==== ONE DIMENSIONAL HELMHOLTZ EQUATION DOF=3====
 ==== 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
 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= 0.13657563877289627
 A2= 0.00289379550996495
 A3= 0.00002449176124772092
 U(X)=F0(X)+ 0.13657563877289627 *F1(X)+ 0.00289379550996495 *F2(X)+ 0.00002449176124772092 *F3(X)
 X-COORDINATE U(X) DU/DX EXACT(X) |U(X)-EXACT(X)|
 0. 1. 0.5463025550915851 1. 0.
 0.05 1.0260540053737506 0.49564056068798223 1.0260540050078621 3.6588843066454046E-10
 0.1 1.0495434085439468 0.44373982059859973 1.0495434093618006 8.178537846958989E-10
 0.15000000000000002 1.0704095008429404 0.39072997912061824 1.0704095017839756 9.410352497241092E-10
 0.2 1.0886001278237958 0.3367435020048444 1.0886001279101831 8.638734172450313E-11
 0.25 1.1040698215158038 0.2819153237680938 1.1040698206486024 8.672014217836477E-10
 0.30000000000000004 1.1167799150459228 0.2263824950239855 1.1167799138238472 1.2220755518654869E-9
 0.35000000000000003 1.126698639626153 0.17028382977825976 1.1266986388222686 8.038842924662504E-10
 0.4 1.1338012039068435 0.11375955277684402 1.1338012039969423 9.009881729582503E-11
 0.45 1.1380698556959308 0.056950946803326186 1.138069856633876 9.379452770019725E-10
 0.5 1.139493926044109 0. 1.1394939273245492 1.2804401983146363E-9