==== DIRICHLET - DIRICHLET PROBLEM ==== ---- GALERKIN WEIGHTING FUNCTION ---- APPROXIMATING FUNCTION: F0(X) + A1*F1(X) + A2*F2(X) WHERE F0(X) = U(0)*X/L + U(L)*(1-X/L), F1(X) = (X/L)*(1-X/L), AND F2(X) = ((X/L)*(1-X/L))**2 SQUARE OF ALPHA = 1. X-COORDINATE OF LEFT END BOUNDARY = 0. X-COORDINATE OF RIGHT END BOUNDARY = 1. U(0) = 1. U(L) = 1. LENGTH OF DOMAIN = 1. NUMBER OF SEGMENTS FOR INTEGRATION = 1000 DX FOR DERIVATIVE EVALUATION = 0.0001 H(F0,F1)= 0.16666666666666644 H(F0,F2)= 0.033333333333333416 H(F1,F1)= -0.299999999999948 H(F1,F2)= -0.05952380952379655 H(F2,F1)= -0.05952380952379655 H(F2,F2)= -0.017460317460313443 A1= 0.5462653288740628 A2= 0.046822742475207305 U(X) = F0(X)+ 0.5462653288740628 *F1(X)+ 0.046822742475207305 *F2(X) X-COORDINATE U(X) DU/DX EXACT(X) |U(X)-EXACT(X)| 0. 1. 0.5462653288740628 1. 0. 0.1 1.049543143812715 0.44375473801570053 1.0495434093618006 2.6554908560960655E-7 0.2 1.0886011148272152 0.3367491638797161 1.0886001279101831 9.86917032097523E-7 0.30000000000000004 1.11678060200671 0.22637235228545008 1.1167799138238472 6.881828626958963E-7 0.4 1.133800668896347 0.11374804905237484 1.1338012039969423 5.351005953890819E-7 0.5 1.1394927536232162 0. 1.1394939273245492 0.0000011737013330126445 0.6000000000000001 1.133800668896347 -0.11374804905249344 1.1338012039969423 5.351005953890819E-7 0.7000000000000001 1.11678060200671 -0.22637235228546537 1.1167799138238472 6.881828626958963E-7 0.8 1.0886011148272152 -0.33674916387962467 1.0886001279101831 9.86917032097523E-7 0.9 1.049543143812715 -0.44375473801561754 1.0495434093618004 2.6554908538756195E-7 1. 1. -0.5462653288740026 1. 0.