fem_nl11_la.c running solve Dc*ux(x) + E(x)*(-ux(x)/(x^2+1)^2 - Fc*uxx(x) = f(x) f(x) = -2 Dc = 1 Fc = 1 E(X) = (x^2+1)^2 Analytic solution u(x) = x^2+1 xmin= 1.00000000000000E+00, xmax= 2.00000000000000E+00 nx= 10 points including boundary x grid and analytic solution i= 1, Ua( 1.00000)= 2.00000 i= 2, Ua( 1.11111)= 2.23457 i= 3, Ua( 1.22222)= 2.49383 i= 4, Ua( 1.33333)= 2.77778 i= 5, Ua( 1.44444)= 3.08642 i= 6, Ua( 1.55556)= 3.41975 i= 7, Ua( 1.66667)= 3.77778 i= 8, Ua( 1.77778)= 4.16049 i= 9, Ua( 1.88889)= 4.56790 i= 10, Ua( 2.00000)= 5.00000 calling gaulegf np:= 24 compute stiffness matrix Legendre integration=-2.96635850445259E+01, at i= 2, j= 1 Legendre integration= 1.03045083734050E+02, at i= 2, j= 2 Legendre integration=-1.88042739594046E+02, at i= 2, j= 3 Legendre integration= 2.68323369425532E+02, at i= 2, j= 4 Legendre integration=-3.02522549563213E+02, at i= 2, j= 5 Legendre integration= 2.50481130907649E+02, at i= 2, j= 6 Legendre integration=-1.49662063097094E+02, at i= 2, j= 7 Legendre integration= 6.37684615297557E+01, at i= 2, j= 8 Legendre integration=-1.88919534492967E+01, at i= 2, j= 9 Legendre integration= 3.16484515118875E+00, at i= 2, j= 10 Legendre integration=-3.51361607142845E-01, i= 2 Legendre integration= 4.16617205452271E+01, at i= 3, j= 1 Legendre integration=-1.88042739594045E+02, at i= 3, j= 2 Legendre integration= 4.12783118446024E+02, at i= 3, j= 3 Legendre integration=-6.23202272646014E+02, at i= 3, j= 4 Legendre integration= 7.16799598539494E+02, at i= 3, j= 5 Legendre integration=-6.21173279816365E+02, at i= 3, j= 6 Legendre integration= 3.96672182485059E+02, at i= 3, j= 7 Legendre integration=-1.86985821908856E+02, at i= 3, j= 8 Legendre integration= 6.37684615297550E+01, at i= 3, j= 9 Legendre integration=-1.22809675802794E+01, at i= 3, j= 10 Legendre integration=-2.41071428571476E-02, i= 3 Legendre integration=-6.12047950889049E+01, at i= 4, j= 1 Legendre integration= 2.68323369425528E+02, at i= 4, j= 2 Legendre integration=-6.23202272646013E+02, at i= 4, j= 3 Legendre integration= 1.01920661272092E+03, at i= 4, j= 4 Legendre integration=-1.23597594102818E+03, at i= 4, j= 5 Legendre integration= 1.12371844227303E+03, at i= 4, j= 6 Legendre integration=-7.69081311077253E+02, at i= 4, j= 7 Legendre integration= 3.96672182485057E+02, at i= 4, j= 8 Legendre integration=-1.49662063097092E+02, at i= 4, j= 9 Legendre integration= 3.12057760329054E+01, at i= 4, j= 10 Legendre integration=-4.31785714285709E-01, i= 4 Legendre integration= 6.78764036636775E+01, at i= 5, j= 1 Legendre integration=-3.02522549563208E+02, at i= 5, j= 2 Legendre integration= 7.16799598539492E+02, at i= 