corner0.adb 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 = 2 Pi alpha = Pi/omega theta = atan2(y,x) 0..2Pi r = sqrt(x^2+y^2) u(x,y) = r^alpha * sin(alpha*theta) xg( 1)=-1.00000000000000E+00 xg( 2)=-8.00000000000000E-01 xg( 3)=-6.00000000000000E-01 xg( 4)=-4.00000000000000E-01 xg( 5)=-2.00000000000000E-01 xg( 6)= 0.00000000000000E+00 xg( 7)= 2.00000000000000E-01 xg( 8)= 4.00000000000000E-01 xg( 9)= 6.00000000000000E-01 xg( 10)= 8.00000000000000E-01 xg( 11)= 1.00000000000000E+00 yg( 1)=-1.00000000000000E+00 yg( 2)=-8.00000000000000E-01 yg( 3)=-6.00000000000000E-01 yg( 4)=-4.00000000000000E-01 yg( 5)=-2.00000000000000E-01 yg( 6)= 0.00000000000000E+00 yg( 7)= 2.00000000000000E-01 yg( 8)= 4.00000000000000E-01 yg( 9)= 6.00000000000000E-01 yg( 10)= 8.00000000000000E-01 yg( 11)= 1.00000000000000E+00 xmin= -1.000, xmax= 1.000, hx= 0.200, nx= 11 ymin= -1.000, ymax= 1.000, hy= 0.200, ny= 11 x= 1.0000, y= 0.0000, th= 0.0000, U= 0.0000 x= 1.0000, y= 1.0000, th= 0.7854, U= 0.4551 x= 0.0000, y= 1.0000, th= 1.5708, U= 0.7071 x=-1.0000, y= 1.0000, th= 2.3562, U= 1.0987 x=-1.0000, y= 0.0000, th= 3.1416, U= 1.0000 x=-1.0000, y=-1.0000, th= 3.9270, U= 1.0987 x= 0.0000, y=-1.0000, th= 4.7124, U= 0.7071 x= 1.0000, y=-1.0000, th= 5.4978, U= 0.4551 x= 0.0000, y= 0.0000, th= 0.0000, U= 0.0000 internal cells zeroed matrix initialized i= 2,j= 2 is bad err=-1.04870956330103E-02 i= 2,j= 3 is bad err=-4.16643098425471E-02 i= 2,j= 4 is bad err=-3.65952883692888E-01 i= 2,j= 5 is bad err=-4.07708031534769E+00 i= 2,j= 6 is bad err=-9.39234874450428E+01 i= 2,j= 7 is bad err=-4.07708031534784E+00 i= 2,j= 8 is bad err=-3.65952883692870E-01 i= 2,j= 9 is bad err=-4.16643098427283E-02 i= 2,j= 10 is bad err=-1.04870956363783E-02 i= 3,j= 2 is bad err=-3.21510863637151E-02 i= 3,j= 3 is bad err= 1.21104682515951E-02 i= 3,j= 4 is bad err= 6.05264801791546E-02 i= 3,j= 5 is bad err= 6.92390530736862E-01 i= 3,j= 6 is bad err= 1.56442289694069E+01 i= 3,j= 7 is bad err= 6.92390530736826E-01 i= 3,j= 8 is bad err= 6.05264801792280E-02 i= 3,j= 9 is bad err= 1.21104682513700E-02 i= 3,j= 10 is bad err=-3.21510863667278E-02 i= 4,j= 2 is bad err=-3.30396407831893E-01 i= 4,j= 3 is bad err= 5.18334440199038E-02 i= 4,j= 4 is bad err=-3.12708763536729E-02 i= 4,j= 5 is bad err=-1.53737298548685E-01 i= 4,j= 6 is bad err=-2.55224742108877E+00 i= 4,j= 7 is bad err=-1.53737298548723E-01 i= 4,j= 8 is bad err=-3.12708763536474E-02 i= 4,j= 9 is bad err= 5.18334440197191E-02 i= 4,j= 10 is bad err=-3.30396407834320E-01 i= 5,j= 2 is bad err=-4.31949735596600E+00 i= 5,j= 3 is bad err= 7.21935457721544E-01 i= 5,j= 4 is bad err=-1.87164929330225E-01 i= 5,j= 5 is bad err= 1.56919733489759E-01 i= 5,j= 6 is bad err=-6.96686328560744E+00 i= 5,j= 7 is bad err= 1.56919733489734E-01 i= 5,j= 8 is bad err=-1.87164929330135E-01 i= 