0.5. The result for n = 6 is already very accurate.

Testing the Gauss-Laguerre Integration Method

In order to test the Gauss-Laguerre method as defined above, a new TestGaussLaguerre() static method has been added and executed. Supporting code and methods are not shown.

►

           static void TestGaussLaguerre();
              {
                 ListBox1.Items.Clear();
                 ListBox2.Items.Clear();
                 double result;
                 for (int n = 1; n < 9; n++)
                 (
                   result = Integration.GaussLaguerre(f3, n);
                   ListBox1.Items.Add(" " + n + );
                   ListBox2.Items.Add(" " + result);
                 )
              }