5, j= 3 Legendre integration=-1.23597594102818E+03, at i= 5, j= 4 Legendre integration= 1.60653238281709E+03, at i= 5, j= 5 Legendre integration=-1.55110014806357E+03, at i= 5, j= 6 Legendre integration= 1.12371844227303E+03, at i= 5, j= 7 Legendre integration=-6.21173279816363E+02, at i= 5, j= 8 Legendre integration= 2.50481130907645E+02, at i= 5, j= 9 Legendre integration=-5.46360397296207E+01, at i= 5, j= 10 Legendre integration=-1.28973214285717E-01, i= 5 Legendre integration=-5.46360397296207E+01, at i= 6, j= 1 Legendre integration= 2.50481130907645E+02, at i= 6, j= 2 Legendre integration=-6.21173279816364E+02, at i= 6, j= 3 Legendre integration= 1.12371844227303E+03, at i= 6, j= 4 Legendre integration=-1.55110014806357E+03, at i= 6, j= 5 Legendre integration= 1.60653238281710E+03, at i= 6, j= 6 Legendre integration=-1.23597594102819E+03, at i= 6, j= 7 Legendre integration= 7.16799598539493E+02, at i= 6, j= 8 Legendre integration=-3.02522549563208E+02, at i= 6, j= 9 Legendre integration= 6.78764036636777E+01, at i= 6, j= 10 Legendre integration=-1.28973214285715E-01, i= 6 Legendre integration= 3.12057760329053E+01, at i= 7, j= 1 Legendre integration=-1.49662063097092E+02, at i= 7, j= 2 Legendre integration= 3.96672182485058E+02, at i= 7, j= 3 Legendre integration=-7.69081311077253E+02, at i= 7, j= 4 Legendre integration= 1.12371844227303E+03, at i= 7, j= 5 Legendre integration=-1.23597594102819E+03, at i= 7, j= 6 Legendre integration= 1.01920661272092E+03, at i= 7, j= 7 Legendre integration=-6.23202272646012E+02, at i= 7, j= 8 Legendre integration= 2.68323369425528E+02, at i= 7, j= 9 Legendre integration=-6.12047950889049E+01, at i= 7, j= 10 Legendre integration=-4.31785714285710E-01, i= 7 Legendre integration=-1.22809675802794E+01, at i= 8, j= 1 Legendre integration= 6.37684615297549E+01, at i= 8, j= 2 Legendre integration=-1.86985821908856E+02, at i= 8, j= 3 Legendre integration= 3.96672182485058E+02, at i= 8, j= 4 Legendre integration=-6.21173279816364E+02, at i= 8, j= 5 Legendre integration= 7.16799598539494E+02, at i= 8, j= 6 Legendre integration=-6.23202272646013E+02, at i= 8, j= 7 Legendre integration= 4.12783118446023E+02, at i= 8, j= 8 Legendre integration=-1.88042739594045E+02, at i= 8, j= 9 Legendre integration= 4.16617205452271E+01, at i= 8, j= 10 Legendre integration=-2.41071428571480E-02, i= 8 Legendre integration= 3.16484515118875E+00, at i= 9, j= 1 Legendre integration=-1.88919534492967E+01, at i= 9, j= 2 Legendre integration= 6.37684615297558E+01, at i= 9, j= 3 Legendre integration=-1.49662063097094E+02, at i= 9, j= 4 Legendre integration= 2.50481130907649E+02, at i= 9, j= 5 Legendre