5,j= 9 is bad err= 7.21935457721274E-01 i= 5,j= 10 is bad err=-4.31949735596805E+00 i= 6,j= 2 is bad err=-1.23873714765612E+02 i= 6,j= 3 is bad err= 2.06033231251614E+01 i= 6,j= 4 is bad err=-3.80208223184765E+00 i= 6,j= 5 is bad err=-5.99580102193564E+00 i= 6,j= 6 is bad err= 3.75042115367842E+01 i= 6,j= 7 is bad err=-5.99580102193534E+00 i= 6,j= 8 is bad err=-3.80208223184603E+00 i= 6,j= 9 is bad err= 2.06033231251582E+01 i= 6,j= 10 is bad err=-1.23873714765619E+02 i= 7,j= 2 is bad err=-6.35258008524818E+01 i= 7,j= 3 is bad err= 1.05866377944087E+01 i= 7,j= 4 is bad err=-2.14980707103144E+00 i= 7,j= 5 is bad err=-1.30295802445850E+00 i= 7,j= 6 is bad err= 1.20564548308107E+01 i= 7,j= 7 is bad err=-1.30295802445835E+00 i= 7,j= 8 is bad err=-2.14980707103063E+00 i= 7,j= 9 is bad err= 1.05866377944070E+01 i= 7,j= 10 is bad err=-6.35258008524853E+01 i= 8,j= 2 is bad err=-4.35684082955132E+01 i= 8,j= 3 is bad err= 7.25800683600817E+00 i= 8,j= 4 is bad err=-1.48119677964789E+00 i= 8,j= 5 is bad err=-1.13725256834905E+00 i= 8,j= 6 is bad err= 7.23351370696381E+00 i= 8,j= 7 is bad err=-1.13725256834893E+00 i= 8,j= 8 is bad err=-1.48119677964729E+00 i= 8,j= 9 is bad err= 7.25800683600695E+00 i= 8,j= 10 is bad err=-4.35684082955157E+01 i= 9,j= 2 is bad err=-3.50696756219474E+01 i= 9,j= 3 is bad err= 5.84192408753888E+00 i= 9,j= 4 is bad err=-1.16975876671578E+00 i= 9,j= 5 is bad err=-5.19136918410737E-01 i= 9,j= 6 is bad err= 2.17763956222071E+01 i= 9,j= 7 is bad err=-5.19136918410629E-01 i= 9,j= 8 is bad err=-1.16975876671532E+00 i= 9,j= 9 is bad err= 5.84192408753790E+00 i= 9,j= 10 is bad err=-3.50696756219493E+01 i= 10,j= 2 is bad err=-3.02180309094214E+01 i= 10,j= 3 is bad err= 5.02901655112042E+00 i= 10,j= 4 is bad err=-1.11974079241330E+00 i= 10,j= 5 is bad err=-2.76844456523937E+00 i= 10,j= 6 is bad err=-7.40668038529076E+01 i= 10,j= 7 is bad err=-2.76844456523938E+00 i= 10,j= 8 is bad err=-1.11974079241303E+00 i= 10,j= 9 is bad err= 5.02901655111962E+00 i= 10,j= 10 is bad err=-3.02180309094231E+01 check_soln against PDE check soln against PDE max error= 2.51000678574975E-11 exact solution u, computed us, error xg( 1)= -1.000, yg( 1)= -1.000, u= 1.09868, us= 1.09868, err= 0.00000000000000E+00 xg( 1)= -1.000, yg( 2)= -0.800, u= 1.06785, us= 1.06785, err= 0.00000000000000E+00 xg( 1)= -1.000, yg( 3)= -0.600, u= 1.04072, us= 1.04072, err= 0.00000000000000E+00 xg( 1)= -1.000, yg( 4)= -0.400, u= 1.01908, us= 1.01908, err= 0.00000000000000E+00 xg( 1)= -1.000, yg( 5)= -0.200, u= 1.00494, us= 1.00494, err= 0.00000000000000E+00 xg( 1)= -1.000, yg( 6)= 0.000, u= 1.00000, us= 1.00000, err= 0.00000000000000E+00 xg( 1)= -1.000, yg( 7)= 0.200, u= 1.00494, us= 1.00494, err= 0.00000000000000E+00 xg( 1)= -1.000, yg( 8)= 0.400, u= 1.01908, us= 1.01908, err= 0.00000000000000E+00 