corner0.java running
differential equation to solve
d^2u/dx^2 + d^2u/dy^2 = 0
uniform grid on rectangle -1,1 to -1,1
known Solution, for testing method
omega = 2Pi
alpha = Pi/omega
theta = atan2(y,x) 0..2Pi
u(x,y) = r^alpha * sin(alpha*theta)
 
xg(0)=-1.0
xg(1)=-0.8
xg(2)=-0.6
xg(3)=-0.3999999999999999
xg(4)=-0.19999999999999996
xg(5)=0.0
xg(6)=0.20000000000000018
xg(7)=0.40000000000000013
xg(8)=0.6000000000000001
xg(9)=0.8
xg(10)=1.0
yg(0)=-1.0
yg(1)=-0.8
yg(2)=-0.6
yg(3)=-0.3999999999999999
yg(4)=-0.19999999999999996
yg(5)=0.0
yg(6)=0.20000000000000018
yg(7)=0.40000000000000013
yg(8)=0.6000000000000001
yg(9)=0.8
yg(10)=1.0
xmin=-1.00000, xmax=1.00000, nx=11, hx=0.20000
ymin=-1.00000, ymax=1.00000, ny=11, hy=0.20000
x=1.0, y=0.0, th=0.0,u=0.0
x=1.0, y=1.0, th=0.7853981633974483,u=0.45508986056222733
x=0.0, y=1.0, th=1.5707963267948966,u=0.7071067811865475
x=-1.0, y=1.0, th=2.356194490192345,u=1.0986841134678098
x=-1.0, y=0.0, th=3.141592653589793,u=1.0
x=-1.0, y=-1.0, th=3.9269908169872414,u=1.0986841134678098
x=0.0, y=-1.0, th=4.71238898038469,u=0.7071067811865476
x=1.0, y=-1.0, th=5.497787143782138,u=0.45508986056222744
internal cells zeroed 
matrix initialized
initial matrix, left side, upper 
row i=1, j=1, is bad err=-0.010487095632932153
row i=1, j=2, is bad err=-0.041664309842563085
row i=1, j=3, is bad err=-0.3659528836928594
row i=1, j=4, is bad err=-4.077080315347713
row i=1, j=5, is bad err=-93.92348744504284
row i=1, j=6, is bad err=-4.0770803153476916
row i=1, j=7, is bad err=-0.3659528836928594
row i=1, j=8, is bad err=-0.041664309843211456
row i=1, j=9, is bad err=-0.01048709563641026
row i=2, j=1, is bad err=-0.03215108636375419
row i=2, j=2, is bad err=0.012110468251595785
row i=2, j=3, is bad err=0.060526480179144526
row i=2, j=4, is bad err=0.692390530736855
row i=2, j=5, is bad err=15.644228969406852
row i=2, j=6, is bad err=0.692390530736801
row i=2, j=7, is bad err=0.06052648017922857
row i=2, j=8, is bad err=0.01211046825102624
row i=2, j=9, is bad err=-0.03215108636666564
row i=3, j=1, is bad err=-0.3303964078318433
row i=3, j=2, is bad err=0.051833444019911634
row i=3, j=3, is bad err=-0.031270876353673094
row i=3, j=4, is bad err=-0.15373729854867924
row i=3, j=5, is bad err=-2.552247421088762
row i=3, j=6, is bad err=-0.15373729854872215
row i=3, j=7, is bad err=-0.031270876353653415
row i=3, j=8, is bad err=0.05183344401944545
row i=3, j=9, is bad err=-0.3303964078344084
row i=4, j=1, is bad err=-4.319497355965931
row i=4, j=2, is bad err=0.7219354577215317
row i=4, j=3, is bad err=-0.1871649293302135
row i=4, j=4, is bad err=0.15691973348974192
row i=4, j=5, is bad err=-6.966863285607456
