pdenu22_eq.java running
differential equation to solve
d^2u/dx^2 + 2*d^2u/dy^2 + 3*d^2u/dxdy + 4*du/dx + 5*du/dy +6*u = c(x,y)
c(x,y) = 6x^3+12y^3+18x^2y+24xy^2+57x^2+82y^2+64xy+122x+114y+110
non uniform grid on rectangle -1.0,-1.1 to 1.2,1.3
known solution, U(x,y), to test method
u(x,y) = x^3+2y^3+3x^2y+4xy^2+5x^2+6y^2+7x+8
xmin=-1.00000, xmax=1.20000, nx=11
ymin=-1.10000, ymax=1.30000, ny=10
u(xg[0],yg[0])=1.45800
c(xg[0],yg[0])=18.40800
internal cells zeroed 
cxx 
82.58234215620661
-133.6493019543259
24.056984291950357
39.535971003894474
-20.83339727416069
12.986556267803962
-8.403753189628787
7.25784288041109
-5.393039728442545
2.0441694565553234
-0.18437391026199634
matrix initialized
initial matrix, left side, upper 
 -354.58205 -188.80600 92.02558 -42.31615 25.45015 -16.16787 13.84091 -10.24254 
 204.88621 -561.05535 6.16219 5.24882 -3.84294 2.61464 -2.29917 1.72086 
 -58.12136 143.09497 -448.67219 -12.29110 9.30565 -5.88172 4.96168 -3.63953 
 36.47831 -62.73758 88.21116 -400.79476 -24.15908 13.80553 -10.74084 7.58932 
 -23.94217 37.90762 -39.34010 77.17160 -406.55978 -19.19916 14.56001 -9.90483 
 22.04129 -33.39712 30.53266 -38.51300 70.95331 -390.95681 -31.90966 20.58756 
 -18.20194 27.03574 -23.47261 25.95286 -34.65293 76.34148 -397.85552 -30.82498 
 13.13690 -19.37355 16.52265 -17.52805 21.59199 -35.52545 129.44643 -472.65892 
initial matrix, right side, upper 
 -1.82772 0.74804 -0.43399 0.27035 -0.22923 0.16886 -0.06367 -420.40970 
 1.98247 -0.64910 0.35305 -0.21249 0.17719 -0.12951 0.04860 -542.84630 
 -2.27016 1.46240 -0.63633 0.34772 -0.27784 0.19921 -0.07391 -867.15676 
 -2.18260 -3.29484 1.55477 -0.62085 0.44662 -0.30686 0.11112 -1415.27637 
 1.25401 -2.05294 -2.88910 1.32492 -0.75007 0.47706 -0.16600 -1955.65170 
 -0.91540 1.09514 -1.76994 -3.50301 1.87836 -0.93736 0.29517 -2636.74189 
 0.66171 -0.71269 0.90647 -1.69927 -3.94267 2.22888 -0.52139 -3330.64980 
 -0.68586 0.70787 -0.83344 1.22586 -3.22209 -2.36695 1.46274 -3745.89329 
initial matrix, left side, lower 
 25.08763 -21.68979 -12.83274 4.20171 -2.28534 1.37550 -1.14696 0.83831 
 -11.30431 23.44934 -16.76784 -9.46630 4.11903 -2.25081 1.79850 -1.28952 
 6.90506 -11.45893 14.12821 -10.13500 -10.06418 4.01886 -2.89101 1.98633 
 -5.28971 8.22961 -8.11732 13.28890 -12.76141 -8.57637 4.85530 -3.08805 
 4.40197 -6.61691 5.92548 -7.08893 11.45699 -8.78746 -12.15882 6.06761 
 -3.37651 4.99146 -4.28331 4.61331 -5.86770 10.99958 -5.94152 -14.42779 
 3.59573 -5.27396 4.43963 -4.58209 5.39495 -7.93511 20.85692 -16.14133 
 -8.09014 11.80952 -9.82832 9.90154 -11.20187 14.91055 -29.11364 56.49996 
initial matrix, right side, lower 
 91.72263 -22.76547 11.39423 -6.55628 5.34799 -3.86846 1.44250 -2795.12283 
 -290.89669 50.82410 -18.15739 9.12524 -7.02955 4.95813 -1.82159 -3050.12440 
