pde4sin_eq.adb running
differential equation to solve
du/dx + du/dy + du/dz +du/dt = c(x,y,z,t)
c(x,y,z,t)=0
uniform grid on rectangle 0,Pi to 0,Pi
known Solution, for testing method
u(x,y,z,t) = sin(x-y+z-t)
do not make nx=ny=nz=nt, this creates a singular matrix
DOF =  5040
xg( 1)= 0.00000000000000E+00
xg( 2)= 3.92699081698724E-01
xg( 3)= 7.85398163397448E-01
xg( 4)= 1.17809724509617E+00
xg( 5)= 1.57079632679490E+00
xg( 6)= 1.96349540849362E+00
xg( 7)= 2.35619449019234E+00
xg( 8)= 2.74889357189107E+00
xg( 9)= 3.14159265358979E+00

yg( 1)= 0.00000000000000E+00
yg( 2)= 3.49065850398866E-01
yg( 3)= 6.98131700797732E-01
yg( 4)= 1.04719755119660E+00
yg( 5)= 1.39626340159546E+00
yg( 6)= 1.74532925199433E+00
yg( 7)= 2.09439510239320E+00
yg( 8)= 2.44346095279206E+00
yg( 9)= 2.79252680319093E+00
yg( 10)= 3.14159265358979E+00

zg( 1)= 0.00000000000000E+00
zg( 2)= 3.14159265358979E-01
zg( 3)= 6.28318530717959E-01
zg( 4)= 9.42477796076938E-01
zg( 5)= 1.25663706143592E+00
zg( 6)= 1.57079632679490E+00
zg( 7)= 1.88495559215388E+00
zg( 8)= 2.19911485751286E+00
zg( 9)= 2.51327412287183E+00
zg( 10)= 2.82743338823081E+00
zg( 11)= 3.14159265358979E+00

tg( 1)= 0.00000000000000E+00
tg( 2)= 2.85599332144527E-01
tg( 3)= 5.71198664289053E-01
tg( 4)= 8.56797996433580E-01
tg( 5)= 1.14239732857811E+00
tg( 6)= 1.42799666072263E+00
tg( 7)= 1.71359599286716E+00
tg( 8)= 1.99919532501169E+00
tg( 9)= 2.28479465715621E+00
tg( 10)= 2.57039398930074E+00
tg( 11)= 2.85599332144527E+00
tg( 12)= 3.14159265358979E+00

xmin=   0.000, xmax=   3.142, hx=   0.393, nx= 9
ymin=   0.000, ymax=   3.142, hy=   0.349, ny= 10
zmin=   0.000, zmax=   3.142, hz=   0.314, nz= 11
tmin=   0.000, tmax=   3.142, ht=   0.286, nt= 12

order=1, point=1, ct( 1)=-1.05738249530165E+01
order=1, point=1, ct( 2)= 3.85154962252656E+01
order=1, point=1, ct( 3)=-9.62887405567449E+01
order=1, point=1, ct( 4)= 1.92577481102485E+02
order=1, point=1, ct( 5)=-2.88866221639608E+02
order=1, point=1, ct( 6)= 3.23530168222814E+02
order=1, point=1, ct( 7)=-2.69608473509299E+02
order=1, point=1, ct( 8)= 1.65066412347487E+02
order=1, point=1, ct( 9)=-7.22165554000652E+01
order=1, point=1, ct( 10)= 2.13974978958063E+01
order=1, point=1, ct( 11)=-3.85154962116424E+00
order=1, point=1, ct( 12)= 3.18309886040695E-01

internal cells zeroed 
matrix initialized in  7.463356000 seconds
solved for U in  2063.485504000 seconds
check_soln against PDE
check_soln max error= 1.88792350641620E-08

exact solution u, computed us, error
...
xg( 2)=  0.393, yg( 3)=  0.698, zg( 8)=  2.199, tg( 9)=  2.285, u= -0.381, us= -0.393, err= 1.15517871814702E-02
xg( 2)=  0.393, yg( 3)=  0.698, zg( 8)=  2.199, tg( 10)=  2.570, u= -0.626, us= -0.637, err= 1.04231066214434E-02
xg( 2)=  0.393, yg( 3)=  0.698, zg( 8)=  2.199, tg( 11)=  2.856, u= -0.821, us= -0.829, err= 8.68276924655209E-03
xg( 2)=  0.393, yg( 9)=  2.793, zg( 7)=  1.885, tg( 6)=  1.428, u= -0.932, us= -0.926, err= 5.31746145635170E-03
xg( 2)=  0.393, yg( 9)=  2.793, zg( 7)=  1.885, tg( 7)=  1.714, u= -0.791, us= -0.783, err= 8.02919927799839E-03
...
xg( 4)=  1.178, yg( 3)=  0.698, zg( 6)=  1.571, tg( 7)=  1.714, u=  0.331, us=  0.323, err= 7.54810497058617E-03
xg( 4)=  1.178, yg( 3)=  0.698, zg( 6)=  1.571, tg( 8)=  1.999, u=  0.052, us=  0.047, err= 4.72095164622238E-03
...
avg_error= 7.69762547968380E-03, max_error= 1.33964314662884E-02
writing pde4sin_eq.dat
finished writing pde4sin_eq.dat
now free
pde4sin_eq.adb finished in  2064.477444000 seconds