integration=-3.02522549563213E+02, at i= 9, j= 6 Legendre integration= 2.68323369425532E+02, at i= 9, j= 7 Legendre integration=-1.88042739594046E+02, at i= 9, j= 8 Legendre integration= 1.03045083734050E+02, at i= 9, j= 9 Legendre integration=-2.96635850445259E+01, at i= 9, j= 10 Legendre integration=-3.51361607142845E-01, i= 9 k computed stiffness matrix i= 1, j= 1, k(i,j)= 1.00000000000000E+00 i= 1, j= 2, k(i,j)= 0.00000000000000E+00 i= 1, j= 3, k(i,j)= 0.00000000000000E+00 i= 1, j= 4, k(i,j)= 0.00000000000000E+00 i= 1, j= 5, k(i,j)= 0.00000000000000E+00 i= 1, j= 6, k(i,j)= 0.00000000000000E+00 i= 1, j= 7, k(i,j)= 0.00000000000000E+00 i= 1, j= 8, k(i,j)= 0.00000000000000E+00 i= 1, j= 9, k(i,j)= 0.00000000000000E+00 i= 1, j= 10, k(i,j)= 0.00000000000000E+00 i= 2, j= 1, k(i,j)=-2.96635850445259E+01 i= 2, j= 2, k(i,j)= 1.03045083734050E+02 i= 2, j= 3, k(i,j)=-1.88042739594046E+02 i= 2, j= 4, k(i,j)= 2.68323369425532E+02 i= 2, j= 5, k(i,j)=-3.02522549563213E+02 i= 2, j= 6, k(i,j)= 2.50481130907649E+02 i= 2, j= 7, k(i,j)=-1.49662063097094E+02 i= 2, j= 8, k(i,j)= 6.37684615297557E+01 i= 2, j= 9, k(i,j)=-1.88919534492967E+01 i= 2, j= 10, k(i,j)= 3.16484515118875E+00 i= 3, j= 1, k(i,j)= 4.16617205452271E+01 i= 3, j= 2, k(i,j)=-1.88042739594045E+02 i= 3, j= 3, k(i,j)= 4.12783118446024E+02 i= 3, j= 4, k(i,j)=-6.23202272646014E+02 i= 3, j= 5, k(i,j)= 7.16799598539494E+02 i= 3, j= 6, k(i,j)=-6.21173279816365E+02 i= 3, j= 7, k(i,j)= 3.96672182485059E+02 i= 3, j= 8, k(i,j)=-1.86985821908856E+02 i= 3, j= 9, k(i,j)= 6.37684615297550E+01 i= 3, j= 10, k(i,j)=-1.22809675802794E+01 i= 4, j= 1, k(i,j)=-6.12047950889049E+01 i= 4, j= 2, k(i,j)= 2.68323369425528E+02 i= 4, j= 3, k(i,j)=-6.23202272646013E+02 i= 4, j= 4, k(i,j)= 1.01920661272092E+03 i= 4, j= 5, k(i,j)=-1.23597594102818E+03 i= 4, j= 6, k(i,j)= 1.12371844227303E+03 i= 4, j= 7, k(i,j)=-7.69081311077253E+02 i= 4, j= 8, k(i,j)= 3.96672182485057E+02 i= 4, j= 9, k(i,j)=-1.49662063097092E+02 i= 4, j= 10, k(i,j)= 3.12057760329054E+01 i= 5, j= 1, k(i,j)= 6.78764036636775E+01 i= 5, j= 2, k(i,j)=-3.02522549563208E+02 i= 5, j= 3, k(i,j)= 7.16799598539492E+02 i= 5, j= 4, k(i,j)=-1.23597594102818E+03 i= 5, j= 5, k(i,j)= 1.60653238281709E+03 i= 5, j= 6, k(i,j)=-1.55110014806357E+03 i= 5, j= 7, k(i,j)= 1.12371844227303E+03 i= 5, j= 8, k(i,j)=-6.21173279816363E+02 i= 5, j= 9, k(i,j)= 2.50481130907645E+02 i= 5, j= 10, k(i,j)=-5.46360397296207E+01 i= 6, j= 1, k(i,j)=-5.46360397296207E+01 i= 6, j= 2, k(i,j)= 2.50481130907645E+02 i= 6, j= 3, k(i,j)=-6.21173279816364E+02 i= 6, j= 4, k(i,j)= 1.12371844227303E+03 i= 6, j= 5, k(i,j)=-1.55110014806357E+03 i= 6, j= 6, k(i,j)= 1.60653238281710E+03 