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 "Numerical Integration Solutions" Gauss-Laguerre Method

 N RESULT
 1 2 3 4 5 6 7 8 0.841470984807897 0.432459454679844 0.496029827480564 0.504879279460199 0.498903320956064 0.500049474797677 0.500038911994668 0.4999877537353

 (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);                  )               }

 Other Implementations...

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Math, Analysis,
expertise..."

EIGENVALUE
SOLUTIONS...

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 Applied Mathematical Algorithms
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