fem_checke_la.f90 running Given x^3 u'''' + x^2 u''' + u'' + u' + u = x^4 + 64 x^3 - x^2 - 4x + 1 0 <= x <= 1 Boundary u(0) = 1, u(1) = 1 Analytic solution u(x) = x^4 - x^2 + 1 x grid and analytic solution i= 1 , Ua( 0.0000000000000000E+000 )= 1.0000000000000000 i= 2 , Ua( 0.1111111111111111 )= 0.9878067367779302 i= 3 , Ua( 0.2222222222222222 )= 0.9530559365950313 i= 4 , Ua( 0.3333333333333333 )= 0.9012345679012346 i= 5 , Ua( 0.4444444444444444 )= 0.8414875781130925 i= 6 , Ua( 0.5555555555555556 )= 0.7866178936137784 i= 7 , Ua( 0.6666666666666666 )= 0.7530864197530864 i= 8 , Ua( 0.7777777777777777 )= 0.7610120408474317 i= 9 , Ua( 0.8888888888888888 )= 0.8341716201798506 i= 10 , Ua( 1.0000000000000000 )= 1.0000000000000000 calling gaulegf np= 24 compute stiffness matrix Legendre integration= 1.2511640845540542E+02 , at i= 2 , j= 1 Legendre integration= -1.2450545957832080E+03 , at i= 2 , j= 2 Legendre integration= 5.5579637642582456E+03 , at i= 2 , j= 3 Legendre integration= -1.4699180060416653E+04 , at i= 2 , j= 4 Legendre integration= 2.5461433647720121E+04 , at i= 2 , j= 5 Legendre integration= -3.0062331805901602E+04 , at i= 2 , j= 6 Legendre integration= 2.4283615651426499E+04 , at i= 2 , j= 7 Legendre integration= -1.2970202420038786E+04 , at i= 2 , j= 8 Legendre integration= 4.1553827739879252E+03 , at i= 2 , j= 9 Legendre integration= -6.0656768290434809E+02 , at i= 2 , j= 10 Legendre integration= -0.2880711754763069 , i= 2 Legendre integration= -5.6084478395358087E+02 , at i= 3 , j= 1 Legendre integration= 5.6359325346114474E+03 , at i= 3 , j= 2 Legendre integration= -2.5345292796676462E+04 , at i= 3 , j= 3 Legendre integration= 6.7298073107822929E+04 , at i= 3 , j= 4 Legendre integration= -1.1679596394142976E+05 , at i= 3 , j= 5 Legendre integration= 1.3803197952842794E+05 , at i= 3 , j= 6 Legendre integration= -1.1155426033238201E+05 , at i= 3 , j= 7 Legendre integration= 5.9600704099842253E+04 , at i= 3 , j= 8 Legendre integration= -1.9098469932269596E+04 , at i= 3 , j= 9 Legendre integration= 2.7881545695781597E+03 , at i= 3 , j= 10 Legendre integration= 1.9154768668830870 , i= 3 Legendre integration= 1.5470266110765288E+03 , at i= 4 , j= 1 Legendre integration= -1.5441583040066742E+04 , at i= 4 , j= 2 Legendre integration= 6.9323769960032558E+04 , at i= 4 , j= 3 Legendre integration= -1.8413529261060749E+05 , at i= 4 , j= 4 Legendre integration= 3.1984661876879894E+05 , at i= 4 , j= 5 Legendre integration= -3.7828559527891624E+05 , at i= 4 , j= 6 Legendre integration= 3.0586107816414814E+05 , at i= 4 , j= 7 Legendre integration= -1.6345053474801133E+05 , at i= 4 , j= 8 Legendre integration= 5.2382371184804673E+04 , at i= 4 , j= 9 Legendre integration= -7.6476431184015964E+03 , at i= 4 , j= 10 Legendre integration= -4.9514615072426693 , i= 4 Legendre integration= -2.8203684136382453E+03 , at i= 5 , j= 1 Legendre integration= 2.8154372801392969E+04 , at i= 5 , j= 2 Legendre integration= -1.2624887966494109E+05 , at i= 5 , j= 3 Legendre integration= 3.3496674781519210E+05 , at i= 5 , j= 4 Legendre integration= -5.8155661020429083E+05 , at i= 5 , j= 5 Legendre integration= 6.8786628418030648E+05 , at i= 5 , j= 6 Legendre integration= -5.5635573150897410E+05 , at i= 5 , j= 7 Legendre integration= 2.9739483396936575E+05 , at i= 5 , j= 8 Legendre integration= -9.5316471718772620E+04 , at i= 5 , j= 9 Legendre integration= 1.3915887230966173E+04 , at i= 5 , j= 