laphi instantiated
fem_nl11_la.java running  
Given:
D*ux(x)+E(x)*(d/dx 1/u(x)-F*uxx(x)=f(x)
D*ux(x)-E(x)*(ux(x)/(x^2+1)^2)-F*uxx(x)=f(x)
f(x)=-2
D=1, F=1, E(x)=(x^2+1)^2
xmin<=x<=xmax  Boundaries  
Analytic solution u(x)=x^2 + 1
xmin=1.0, xmax=2.0
nx=10
x grid and analytic solution 
i=0, Ua(1.0)=2.0
i=1, Ua(1.1111111111111112)=2.234567901234568
i=2, Ua(1.2222222222222223)=2.4938271604938276
i=3, Ua(1.3333333333333333)=2.7777777777777777
i=4, Ua(1.4444444444444444)=3.0864197530864197
i=5, Ua(1.5555555555555556)=3.419753086419753
i=6, Ua(1.6666666666666665)=3.7777777777777772
i=7, Ua(1.7777777777777777)=4.160493827160494
i=8, Ua(1.8888888888888888)=4.567901234567901
i=9, Ua(2.0)=5.0
 
observing Lagrange Phi functions,j=1
L.phi(x,j,nx-1,xg)=1.0
L.phip(x,j,nx-1,xg)=-15.46071428571429
L.phipp(x,j,nx-1,xg)=34.312500000000306
observing Lagrange Phi functions, j=2
L.phi(x,j,nx-1,xg)=1.0
L.phip(x,j,nx-1,xg)=-9.835714285714316
L.phipp(x,j,nx-1,xg)=-126.96428571428544
observing Lagrange Phi functions, j=nx-2
L.phi(x,j,nx-1,xg)=1.0
L.phip(x,j,nx-1,xg)=15.460714285714285
L.phipp(x,j,nx-1,xg)=34.31250000000013
 
calling gauleg xmin=1.0, xmax=2.0, npx=24
xx[1]=1.0024063900014892, xx[2]=1.0126357220143452
xx[3]=1.0308627239986337, xx[4]=1.0567922364977995, xx[npx]=1.9975936099985108
wx[1]=0.006170614899993272, wx[2]=0.014265694314466906
wx[3]=0.022138719408709838, wx[4]=0.02964929245771833, wx[npx]=0.006170614899993272
galk(xx[2])=1683.7194889617526
galf(xx[2])=-1.656630491143925
 
solution at i=0,x=1.0 is 2.0
solution at i=1,x=1.1111111111111112 is 2.234567901234568
solution at i=2,x=1.2222222222222223 is 2.4938271604938276
solution at i=3,x=1.3333333333333333 is 2.7777777777777777
solution at i=4,x=1.4444444444444444 is 3.0864197530864197
solution at i=5,x=1.5555555555555556 is 3.419753086419753
solution at i=6,x=1.6666666666666665 is 3.7777777777777772
solution at i=7,x=1.7777777777777777 is 4.160493827160494
solution at i=8,x=1.8888888888888888 is 4.567901234567901
solution at i=9,x=2.0 is 5.0
 
boundary i=0 is 2.0
boundary i=9 is 5.0
compute stiffness matrix  
Legendre integration=-0.3513616071428445, f at i=1
Legendre integration=-0.0241071428571482, f at i=2
Legendre integration=-0.4317857142857088, f at i=3
Legendre integration=-0.12897321428571756, f at i=4
Legendre integration=-0.12897321428571587, f at i=5
Legendre integration=-0.43178571428570894, f at i=6
Legendre integration=-0.024107142857148434, f at i=7
Legendre integration=-0.35136160714284453, f at i=8
k computed stiffness matrix, see above  
f computed forcing function, see above  
 
check_soln on known solution
maxerr=4.831690603168681E-13, rmserr=2.4186410530424826E-13, avgerr=1.814381977993662E-13
check_soln based on numeric approximation of PDE
maxerr=1.290700879508222E-11, rmserr=8.260028440744105E-12, avgerr=7.157496817455922E-12
 
ug computed Galerkin, Ua analytic, error  
ug[0]=2.0000000000000044, Ua=2.0, err=4.440892098500626E-15
ug[1]=2.234567901234734, Ua=2.234567901234568, err=1.6608936448392342E-13
ug[2]=2.4938271604941895, Ua=2.4938271604938276, err=3.6193270602780103E-13
ug[3]=2.7777777777783395, Ua=2.7777777777777777, err=5.617728504603292E-13
ug[4]=3.0864197530870863, Ua=3.0864197530864197, err=6.66577903984944E-13
ug[5]=3.4197530864204215, Ua=3.419753086419753, err=6.683542608243442E-13
ug[6]=3.777777777778333, Ua=3.7777777777777772, err=5.555556015224283E-13
ug[7]=4.160493827160867, Ua=4.160493827160494, err=3.730349362740526E-13
ug[8]=4.567901234568091, Ua=4.567901234567901, err=1.900701818158268E-13
ug[9]=5.0, Ua=5.0, err=0.0
                  maxerr=6.683542608243442E-13, avgerr=3.54782869749215E-13