 -5.98663 -287.24276 42.94238 -12.98963 8.53457 -5.65422 2.00598 -3329.35483 
 14.78093 -11.43023 -275.49657 37.98253 -17.81197 10.68433 -3.60845 -4012.91553 
 -8.97464 8.75141 -5.43452 -286.38932 49.15749 -19.86732 5.74785 -5073.51459 
 5.08576 -4.80572 4.46909 3.00336 -312.26296 65.37022 -11.12263 -6394.18130 
 -13.07795 13.02238 -14.37805 17.38071 -9.61408 -319.06055 68.04425 -7413.05142 
 75.25806 -74.99544 83.35413 -106.32242 185.46866 -235.85568 -156.84442 -8825.99344 
 
exact solution u, computed us, error
xg[1]=-0.90000, yg[1]=-1.00000, u=2.99100, us=2.99100, err=-3.11E-11
xg[1]=-0.90000, yg[2]=-0.90000, u=3.32000, us=3.32000, err=-3.03E-11
xg[1]=-0.90000, yg[3]=-0.60000, u=3.99500, us=3.99500, err=1.86E-11
xg[1]=-0.90000, yg[4]=-0.20000, u=4.61500, us=4.61500, err=9.70E-12
xg[1]=-0.90000, yg[5]=0.30000, u=6.02000, us=6.02000, err=-2.25E-12
xg[1]=-0.90000, yg[6]=0.80000, u=9.52500, us=9.52500, err=-8.85E-13
xg[1]=-0.90000, yg[7]=1.00000, u=11.85100, us=11.85100, err=-1.36E-12
xg[1]=-0.90000, yg[8]=1.20000, u=14.84900, us=14.84900, err=9.88E-13
xg[2]=-0.80000, yg[1]=-1.00000, u=3.96800, us=3.96800, err=-4.68E-11
xg[2]=-0.80000, yg[2]=-0.90000, u=4.17000, us=4.17000, err=-6.32E-11
xg[2]=-0.80000, yg[3]=-0.60000, u=4.51200, us=4.51200, err=-4.46E-12
xg[2]=-0.80000, yg[4]=-0.20000, u=4.80000, us=4.80000, err=3.24E-11
xg[2]=-0.80000, yg[5]=0.30000, u=5.97000, us=5.97000, err=-6.90E-12
xg[2]=-0.80000, yg[6]=0.80000, u=9.44000, us=9.44000, err=1.45E-12
xg[2]=-0.80000, yg[7]=1.00000, u=11.80800, us=11.80800, err=-1.32E-12
xg[2]=-0.80000, yg[8]=1.20000, u=14.88000, us=14.88000, err=1.60E-13
xg[3]=-0.60000, yg[1]=-1.00000, u=5.90400, us=5.90400, err=-6.24E-11
xg[3]=-0.60000, yg[2]=-0.90000, u=5.87000, us=5.87000, err=-9.99E-11
xg[3]=-0.60000, yg[3]=-0.60000, u=5.60000, us=5.60000, err=-9.05E-11
xg[3]=-0.60000, yg[4]=-0.20000, u=5.29600, us=5.29600, err=2.43E-11
xg[3]=-0.60000, yg[5]=0.30000, u=6.08600, us=6.08600, err=1.31E-11
xg[3]=-0.60000, yg[6]=0.80000, u=9.57600, us=9.57600, err=-1.55E-12
xg[3]=-0.60000, yg[7]=1.00000, u=12.06400, us=12.06400, err=1.44E-12
xg[3]=-0.60000, yg[8]=1.20000, u=15.32000, us=15.32000, err=-4.71E-13
xg[4]=-0.30000, yg[1]=-1.00000, u=8.85300, us=8.85300, err=-7.53E-11
xg[4]=-0.30000, yg[2]=-0.90000, u=8.51000, us=8.51000, err=-1.31E-10
xg[4]=-0.30000, yg[3]=-0.60000, u=7.45700, us=7.45700, err=-1.80E-10
xg[4]=-0.30000, yg[4]=-0.20000, u=6.44500, us=6.44500, err=-8.03E-11
xg[4]=-0.30000, yg[5]=0.30000, u=6.89000, us=6.89000, err=2.34E-11
xg[4]=-0.30000, yg[6]=0.80000, u=10.63500, us=10.63500, err=2.48E-12
xg[4]=-0.30000, yg[7]=1.00000, u=13.39300, us=13.39300, err=-1.46E-12
xg[4]=-0.30000, yg[8]=1.20000, u=17.01500, us=17.01500, err=5.61E-13
xg[5]=0.00000, yg[1]=-1.00000, u=12.00000, us=12.00000, err=-4.38E-11
