==== ONE DIMENSIONAL HELMHOLTZ EQUATION DOF=4 ====
 ==== DIRICHLET ------- NEUMANN PROBLEM ====
 ---- GALERKINS WEIGHTING FUNCTION----
 # OF GL INTEGRATION SAMPLING POINTS = 6
 APPROXIMATING FUNCTION: U(X) = F0(X) + A1*F1(X)......
 WHERE F0(X) = U0+SL(X/L)
 F1(X) = (X/L)*(1-X/L) + (X/L)
 F2(X) = ((X/L)**K*(1-X/L))**2
 F3(X) = ((X/L)**K*(1-X/L))**3
 F4(X) = ((X/L)**K*(1-X/L))**4
 LENGTH OF DOMAIN = 0.5
 NUMBER OF SEGMENTS FOR INTEGRATION = 10000
 DX FOR DERIVATIVE EVALUATION = 0.000005
 X-COORDINATE OF LEFT  END BOUNDARY = 0.
 X-COORDINATE OF RIGHT END BOUNDARY = 0.5
 ALPHASQ = 1.
 NUMBER OF SEGMENTS = 10000
 DX FOR DERIVATIVE EVALUATION = 0.000005
 U(X) AT X=0 = 1.
 S    AT X=L = 0.
 A1= 0.13657562244503305
 A2= 0.0028939057911625513
 A3= 0.000024289499359795746
 A4= 1.0958845344879018E-7
 U(X)=F0(X)+ 0.13657562244503305 *F1(X)+ 0.0028939057911625513 *F2(X)+ 0.000024289499359795746 *F3(X)+ 1.0958845344879018E-7 *F4(X)
 X-COORDINATE U(X) DU/DX EXACT(X) |U(X)-EXACT(X)|
 0. 1. 0.5463024897801322 1. 0.
 0.05 1.02605400500811 0.4956405847384958 1.0260540050078621 2.4780177909633494E-13
 0.1 1.0495434093622937 0.4437398362370399 1.0495434093618006 4.931610675384945E-13
 0.15000000000000002 1.070409501783507 0.39072996927043924 1.0704095017839756 4.687361609967411E-13
 0.2 1.088600127909293 0.3367434808956059 1.0886001279101831 8.901768211444505E-13
 0.25 1.1040698206483177 0.2819153091831188 1.1040698206486024 2.8466118351389014E-13
 0.30000000000000004 1.116779913824453 0.22638249600101468 1.1167799138238472 6.057376822354854E-13
 0.35000000000000003 1.126698638823203 0.17028384446077582 1.1266986388222686 9.343636975245317E-13
 0.4 1.1338012039974488 0.1137595719974586 1.1338012039969423 5.064837438339964E-13
 0.45 1.1380698566336718 0.05695095986434464 1.138069856633876 2.042810365310288E-13
 0.5 1.1394939273240088 0. 1.1394939273245492 5.404565683875262E-13