xg( 1)= -1.000, yg( 9)= 0.600, u= 1.04072, us= 1.04072, err= 0.00000000000000E+00 xg( 1)= -1.000, yg( 10)= 0.800, u= 1.06785, us= 1.06785, err= 0.00000000000000E+00 xg( 1)= -1.000, yg( 11)= 1.000, u= 1.09868, us= 1.09868, err= 0.00000000000000E+00 xg( 2)= -0.800, yg( 1)= -1.000, u= 1.01996, us= 1.01996, err= 0.00000000000000E+00 xg( 2)= -0.800, yg( 2)= -0.800, u= 0.98269, us= 0.99497, err= 1.22753394015963E-02 xg( 2)= -0.800, yg( 3)= -0.600, u= 0.94868, us= 0.97455, err= 2.58701878575405E-02 xg( 2)= -0.800, yg( 4)= -0.400, u= 0.92044, us= 0.95769, err= 3.72485472635742E-02 xg( 2)= -0.800, yg( 5)= -0.200, u= 0.90128, us= 0.94669, err= 4.54061404093639E-02 xg( 2)= -0.800, yg( 6)= 0.000, u= 0.89443, us= 0.94298, err= 4.85509013437060E-02 xg( 2)= -0.800, yg( 7)= 0.200, u= 0.90128, us= 0.94669, err= 4.54061404094145E-02 xg( 2)= -0.800, yg( 8)= 0.400, u= 0.92044, us= 0.95769, err= 3.72485472636069E-02 xg( 2)= -0.800, yg( 9)= 0.600, u= 0.94868, us= 0.97455, err= 2.58701878575520E-02 xg( 2)= -0.800, yg( 10)= 0.800, u= 0.98269, us= 0.99497, err= 1.22753394014415E-02 xg( 2)= -0.800, yg( 11)= 1.000, u= 1.01996, us= 1.01996, err= 0.00000000000000E+00 xg( 3)= -0.600, yg( 1)= -1.000, u= 0.93973, us= 0.93973, err= 0.00000000000000E+00 xg( 3)= -0.600, yg( 2)= -0.800, u= 0.89443, us= 0.92087, err= 2.64415813588853E-02 xg( 3)= -0.600, yg( 3)= -0.600, u= 0.85104, us= 0.90380, err= 5.27585876460628E-02 xg( 3)= -0.600, yg( 4)= -0.400, u= 0.81275, us= 0.89013, err= 7.73890726058087E-02 xg( 3)= -0.600, yg( 5)= -0.200, u= 0.78500, us= 0.88123, err= 9.62294980594954E-02 xg( 3)= -0.600, yg( 6)= 0.000, u= 0.77460, us= 0.87814, err= 1.03546929725727E-01 xg( 3)= -0.600, yg( 7)= 0.200, u= 0.78500, us= 0.88123, err= 9.62294980594843E-02 xg( 3)= -0.600, yg( 8)= 0.400, u= 0.81275, us= 0.89013, err= 7.73890726057698E-02 xg( 3)= -0.600, yg( 9)= 0.600, u= 0.85104, us= 0.90380, err= 5.27585876460034E-02 xg( 3)= -0.600, yg( 10)= 0.800, u= 0.89443, us= 0.92087, err= 2.64415813587923E-02 xg( 3)= -0.600, yg( 11)= 1.000, u= 0.93973, us= 0.93973, err= 0.00000000000000E+00 xg( 4)= -0.400, yg( 1)= -1.000, u= 0.85937, us= 0.85937, err= 0.00000000000000E+00 xg( 4)= -0.400, yg( 2)= -0.800, u= 0.80450, us= 0.84441, err= 3.99094841834434E-02 xg( 4)= -0.400, yg( 3)= -0.600, u= 0.74870, us= 0.82981, err= 8.11092910306917E-02 xg( 4)= -0.400, yg( 4)= -0.400, u= 0.69487, us= 0.81774, err= 1.22873591830795E-01 xg( 4)= -0.400, yg( 5)= -0.200, u= 0.65085, us= 0.80981, err= 1.58958948540795E-01 xg( 4)= -0.400, yg( 6)= 0.000, u= 0.63246, us= 0.80705, err= 1.74592027390148E-01 xg( 4)= -0.400, yg( 7)= 0.200, u= 0.65085, us= 0.80981, err= 1.58958948540755E-01 xg( 4)= -0.400, yg( 8)= 0.400, u= 0.69487, us= 0.81774, err= 1.22873591830745E-01 xg( 4)= -0.400, yg( 9)= 0.600, u= 0.74870, us= 0.82981, err= 8.11092910306241E-02 