April 29 2007 8:23:39.767 AM FEM1D_ADAPTIVE FORTRAN90 version Solve the two-point boundary value problem: -d/dx ( P(x) * dU(x)/dx ) + Q(x) * U(x) = F(x) on the interval [0,1], specifying the value of U at each endpoint. The number of basis functions per element is 2 The number of quadrature points per element is 2 Problem index = 6 "ARCTAN" problem: U(X) = ATAN((X-0.5)/A) P(X) = 1.0 Q(X) = 0.0 F(X) = 2*A*(X-0.5)/(A**2+(X-0.5)**2)**2 IBC = 3 UL = ATAN(-0.5/A) UR = ATAN( 0.5/A) A = 0.100000E-01 Arctangent problem The equation is to be solved for X greater than .000000 and less than 1.00000 The boundary conditions are: At X = XL, U= -1.55080 At X = XR, U= 1.55080 Begin new iteration with 4 nodes. Printout of tridiagonal linear system: Equation A-Left A-Diag A-Rite RHS 1 8.00000 -4.00000 -9.87506 2 -4.00000 8.00000 -4.00000 0.138778E-15 3 -4.00000 8.00000 9.87506 Basic solution Node X(I) U(X(I)) U exact Error 0 .000000 -1.55080 -1.55080 .000000 1 .250000 -1.23438 -1.53082 .296435 2 .500000 -0.555112E-15 .000000 -0.555112E-15 3 .750000 1.23438 1.53082 -.296435 4 1.00000 1.55080 1.55080 .000000 ETA .244233 2.19633 2.19633 .244233 Tolerance = 1.46435 Subdivide interval 2 Subdivide interval 3 Begin new iteration with 6 nodes. Basic solution Node X(I) U(X(I)) U exact Error 0 .000000 -1.55080 -1.55080 .000000 1 .250000 -1.57269 -1.53082 -0.418763E-01 2 .375000 -1.55364 -1.49097 -0.626714E-01 3 .500000 -0.655032E-13 .000000 -0.655032E-13 4 .625000 1.55364 1.49097 0.626714E-01 5 .750000 1.57269 1.53082 0.418763E-01 6 1.00000 1.55080 1.55080 .000000 ETA 0.944353E-02 .185938 3.52685 3.52685 .185938 0.944353E-02 Tolerance = 1.48890 Subdivide interval 3 Subdivide interval 4 Begin new iteration with 8 nodes. Basic solution Node X(I) U(X(I)) U exact Error 0 .000000 -1.55080 -1.55080 .000000 1 .250000 -1.74416 -1.53082 -.213342 2 .375000 -1.81084 -1.49097 -.319870 3 .437500 -1.78503 -1.41214 -.372888 4 .500000 -0.244249E-14 .000000 -0.244249E-14 5 .562500 1.78503 1.41214 .372888 6 .625000 1.81084 1.49097 .319870 7 .750000 1.74416 1.53082 .213342 8 1.00000 1.55080 1.55080 .000000 ETA 0.944353E-02 0.265730E-01 .292454 3.34330 3.34330 .292454 0.265730E-01 0.944353E-02 Tolerance = 1.10154 Subdivide interval 4 Subdivide interval 5 Begin new iteration with 10 nodes. Basic solution Node X(I) U(X(I)) U exact Error 0 .000000 -1.55080 -1.55080 .000000 1 .250000 -1.56403 -1.53082 -0.332166E-01 2 .375000 -1.54065 -1.49097 -0.496819E-01 3 .437500 -1.46981 -1.41214 -0.576689E-01 4 .468750 -1.32254 -1.26109 -0.614455E-01 5 .500000 0.688338E-13 .000000 0.688338E-13 6 .531250 1.32254 1.26109 0.614455E-01 7 .562500 1.46981 1.41214 0.576689E-01 8 .625000 1.54065 1.49097 0.496819E-01 9 .750000 1.56403 1.53082 0.332166E-01 10 1.00000 1.55080 1.55080 .000000 ETA 0.944353E-02 0.265730E-01 0.736369E-01 .235021 2.82238 2.82238 .235021 0.736369E-01 0.265730E-01 0.944353E-02 Tolerance = .760103 Subdivide interval 5 Subdivide interval 6 Begin new iteration with 12 nodes. Basic solution Node X(I) U(X(I)) U exact Error 0 .000000 -1.55080 -1.55080 .000000 1 .250000 -1.51216 -1.53082 0.186565E-01 2 .375000 -1.46284 -1.49097 0.281279E-01 3 .437500 -1.37903 -1.41214 0.331091E-01 4 .468750 -1.22528 -1.26109 0.358167E-01 5 .484375 -.964992 -1.00148 0.364909E-01 6 .500000 0.455191E-13 .000000 0.455191E-13 7 .515625 .964992 1.00148 -0.364909E-01 8 .531250 1.22528 1.26109 -0.358167E-01 9 .562500 1.37903 1.41214 -0.331091E-01 10 .625000 1.46284 1.49097 -0.281279E-01 11 .750000 1.51216 1.53082 -0.186565E-01 12 1.00000 1.55080 1.55080 .000000 ETA 0.944353E-02 0.265730E-01 0.736369E-01 .192415 .416090 1.83110 1.83110 .416090 .192415 0.736369E-01 0.265730E-01 0.944353E-02 Tolerance = .509861 Subdivide interval 6 Subdivide interval 7 Begin new iteration with 14 nodes. Basic solution Node X(I) U(X(I)) U exact Error 0 .000000 -1.55080 -1.55080 .000000 1 .250000 -1.52873 -1.53082 0.209243E-02 2 .375000 -1.48768 -1.49097 0.328175E-02 3 .437500 -1.40802 -1.41214 0.412196E-02 4 .468750 -1.25633 -1.26109 0.475898E-02 5 .484375 -.997085 -1.00148 0.439793E-02 6 .492188 -.660270 -.663203 0.293290E-02 7 .500000 0.208722E-13 .000000 0.208722E-13 8 .507812 .660270 .663203 -0.293290E-02 9 .515625 .997085 1.00148 -0.439793E-02 10 .531250 1.25633 1.26109 -0.475898E-02 11 .562500 1.40802 1.41214 -0.412196E-02 12 .625000 1.48768 1.49097 -0.328175E-02 13 .750000 1.52873 1.53082 -0.209243E-02 14 1.00000 1.55080 1.55080 .000000 ETA 0.944353E-02 0.265730E-01 0.736369E-01 .192415 .410124 .512307 .653928 .653928 .512307 .410124 .192415 0.736369E-01 0.265730E-01 0.944353E-02 Tolerance = .322026 Subdivide interval 5 Subdivide interval 6 Subdivide interval 7 Subdivide interval 8 Subdivide interval 9 Subdivide interval 10 Begin new iteration with 20 nodes. Basic solution Node X(I) U(X(I)) U exact Error 0 .000000 -1.55080 -1.55080 .000000 1 .250000 -1.52941 -1.53082 0.140268E-02 2 .375000 -1.48872 -1.49097 0.224713E-02 3 .437500 -1.40923 -1.41214 0.291490E-02 4 .468750 -1.25763 -1.26109 0.346570E-02 5 .476562 -1.16490 -1.16751 0.261453E-02 6 .484375 -.999675 -1.00148 0.180788E-02 7 .488281 -.863012 -.864370 0.135779E-02 8 .492188 -.662316 -.663203 0.886981E-03 9 .496094 -.372028 -.372398 0.370799E-03 10 .500000 -0.344724E-13 .000000 -0.344724E-13 11 .503906 .372028 .372398 -0.370799E-03 12 .507812 .662316 .663203 -0.886981E-03 13 .511719 .863012 .864370 -0.135779E-02 14 .515625 .999675 1.00148 -0.180788E-02 15 .523438 1.16490 1.16751 -0.261453E-02 16 .531250 1.25763 1.26109 -0.346570E-02 17 .562500 1.40923 1.41214 -0.291490E-02 18 .625000 1.48872 1.49097 -0.224713E-02 19 .750000 1.52941 1.53082 -0.140268E-02 20 1.00000 1.55080 1.55080 .000000 ETA 0.944353E-02 0.265730E-01 0.736369E-01 .192422 0.942854E-01 .209540 .143922 .220710 .276384 .151308 .151308 .276384 .220710 .143922 .209540 0.942854E-01 .192422 0.736369E-01 0.265730E-01 0.944353E-02 Tolerance = .167797 Subdivide interval 4 Subdivide interval 6 Subdivide interval 8 Subdivide interval 9 Subdivide interval 12 Subdivide interval 13 Subdivide interval 15 Subdivide interval 17 Begin new iteration with 28 nodes. Basic solution Node X(I) U(X(I)) U exact Error 0 .000000 -1.55080 -1.55080 .000000 1 .250000 -1.52982 -1.53082 0.998794E-03 2 .375000 -1.48933 -1.49097 0.164130E-02 3 .437500 -1.40993 -1.41214 0.220810E-02 4 .453125 -1.35893 -1.36061 0.167961E-02 5 .468750 -1.25983 -1.26109 0.126092E-02 6 .476562 -1.16656 -1.16751 0.954394E-03 7 .480469 -1.09681 -1.09759 0.785440E-03 8 .484375 -1.00087 -1.00148 0.617209E-03 9 .488281 -.863924 -.864370 0.446597E-03 10 .490234 -.773179 -.773541 0.361764E-03 11 .492188 -.662927 -.663203 0.276314E-03 12 .494141 -.529825 -.530015 0.190069E-03 13 .496094 -.372295 -.372398 0.103811E-03 14 .500000 -0.500711E-13 .000000 -0.500711E-13 15 .503906 .372295 .372398 -0.103811E-03 16 .505859 .529825 .530015 -0.190069E-03 17 .507812 .662927 .663203 -0.276314E-03 18 .509766 .773179 .773541 -0.361764E-03 19 .511719 .863924 .864370 -0.446597E-03 20 .515625 1.00087 1.00148 -0.617209E-03 21 .519531 1.09681 1.09759 -0.785440E-03 22 .523438 1.16656 1.16751 -0.954394E-03 23 .531250 1.25983 1.26109 -0.126092E-02 24 .546875 1.35893 1.36061 -0.167961E-02 25 .562500 1.40993 1.41214 -0.220810E-02 26 .625000 1.48933 1.49097 -0.164130E-02 27 .750000 1.52982 1.53082 -0.998794E-03 28 1.00000 1.55080 1.55080 .000000 ETA 0.944353E-02 0.265730E-01 0.736427E-01 0.403251E-01 .105528 0.941991E-01 0.590606E-01 0.911395E-01 .143922 0.706817E-01 0.853153E-01 0.966675E-01 0.967009E-01 .151307 .151307 0.967009E-01 0.966675E-01 0.853153E-01 0.706817E-01 .143922 0.911395E-01 0.590606E-01 0.941991E-01 .105528 0.403251E-01 0.736427E-01 0.265730E-01 0.944353E-02 Tolerance = 0.981105E-01 Subdivide interval 5 Subdivide interval 9 Subdivide interval 14 Subdivide interval 15 Subdivide interval 20 Subdivide interval 24 The iterations did not reach their goal. The next value of N is 34 which exceeds NMAX = 30 FEM1D_ADAPTIVE: Normal end of execution. April 29 2007 8:23:39.773 AM