28 July 2014 7:29:04.625 PM LINE_NCO_RULE_PRB FORTRAN90 version: Test the LINE_NCO_RULE library. TEST01 LINE_NCO_RULE computes the Newton-Cotes Open (NCO) rule using N equally spaced points for an interval [A,B]. Newton-Cotes Open (NCO) Rule # 1 I X(I) W(I) 1 0.00000 2.00000 Sum(|W)|) = 2.00000 Newton-Cotes Open (NCO) Rule # 2 I X(I) W(I) 1 -0.333333 1.00000 2 0.333333 1.00000 Sum(|W)|) = 2.00000 Newton-Cotes Open (NCO) Rule # 3 I X(I) W(I) 1 -0.500000 1.33333 2 0.00000 -0.666667 3 0.500000 1.33333 Sum(|W)|) = 3.33333 Newton-Cotes Open (NCO) Rule # 4 I X(I) W(I) 1 -0.600000 0.916667 2 -0.200000 0.833333E-01 3 0.200000 0.833333E-01 4 0.600000 0.916667 Sum(|W)|) = 2.00000 Newton-Cotes Open (NCO) Rule # 5 I X(I) W(I) 1 -0.666667 1.10000 2 -0.333333 -1.40000 3 0.00000 2.60000 4 0.333333 -1.40000 5 0.666667 1.10000 Sum(|W)|) = 7.60000 Newton-Cotes Open (NCO) Rule # 6 I X(I) W(I) 1 -0.714286 0.848611 2 -0.428571 -0.629167 3 -0.142857 0.780556 4 0.142857 0.780556 5 0.428571 -0.629167 6 0.714286 0.848611 Sum(|W)|) = 4.51667 Newton-Cotes Open (NCO) Rule # 7 I X(I) W(I) 1 -0.750000 0.973545 2 -0.500000 -2.01905 3 -0.250000 4.64762 4 0.00000 -5.20423 5 0.250000 4.64762 6 0.500000 -2.01905 7 0.750000 0.973545 Sum(|W)|) = 20.4847 Newton-Cotes Open (NCO) Rule # 8 I X(I) W(I) 1 -0.777778 0.797768 2 -0.555556 -1.25134 3 -0.333333 2.21741 4 -0.111111 -0.763839 5 0.111111 -0.763839 6 0.333333 2.21741 7 0.555556 -1.25134 8 0.777778 0.797768 Sum(|W)|) = 10.0607 Newton-Cotes Open (NCO) Rule # 9 I X(I) W(I) 1 -0.800000 0.891755 2 -0.600000 -2.57716 3 -0.400000 7.35009 4 -0.200000 -12.1407 5 0.00000 14.9519 6 0.200000 -12.1407 7 0.400000 7.35009 8 0.600000 -2.57716 9 0.800000 0.891755 Sum(|W)|) = 60.8713 Newton-Cotes Open (NCO) Rule #10 I X(I) W(I) 1 -0.818182 0.758509 2 -0.636364 -1.81966 3 -0.454545 4.31930 4 -0.272727 -4.70834 5 -0.909091E-01 2.45019 6 0.909091E-01 2.45019 7 0.272727 -4.70834 8 0.454545 4.31930 9 0.636364 -1.81966 10 0.818182 0.758509 Sum(|W)|) = 28.1120 Newton-Cotes Open (NCO) Rule #11 I X(I) W(I) 1 -0.833333 0.833420 2 -0.666667 -3.09706 3 -0.500000 10.6544 4 -0.333333 -23.0561 5 -0.166667 37.0525 6 0.00000 -42.7742 7 0.166667 37.0525 8 0.333333 -23.0561 9 0.500000 10.6544 10 0.666667 -3.09706 11 0.833333 0.833420 Sum(|W)|) = 192.161 Newton-Cotes Open (NCO) Rule #12 I X(I) W(I) 1 -0.846154 0.727116 2 -0.692308 -2.35157 3 -0.538462 7.03889 4 -0.384615 -11.9379 5 -0.230769 13.1062 6 -0.769231E-01 -5.58266 7 0.769231E-01 -5.58266 8 0.230769 13.1062 9 0.384615 -11.9379 10 0.538462 7.03889 11 0.692308 -2.35157 12 0.846154 0.727116 Sum(|W)|) = 81.4887 TEST02 Use a sequence of NCO rules to compute an estimate Q of the integral: I = integral ( 0 <= x <= 1 ) exp(x) dx. The exact value is: I = 1.71828 N Q |Q-I| 1 1.64872 0.695606E-01 2 1.67167 0.466086E-01 3 1.71778 0.505296E-03 4 1.71793 0.351660E-03 5 1.71828 0.173578E-05 6 1.71828 0.122681E-05 7 1.71828 0.344711E-08 8 1.71828 0.245789E-08 9 1.71828 0.495142E-10 10 1.71828 0.979866E-09 11 1.71828 0.180838E-08 12 1.71828 0.410579E-07 13 1.71828 0.230888E-06 14 1.71828 0.192466E-05 15 1.71829 0.318399E-05 16 1.71825 0.275244E-04 17 1.71817 0.112160E-03 18 1.71263 0.565305E-02 19 1.71834 0.548642E-04 20 1.73082 0.125421E-01 21 2.26518 0.546896E+00 22 2.57597 0.857689E+00 LINE_NCO_RULE_PRB Normal end of execution. 28 July 2014 7:29:04.627 PM