REQUEST
A mine project reported a problem of tube fitting components not matching their nominal values. In order to determine these variations (i.e. temperature can cause these problems) and satisfy the project structural integrity, we were asked to confirm certain operating variations given that different manufacturers had components specifying different tube-value diametric contractions.

SOLUTION
To determine diameter variations due to diametric contractions we were given initial data regarding site temperatures and other tube length, fabric and diameter values. To find variations (contraction) it is necessary to calculate approximate values of change as well as the true and relative errors for different conditions.

After finalizing the set up of all classes and code involved we applied the Simpson Method (illustrated as sample model of execution under SIMPSON METHOD and IMPLEMENTATION) and solved the problem. We produced reports listing related true and relative error variations for all the parts involved.

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           static void TestSimpson();
              {
                 int n = 101;
                 double result;
                 result = f1(1) - f1(0);
                 listBox1.Items.Add("Analytic result = " + result.ToString());
                 result = Integration.Simpson(f, 0, 1, n);
                 listBox1.Items.Add("Result for function = " + result.ToString());
                 double[] ya = new double[n];
                 double h = 1.0 / (n - 1);
                 for (int i = 0; i < n; i++)
                 {
                    double x = i * h;
                    ya[i] = f(x);
                 }
                 result = Integration.Simpson(ya, h);
                 listBox1.Items.Add("Result for data array = " + result.ToString());
                 this.Text = "Simpson Method / KeystoneMiningPost";
              }