i= 6, j= 7, k(i,j)=-1.23597594102819E+03 i= 6, j= 8, k(i,j)= 7.16799598539493E+02 i= 6, j= 9, k(i,j)=-3.02522549563208E+02 i= 6, j= 10, k(i,j)= 6.78764036636777E+01 i= 7, j= 1, k(i,j)= 3.12057760329053E+01 i= 7, j= 2, k(i,j)=-1.49662063097092E+02 i= 7, j= 3, k(i,j)= 3.96672182485058E+02 i= 7, j= 4, k(i,j)=-7.69081311077253E+02 i= 7, j= 5, k(i,j)= 1.12371844227303E+03 i= 7, j= 6, k(i,j)=-1.23597594102819E+03 i= 7, j= 7, k(i,j)= 1.01920661272092E+03 i= 7, j= 8, k(i,j)=-6.23202272646012E+02 i= 7, j= 9, k(i,j)= 2.68323369425528E+02 i= 7, j= 10, k(i,j)=-6.12047950889049E+01 i= 8, j= 1, k(i,j)=-1.22809675802794E+01 i= 8, j= 2, k(i,j)= 6.37684615297549E+01 i= 8, j= 3, k(i,j)=-1.86985821908856E+02 i= 8, j= 4, k(i,j)= 3.96672182485058E+02 i= 8, j= 5, k(i,j)=-6.21173279816364E+02 i= 8, j= 6, k(i,j)= 7.16799598539494E+02 i= 8, j= 7, k(i,j)=-6.23202272646013E+02 i= 8, j= 8, k(i,j)= 4.12783118446023E+02 i= 8, j= 9, k(i,j)=-1.88042739594045E+02 i= 8, j= 10, k(i,j)= 4.16617205452271E+01 i= 9, j= 1, k(i,j)= 3.16484515118875E+00 i= 9, j= 2, k(i,j)=-1.88919534492967E+01 i= 9, j= 3, k(i,j)= 6.37684615297558E+01 i= 9, j= 4, k(i,j)=-1.49662063097094E+02 i= 9, j= 5, k(i,j)= 2.50481130907649E+02 i= 9, j= 6, k(i,j)=-3.02522549563213E+02 i= 9, j= 7, k(i,j)= 2.68323369425532E+02 i= 9, j= 8, k(i,j)=-1.88042739594046E+02 i= 9, j= 9, k(i,j)= 1.03045083734050E+02 i= 9, j= 10, k(i,j)=-2.96635850445259E+01 i= 10, j= 1, k(i,j)= 0.00000000000000E+00 i= 10, j= 2, k(i,j)= 0.00000000000000E+00 i= 10, j= 3, k(i,j)= 0.00000000000000E+00 i= 10, j= 4, k(i,j)= 0.00000000000000E+00 i= 10, j= 5, k(i,j)= 0.00000000000000E+00 i= 10, j= 6, k(i,j)= 0.00000000000000E+00 i= 10, j= 7, k(i,j)= 0.00000000000000E+00 i= 10, j= 8, k(i,j)= 0.00000000000000E+00 i= 10, j= 9, k(i,j)= 0.00000000000000E+00 i= 10, j= 10, k(i,j)= 1.00000000000000E+00 f computed forcing function f( 1)= 2.00000000000000E+00 f( 2)=-3.51361607142845E-01 f( 3)=-2.41071428571476E-02 f( 4)=-4.31785714285709E-01 f( 5)=-1.28973214285717E-01 f( 6)=-1.28973214285715E-01 f( 7)=-4.31785714285710E-01 f( 8)=-2.41071428571480E-02 f( 9)=-3.51361607142845E-01 f( 10)= 5.00000000000000E+00 u computed Galerkin, Ua analytic, error u( 1)= 2.00000, Ua= 2.00000, err= 0.00000 u( 2)= 2.23457, Ua= 2.23457, err= -0.00000 u( 3)= 2.49383, Ua= 2.49383, err= -0.00000 u( 4)= 2.77778, Ua= 2.77778, err= -0.00000 u( 5)= 3.08642, Ua= 3.08642, err= -0.00000 u( 6)= 3.41975, Ua= 3.41975, err= -0.00000 u( 7)= 3.77778, Ua= 3.77778, err= 0.00000 u( 8)= 4.16049, Ua= 4.16049, err= 0.00000 u( 9)= 4.56790, Ua= 4.56790, err= 0.00000 u( 10)= 5.00000, Ua= 5.00000, err= 0.00000 maxerr= 1.75859327100625E-13, avgerr= 6.72351063712995E-14