row i=4, j=6, is bad err=0.1569197334897514
row i=4, j=7, is bad err=-0.18716492933012274
row i=4, j=8, is bad err=0.7219354577210512
row i=4, j=9, is bad err=-4.319497355968
row i=5, j=1, is bad err=-123.87371476561243
row i=5, j=2, is bad err=20.60332312516137
row i=5, j=3, is bad err=-3.8020822318476646
row i=5, j=4, is bad err=-5.995801021935637
row i=5, j=5, is bad err=37.50421153678421
row i=5, j=6, is bad err=-5.99580102193534
row i=5, j=7, is bad err=-3.8020822318460312
row i=5, j=8, is bad err=20.603323125158155
row i=5, j=9, is bad err=-123.87371476561903
row i=6, j=1, is bad err=-63.52580085248174
row i=6, j=2, is bad err=10.586637794408727
row i=6, j=3, is bad err=-2.1498070710314416
row i=6, j=4, is bad err=-1.3029580244584933
row i=6, j=5, is bad err=12.056454830810676
row i=6, j=6, is bad err=-1.3029580244583507
row i=6, j=7, is bad err=-2.1498070710306294
row i=6, j=8, is bad err=10.586637794407025
row i=6, j=9, is bad err=-63.52580085248529
row i=7, j=1, is bad err=-43.56840829551324
row i=7, j=2, is bad err=7.258006836008172
row i=7, j=3, is bad err=-1.4811967796478875
row i=7, j=4, is bad err=-1.13725256834905
row i=7, j=5, is bad err=7.233513706963806
row i=7, j=6, is bad err=-1.1372525683489292
row i=7, j=7, is bad err=-1.4811967796472878
row i=7, j=8, is bad err=7.258006836006951
row i=7, j=9, is bad err=-43.56840829551576
row i=8, j=1, is bad err=-35.06967562194761
row i=8, j=2, is bad err=5.841924087538627
row i=8, j=3, is bad err=-1.1697587667159857
row i=8, j=4, is bad err=-0.5191369184108808
row i=8, j=5, is bad err=21.776395622207076
row i=8, j=6, is bad err=-0.5191369184107855
row i=8, j=7, is bad err=-1.1697587667155278
row i=8, j=8, is bad err=5.84192408753766
row i=8, j=9, is bad err=-35.06967562194962
row i=9, j=1, is bad err=-30.218030909421394
row i=9, j=2, is bad err=5.02901655112041
row i=9, j=3, is bad err=-1.1197407924132885
row i=9, j=4, is bad err=-2.768444565239406
row i=9, j=5, is bad err=-74.06680385290758
row i=9, j=6, is bad err=-2.7684445652393608
row i=9, j=7, is bad err=-1.119740792413016
row i=9, j=8, is bad err=5.029016551119597
row i=9, j=9, is bad err=-30.218030909423224
time to compute solution = 0.16199994087219238 seconds 
check_soln against PDE
check soln against PDE max error=2.4976631873840915E-11
exact solution u, computed us, error
xg[1]=-0.80000, yg[1]=-0.80000, u=0.98269, us=0.99497, err=-1.23E-02
xg[1]=-0.80000, yg[2]=-0.60000, u=0.94868, us=0.97455, err=-2.59E-02
xg[1]=-0.80000, yg[3]=-0.40000, u=0.92044, us=0.95769, err=-3.72E-02
xg[1]=-0.80000, yg[4]=-0.20000, u=0.90128, us=0.94669, err=-4.54E-02
xg[1]=-0.80000, yg[5]=0.00000, u=0.89443, us=0.94298, err=-4.86E-02
