==== DIRICHLET ------- NEUMANN PROBLEM ====
 ---- GALERKINS WEIGHTING FUNCTION----
 # OF GL INTEGRATION SAMPLING POINTS = 3
 APPROXIMATING FUNCTION: U(X) = F0(X) + A1*F1(X)
 WHERE F0(X) = U0+SL(X/L)
 AND   F1(X) = (X/L)*(1-X/L) + (X/L)
 LENGTH OF DOMAIN = 0.5
 NUMBER OF SEGMENTS FOR INTEGRATION = 100
 DX FOR DERIVATIVE EVALUATION = 0.0005
 X-COORDINATE OF LEFT  END BOUNDARY = 0.
 X-COORDINATE OF RIGHT END BOUNDARY = 0.5
 ALPHASQ = 1.
 NUMBER OF SEGMENTS = 100
 DX FOR DERIVATIVE EVALUATION = 0.0005
 U(X) AT X=0 = 1.
 S    AT X=L = 0.5
 H(F1,F1)= -2.399999999999757
 H(F0,F1)= -0.11458333333332692
 A1 = -(H(F0,F1)+S)/H(F1,F1) = 0.16059027777779672
 X-COORDINATE U(X)-RIGHT-NEUMANN DU/DX EXACT
 0. 1. 1.1423611111112428 1.
 0.05 1.0555121527777813 1.0781250000000162 1.054529484946194
 0.1 1.107812500000007 1.0138888888888913 1.1064231953683616
 0.15000000000000002 1.1569010416666763 0.9496527777777797 1.1555514240161697
 0.2 1.20277777777779 0.8854166666666681 1.2017913759034853
 0.25 1.2454427083333475 0.8211805555557607 1.2450274752318917
 0.30000000000000004 1.2848958333333491 0.756944444444427 1.2851516542699934
 0.35000000000000003 1.321137152777795 0.6927083333335197 1.3220636234664633
 0.4 1.3541666666666847 0.628472222222186 1.3556711221216922
 0.45 1.383984375000019 0.5642361111110744 1.385890148991489
 0.5 1.4105902777777968 0.49999999999994493 1.4126451722464444