xg[5]=0.00000, yg[2]=-0.90000, u=11.40200, us=11.40200, err=-9.78E-11
xg[5]=0.00000, yg[3]=-0.60000, u=9.72800, us=9.72800, err=-2.12E-10
xg[5]=0.00000, yg[4]=-0.20000, u=8.22400, us=8.22400, err=-1.61E-10
xg[5]=0.00000, yg[5]=0.30000, u=8.59400, us=8.59400, err=-2.93E-11
xg[5]=0.00000, yg[6]=0.80000, u=12.86400, us=12.86400, err=1.20E-11
xg[5]=0.00000, yg[7]=1.00000, u=16.00000, us=16.00000, err=5.42E-12
xg[5]=0.00000, yg[8]=1.20000, u=20.09600, us=20.09600, err=1.21E-13
xg[6]=0.35000, yg[1]=-1.00000, u=16.13788, us=16.13787, err=9.29E-12
xg[6]=0.35000, yg[2]=-0.90000, u=15.31062, us=15.31062, err=3.18E-13
xg[6]=0.35000, yg[3]=-0.60000, u=13.11688, us=13.11688, err=-1.04E-10
xg[6]=0.35000, yg[4]=-0.20000, u=11.31188, us=11.31188, err=-1.91E-10
xg[6]=0.35000, yg[5]=0.30000, u=11.93562, us=11.93563, err=-8.07E-11
xg[6]=0.35000, yg[6]=0.80000, u=17.15938, us=17.15938, err=-8.72E-12
xg[6]=0.35000, yg[7]=1.00000, u=20.87288, us=20.87287, err=1.17E-12
xg[6]=0.35000, yg[8]=1.20000, u=25.65838, us=25.65837, err=2.24E-12
xg[7]=0.65000, yg[1]=-1.00000, u=20.26962, us=20.26962, err=2.31E-11
xg[7]=0.65000, yg[2]=-0.90000, u=19.30438, us=19.30437, err=4.15E-11
xg[7]=0.65000, yg[3]=-0.60000, u=16.84062, us=16.84062, err=2.18E-11
xg[7]=0.65000, yg[4]=-0.20000, u=15.01162, us=15.01163, err=-9.84E-11
xg[7]=0.65000, yg[5]=0.30000, u=16.14538, us=16.14538, err=-1.10E-10
xg[7]=0.65000, yg[6]=0.80000, u=22.47913, us=22.47913, err=-1.90E-11
xg[7]=0.65000, yg[7]=1.00000, u=26.80462, us=26.80463, err=-7.08E-12
xg[7]=0.65000, yg[8]=1.20000, u=32.29812, us=32.29813, err=-2.03E-12
xg[8]=0.85000, yg[1]=-1.00000, u=23.40912, us=23.40912, err=2.68E-12
xg[8]=0.85000, yg[2]=-0.90000, u=22.38188, us=22.38187, err=2.32E-11
xg[8]=0.85000, yg[3]=-0.60000, u=19.82812, us=19.82812, err=6.29E-11
xg[8]=0.85000, yg[4]=-0.20000, u=18.10312, us=18.10313, err=-2.41E-11
xg[8]=0.85000, yg[5]=0.30000, u=19.72688, us=19.72688, err=-8.99E-11
xg[8]=0.85000, yg[6]=0.80000, u=26.95062, us=26.95063, err=-3.22E-11
xg[8]=0.85000, yg[7]=1.00000, u=31.74412, us=31.74413, err=-6.91E-12
xg[8]=0.85000, yg[8]=1.20000, u=37.76963, us=37.76963, err=-1.92E-12
xg[9]=1.00000, yg[1]=-1.00000, u=26.00000, us=26.00000, err=-2.08E-11
xg[9]=1.00000, yg[2]=-0.90000, u=24.94200, us=24.94200, err=-1.70E-11
xg[9]=1.00000, yg[3]=-0.60000, u=22.36800, us=22.36800, err=5.68E-11
xg[9]=1.00000, yg[4]=-0.20000, u=20.78400, us=20.78400, err=2.13E-11
xg[9]=1.00000, yg[5]=0.30000, u=22.85400, us=22.85400, err=-6.14E-11
xg[9]=1.00000, yg[6]=0.80000, u=30.82400, us=30.82400, err=-4.26E-11
xg[9]=1.00000, yg[7]=1.00000, u=36.00000, us=36.00000, err=-1.70E-11
xg[9]=1.00000, yg[8]=1.20000, u=42.45600, us=42.45600, err=2.52E-12
 
total error=2.80E-09, average error=3.89E-11, max error=2.12E-10