xg[1]=-0.80000, yg[6]=0.20000, u=0.90128, us=0.94669, err=-4.54E-02
xg[1]=-0.80000, yg[7]=0.40000, u=0.92044, us=0.95769, err=-3.72E-02
xg[1]=-0.80000, yg[8]=0.60000, u=0.94868, us=0.97455, err=-2.59E-02
xg[1]=-0.80000, yg[9]=0.80000, u=0.98269, us=0.99497, err=-1.23E-02
xg[2]=-0.60000, yg[1]=-0.80000, u=0.89443, us=0.92087, err=-2.64E-02
xg[2]=-0.60000, yg[2]=-0.60000, u=0.85104, us=0.90380, err=-5.28E-02
xg[2]=-0.60000, yg[3]=-0.40000, u=0.81275, us=0.89013, err=-7.74E-02
xg[2]=-0.60000, yg[4]=-0.20000, u=0.78500, us=0.88123, err=-9.62E-02
xg[2]=-0.60000, yg[5]=0.00000, u=0.77460, us=0.87814, err=-1.04E-01
xg[2]=-0.60000, yg[6]=0.20000, u=0.78500, us=0.88123, err=-9.62E-02
xg[2]=-0.60000, yg[7]=0.40000, u=0.81275, us=0.89013, err=-7.74E-02
xg[2]=-0.60000, yg[8]=0.60000, u=0.85104, us=0.90380, err=-5.28E-02
xg[2]=-0.60000, yg[9]=0.80000, u=0.89443, us=0.92087, err=-2.64E-02
xg[3]=-0.40000, yg[1]=-0.80000, u=0.80450, us=0.84441, err=-3.99E-02
xg[3]=-0.40000, yg[2]=-0.60000, u=0.74870, us=0.82981, err=-8.11E-02
xg[3]=-0.40000, yg[3]=-0.40000, u=0.69487, us=0.81774, err=-1.23E-01
xg[3]=-0.40000, yg[4]=-0.20000, u=0.65085, us=0.80981, err=-1.59E-01
xg[3]=-0.40000, yg[5]=0.00000, u=0.63246, us=0.80705, err=-1.75E-01
xg[3]=-0.40000, yg[6]=0.20000, u=0.65085, us=0.80981, err=-1.59E-01
xg[3]=-0.40000, yg[7]=0.40000, u=0.69487, us=0.81774, err=-1.23E-01
xg[3]=-0.40000, yg[8]=0.60000, u=0.74870, us=0.82981, err=-8.11E-02
xg[3]=-0.40000, yg[9]=0.80000, u=0.80450, us=0.84441, err=-3.99E-02
xg[4]=-0.20000, yg[1]=-0.80000, u=0.71576, us=0.76746, err=-5.17E-02
xg[4]=-0.20000, yg[2]=-0.60000, u=0.64516, us=0.75321, err=-1.08E-01
xg[4]=-0.20000, yg[3]=-0.40000, u=0.56886, us=0.74112, err=-1.72E-01
xg[4]=-0.20000, yg[4]=-0.20000, u=0.49135, us=0.73311, err=-2.42E-01
xg[4]=-0.20000, yg[5]=0.00000, u=0.44721, us=0.73030, err=-2.83E-01
xg[4]=-0.20000, yg[6]=0.20000, u=0.49135, us=0.73311, err=-2.42E-01
xg[4]=-0.20000, yg[7]=0.40000, u=0.56886, us=0.74112, err=-1.72E-01
xg[4]=-0.20000, yg[8]=0.60000, u=0.64516, us=0.75321, err=-1.08E-01
xg[4]=-0.20000, yg[9]=0.80000, u=0.71576, us=0.76746, err=-5.17E-02
xg[5]=0.00000, yg[1]=-0.80000, u=0.63246, us=0.69105, err=-5.86E-02
xg[5]=0.00000, yg[2]=-0.60000, u=0.54772, us=0.67428, err=-1.27E-01
xg[5]=0.00000, yg[3]=-0.40000, u=0.44721, us=0.66030, err=-2.13E-01
xg[5]=0.00000, yg[4]=-0.20000, u=0.31623, us=0.65106, err=-3.35E-01
xg[5]=0.00000, yg[5]=0.00000, u=0.00000, us=0.64782, err=-6.48E-01
xg[5]=0.00000, yg[6]=0.20000, u=0.31623, us=0.65106, err=-3.35E-01
xg[5]=0.00000, yg[7]=0.40000, u=0.44721, us=0.66030, err=-2.13E-01
xg[5]=0.00000, yg[8]=0.60000, u=0.54772, us=0.67428, err=-1.27E-01
xg[5]=0.00000, yg[9]=0.80000, u=0.63246, us=0.69105, err=-5.86E-02