10 Legendre integration= 10.0379508772475834 , i= 5 Legendre integration= 3.5888360315702316E+03 , at i= 6 , j= 1 Legendre integration= -3.5823197836684260E+04 , at i= 6 , j= 2 Legendre integration= 1.6068278667036485E+05 , at i= 6 , j= 3 Legendre integration= -4.2620272773681773E+05 , at i= 6 , j= 4 Legendre integration= 7.3938611612911278E+05 , at i= 6 , j= 5 Legendre integration= -8.7387378251743619E+05 , at i= 6 , j= 6 Legendre integration= 7.0654889742411603E+05 , at i= 6 , j= 7 Legendre integration= -3.7773369968985784E+05 , at i= 6 , j= 8 Legendre integration= 1.2110951097200735E+05 , at i= 6 , j= 9 Legendre integration= -1.7682674959767217E+04 , at i= 6 , j= 10 Legendre integration= -11.1016153377869955 , i= 6 Legendre integration= -3.2910614320786785E+03 , at i= 7 , j= 1 Legendre integration= 3.2850215597547758E+04 , at i= 7 , j= 2 Legendre integration= -1.4737221409548842E+05 , at i= 7 , j= 3 Legendre integration= 3.9103646207821753E+05 , at i= 7 , j= 4 Legendre integration= -6.7835021933572658E+05 , at i= 7 , j= 5 Legendre integration= 8.0098273274536792E+05 , at i= 7 , j= 6 Legendre integration= -6.4645276999434270E+05 , at i= 7 , j= 7 Legendre integration= 3.4492960572912544E+05 , at i= 7 , j= 8 Legendre integration= -1.1047858265163212E+05 , at i= 7 , j= 9 Legendre integration= 1.6146047251866348E+04 , at i= 7 , j= 10 Legendre integration= 13.0131897789708226 , i= 7 Legendre integration= 2.2816828920655535E+03 , at i= 8 , j= 1 Legendre integration= -2.2782903834108514E+04 , at i= 8 , j= 2 Legendre integration= 1.0226722492746357E+05 , at i= 8 , j= 3 Legendre integration= -2.7157944318764569E+05 , at i= 8 , j= 4 Legendre integration= 4.7174355581905507E+05 , at i= 8 , j= 5 Legendre integration= -5.5769621223128214E+05 , at i= 8 , j= 6 Legendre integration= 4.4981897346832615E+05 , at i= 8 , j= 7 Legendre integration= -2.3886117627266672E+05 , at i= 8 , j= 8 Legendre integration= 7.5667060797630969E+04 , at i= 8 , j= 9 Legendre integration= -1.0858750325266394E+04 , at i= 8 , j= 10 Legendre integration= -4.4033532761879375 , i= 8 Legendre integration= -1.5534677683773416E+03 , at i= 9 , j= 1 Legendre integration= 1.5554351724864708E+04 , at i= 9 , j= 2 Legendre integration= -7.0079035905094323E+04 , at i= 9 , j= 3 Legendre integration= 1.8705276085276651E+05 , at i= 9 , j= 4 Legendre integration= -3.2735545172167767E+05 , at i= 9 , j= 5 Legendre integration= 3.9174467701322550E+05 , at i= 9 , j= 6 Legendre integration= -3.2238331886712566E+05 , at i= 9 , j= 7 Legendre integration= 1.7652146885166352E+05 , at i= 9 , j= 8 Legendre integration= -5.8312872138482438E+04 , at i= 9 , j= 9 Legendre integration= 8.8110636390404943E+03 , at i= 9 , j= 10 Legendre integration= 8.8094488602911998 , i= 9 k computed stiffness matrix, see above f computed forcing function, see above u computed Galerkin, Ua analytic, error u( 1)= 1.0000, Ua(i)= 1.0000, err= 0.2153833E-13 u( 2)= 0.9878, Ua(i)= 0.9878, err= -0.9447110E-11 u( 3)= 0.9531, Ua(i)= 0.9531, err= 0.2820744E-11 u( 4)= 0.9012, Ua(i)= 0.9012, err= 0.3104994E-10 u( 5)= 0.8415, Ua(i)= 0.8415, err= 0.6437550E-10 u( 6)= 0.7866, Ua(i)= 0.7866, err= 0.9294854E-10 u( 7)= 0.7531, Ua(i)= 0.7531, err= 0.1079186E-09 u( 8)= 0.7610, Ua(i)= 0.7610, err= 0.1014129E-09 u( 9)= 0.8342, Ua(i)= 0.8342, err= 0.6702916E-10 u(10)= 1.0000, Ua(i)= 1.0000, err= 0.0000000E+00 maxerr= 1.0791856297487357E-10 , avgerr= 4.7702397587556788E-11