abc_eq.c running 
Given  a1(x,y)*uxx(x,y) + b1(x,y)*uxy(x,y) + c1(x,y)*uyy(x,y) +
       d1(x,y)*ux(x,y) + e1(x,y)*uy(x,y)  + f1(x,y) = c(x,y) 
where, for this test case 
  a1(x,y) = exp(x/2)*exp(y)/2 
  b1(x,y) = 0.7/(x*x*y*y + 0.5) 
  c1(x,y) = (4 - exp(x) - exp(y/2))*2 
  d1(x,y) = x*x+y 
  e1(x,y) = x*y*y 
  f1(x,y) = 3.0*x + 2.0*y 
 
  c(x,y) = 0.5*exp(x/2.0)*exp(y)*(6.0*x+6.0*y)            + 
     0.7*(6.0*x + 8.0*y + 5.0)/(x*x*y*y+0.5)              + 
     (8.0 - 2.0*exp(x) - 2.0*exp(y/2.0))*(12.0*y + 8.0*x) + 
     (x*x+y)*(3.0*x*x + 6.0*x*y + 4.0*y*y + 5.0*y + 6.0)  + 
     x*y*y*(6.0*y*y + 3.0*x*x + 8.0*x*y + 5.0*x +7.0)     + 
     3.0*x + 2.0*y; 
 
xmin<=x<=xmax ymin<=y<=ymax zmin<=z<=zmax Boundaries 
Analytic solution 
 u(x,y) = x^3 + 2y^3 + 3x^2 y + 4xy^2 + 5xy + 6x + 7y + 8 
 
xmin=-1, xmax=1, ymin=-1, ymax=1 
nx=7, ny=7 
time start = 0.000000 seconds 
x grid and analytic solution at ymin 
i=0, Ua(-1.000,-1.000)=-10.0000 
i=1, Ua(-0.667,-1.000)=-5.9630 
i=2, Ua(-0.333,-1.000)=-3.0370 
i=3, Ua(-0.000,-1.000)=-1.0000 
i=4, Ua( 0.333,-1.000)= 0.3704 
i=5, Ua( 0.667,-1.000)= 1.2963 
i=6, Ua( 1.000,-1.000)= 2.0000 

y grid and analytic solution at xmin 
ii=0, Ua(-1.000,-1.000)=-10.0000 
ii=1, Ua(-1.000,-0.667)=-4.7037 
ii=2, Ua(-1.000,-0.333)=-1.1852 
ii=3, Ua(-1.000,-0.000)= 1.0000 
ii=4, Ua(-1.000, 0.333)= 2.2963 
ii=5, Ua(-1.000, 0.667)= 3.1481 
ii=6, Ua(-1.000, 1.000)= 4.0000 

check rderiv(2,nx,0,hx,cxx 
cxx[0]=40.600000 
cxx[1]=-156.600000 
cxx[2]=263.250000 
cxx[3]=-254.000000 
cxx[4]=148.500000 
cxx[5]=-48.600000 
cxx[6]=6.850000 
check rderiv(2,nx,nx-1,hx,cxx 
cxx[0]=6.850000 
cxx[1]=-48.600000 
cxx[2]=148.500000 
cxx[3]=-254.000000 
cxx[4]=263.250000 
cxx[5]=-156.600000 
cxx[6]=40.600000 

put solution in Ua vector 
time now = 0.000000 seconds, time for previous section = 0.000000 seconds 

initialize A 
time now = 0.000000 seconds, time for previous section = 0.000000 seconds 

compute A matrix 
A computed stiffness matrix 
time now = 0.000000 seconds, time for previous section = 0.000000 seconds 

solve 25 equations in 25 unknowns 
equations solved 
time now = 0.000000 seconds, time for previous section = 0.000000 seconds 

check PDE against known solution
check_soln maxerr=1.15383e-13 
check PDE against computer solution
check_soln maxerr=4.62609e-13 

          U computed, Ua analytic, error 
ug[1,1]=  -1.4074, Ua=  -1.4074, err=6.21725e-15 
ug[1,2]=   1.6667, Ua=   1.6667, err=4.44089e-16 
ug[1,3]=   3.7037, Ua=   3.7037, err=4.44089e-16 
ug[1,4]=   5.1481, Ua=   5.1481, err=1.77636e-15 
ug[1,5]=   6.4444, Ua=   6.4444, err=1.77636e-15 
ug[2,1]=   1.0000, Ua=   1.0000, err=5.32907e-15 
ug[2,2]=   3.8519, Ua=   3.8519, err=7.99361e-15 
ug[2,3]=   5.9630, Ua=   5.9630, err=8.88178e-15 
ug[2,4]=   7.7778, Ua=   7.7778, err=7.99361e-15 
ug[2,5]=   9.7407, Ua=   9.7407, err=8.88178e-15 
ug[3,1]=   2.7407, Ua=   2.7407, err=2.66454e-15 
ug[3,2]=   5.5926, Ua=   5.5926, err=9.76996e-15 
ug[3,3]=   8.0000, Ua=   8.0000, err=1.68754e-14 
ug[3,4]=  10.4074, Ua=  10.4074, err=1.59872e-14 
ug[3,5]=  13.2593, Ua=  13.2593, err=1.24345e-14 
ug[4,1]=   4.0370, Ua=   4.0370, err=1.15463e-14 
ug[4,2]=   7.1111, Ua=   7.1111, err=1.5099e-14 
ug[4,3]=  10.0370, Ua=  10.0370, err=2.30926e-14 
ug[4,4]=  13.2593, Ua=  13.2593, err=2.4869e-14 
ug[4,5]=  17.2222, Ua=  17.2222, err=2.13163e-14 
ug[5,1]=   5.1111, Ua=   5.1111, err=8.88178e-16 
ug[5,2]=   8.6296, Ua=   8.6296, err=3.55271e-15 
ug[5,3]=  12.2963, Ua=  12.2963, err=1.77636e-15 
ug[5,4]=  16.5556, Ua=  16.5556, err=0 
ug[5,5]=  21.8519, Ua=  21.8519, err=7.10543e-15 
total CPU time  = 0.000000 seconds 

                                        maxerr=2.4869e-14, avgerr=4.42277e-15 

end abc_eq.c