xg[6]=0.20000, yg[1]=-0.80000, u=0.55885, us=0.61474, err=-5.59E-02
xg[6]=0.20000, yg[2]=-0.60000, u=0.46500, us=0.59233, err=-1.27E-01
xg[6]=0.20000, yg[3]=-0.40000, u=0.35158, us=0.57468, err=-2.23E-01
xg[6]=0.20000, yg[4]=-0.20000, u=0.20352, us=0.56289, err=-3.59E-01
xg[6]=0.20000, yg[5]=0.00000, u=0.00000, us=0.55867, err=-5.59E-01
xg[6]=0.20000, yg[6]=0.20000, u=0.20352, us=0.56289, err=-3.59E-01
xg[6]=0.20000, yg[7]=0.40000, u=0.35158, us=0.57468, err=-2.23E-01
xg[6]=0.20000, yg[8]=0.60000, u=0.46500, us=0.59233, err=-1.27E-01
xg[6]=0.20000, yg[9]=0.80000, u=0.55885, us=0.61474, err=-5.59E-02
xg[7]=0.40000, yg[1]=-0.80000, u=0.49721, us=0.53410, err=-3.69E-02
xg[7]=0.40000, yg[2]=-0.60000, u=0.40069, us=0.50571, err=-1.05E-01
xg[7]=0.40000, yg[3]=-0.40000, u=0.28782, us=0.48336, err=-1.96E-01
xg[7]=0.40000, yg[4]=-0.20000, u=0.15365, us=0.46699, err=-3.13E-01
xg[7]=0.40000, yg[5]=0.00000, u=0.00000, us=0.46073, err=-4.61E-01
xg[7]=0.40000, yg[6]=0.20000, u=0.15365, us=0.46699, err=-3.13E-01
xg[7]=0.40000, yg[7]=0.40000, u=0.28782, us=0.48336, err=-1.96E-01
xg[7]=0.40000, yg[8]=0.60000, u=0.40069, us=0.50571, err=-1.05E-01
xg[7]=0.40000, yg[9]=0.80000, u=0.49721, us=0.53410, err=-3.69E-02
xg[8]=0.60000, yg[1]=-0.80000, u=0.44721, us=0.43727, err=9.94E-03
xg[8]=0.60000, yg[2]=-0.60000, u=0.35251, us=0.41498, err=-6.25E-02
xg[8]=0.60000, yg[3]=-0.40000, u=0.24608, us=0.38677, err=-1.41E-01
xg[8]=0.60000, yg[4]=-0.20000, u=0.12739, us=0.36061, err=-2.33E-01
xg[8]=0.60000, yg[5]=0.00000, u=0.00000, us=0.34926, err=-3.49E-01
xg[8]=0.60000, yg[6]=0.20000, u=0.12739, us=0.36061, err=-2.33E-01
xg[8]=0.60000, yg[7]=0.40000, u=0.24608, us=0.38677, err=-1.41E-01
xg[8]=0.60000, yg[8]=0.60000, u=0.35251, us=0.41498, err=-6.25E-02
xg[8]=0.60000, yg[9]=0.80000, u=0.44721, us=0.43727, err=9.94E-03
xg[9]=0.80000, yg[1]=-0.80000, u=0.40704, us=0.32370, err=8.33E-02
xg[9]=0.80000, yg[2]=-0.60000, u=0.31623, us=0.33401, err=-1.78E-02
xg[9]=0.80000, yg[3]=-0.40000, u=0.21729, us=0.28892, err=-7.16E-02
xg[9]=0.80000, yg[4]=-0.20000, u=0.11095, us=0.23904, err=-1.28E-01
xg[9]=0.80000, yg[5]=0.00000, u=0.00000, us=0.21119, err=-2.11E-01
xg[9]=0.80000, yg[6]=0.20000, u=0.11095, us=0.23904, err=-1.28E-01
xg[9]=0.80000, yg[7]=0.40000, u=0.21729, us=0.28892, err=-7.16E-02
xg[9]=0.80000, yg[8]=0.60000, u=0.31623, us=0.33401, err=-1.78E-02
xg[9]=0.80000, yg[9]=0.80000, u=0.40704, us=0.32370, err=8.33E-02
max_error=0.6478206566170432, avg_error=0.13989358050548237
 
total error=1.13E01, average error=1.40E-01, max error=6.48E-01
writing corner0_java.dat
finished writing corner0_java.dat
total time = 0.2199997901916504 seconds 
finished corner0.java