xg( 4)= -0.400, yg( 10)= 0.800, u= 0.80450, us= 0.84441, err= 3.99094841833358E-02 xg( 4)= -0.400, yg( 11)= 1.000, u= 0.85937, us= 0.85937, err= 0.00000000000000E+00 xg( 5)= -0.200, yg( 1)= -1.000, u= 0.78096, us= 0.78096, err= 0.00000000000000E+00 xg( 5)= -0.200, yg( 2)= -0.800, u= 0.71576, us= 0.76746, err= 5.17003595738652E-02 xg( 5)= -0.200, yg( 3)= -0.600, u= 0.64516, us= 0.75321, err= 1.08050650071212E-01 xg( 5)= -0.200, yg( 4)= -0.400, u= 0.56886, us= 0.74112, err= 1.72255627443915E-01 xg( 5)= -0.200, yg( 5)= -0.200, u= 0.49135, us= 0.73311, err= 2.41758733806353E-01 xg( 5)= -0.200, yg( 6)= 0.000, u= 0.44721, us= 0.73030, err= 2.83089354474199E-01 xg( 5)= -0.200, yg( 7)= 0.200, u= 0.49135, us= 0.73311, err= 2.41758733806331E-01 xg( 5)= -0.200, yg( 8)= 0.400, u= 0.56886, us= 0.74112, err= 1.72255627443874E-01 xg( 5)= -0.200, yg( 9)= 0.600, u= 0.64516, us= 0.75321, err= 1.08050650071144E-01 xg( 5)= -0.200, yg( 10)= 0.800, u= 0.71576, us= 0.76746, err= 5.17003595737544E-02 xg( 5)= -0.200, yg( 11)= 1.000, u= 0.78096, us= 0.78096, err= 0.00000000000000E+00 xg( 6)= 0.000, yg( 1)= -1.000, u= 0.70711, us= 0.70711, err= 0.00000000000000E+00 xg( 6)= 0.000, yg( 2)= -0.800, u= 0.63246, us= 0.69105, err= 5.85941590669676E-02 xg( 6)= 0.000, yg( 3)= -0.600, u= 0.54772, us= 0.67428, err= 1.26554933534926E-01 xg( 6)= 0.000, yg( 4)= -0.400, u= 0.44721, us= 0.66030, err= 2.13091252364112E-01 xg( 6)= 0.000, yg( 5)= -0.200, u= 0.31623, us= 0.65106, err= 3.34835843099435E-01 xg( 6)= 0.000, yg( 6)= 0.000, u= 0.00000, us= 0.64782, err= 6.47820656616987E-01 xg( 6)= 0.000, yg( 7)= 0.200, u= 0.31623, us= 0.65106, err= 3.34835843099413E-01 xg( 6)= 0.000, yg( 8)= 0.400, u= 0.44721, us= 0.66030, err= 2.13091252364069E-01 xg( 6)= 0.000, yg( 9)= 0.600, u= 0.54772, us= 0.67428, err= 1.26554933534856E-01 xg( 6)= 0.000, yg( 10)= 0.800, u= 0.63246, us= 0.69105, err= 5.85941590668787E-02 xg( 6)= 0.000, yg( 11)= 1.000, u= 0.70711, us= 0.70711, err= 0.00000000000000E+00 xg( 7)= 0.200, yg( 1)= -1.000, u= 0.64024, us= 0.64024, err= 0.00000000000000E+00 xg( 7)= 0.200, yg( 2)= -0.800, u= 0.55885, us= 0.61474, err= 5.58938450002987E-02 xg( 7)= 0.200, yg( 3)= -0.600, u= 0.46500, us= 0.59233, err= 1.27326852527034E-01 xg( 7)= 0.200, yg( 4)= -0.400, u= 0.35158, us= 0.57468, err= 2.23101578259508E-01 xg( 7)= 0.200, yg( 5)= -0.200, u= 0.20352, us= 0.56289, err= 3.59370101840921E-01 xg( 7)= 0.200, yg( 6)= 0.000, u= 0.00000, us= 0.55867, err= 5.58674121102257E-01 xg( 7)= 0.200, yg( 7)= 0.200, u= 0.20352, us= 0.56289, err= 3.59370101840903E-01 xg( 7)= 0.200, yg( 8)= 0.400, u= 0.35158, us= 0.57468, err= 2.23101578259469E-01 xg( 7)= 0.200, yg( 9)= 0.600, u= 0.46500, us= 0.59233, err= 1.27326852526975E-01 xg( 7)= 0.200, yg( 10)= 0.800, u= 0.55885, us= 0.61474, err= 5.58938450002229E-02 xg( 7)= 0.200, yg( 11)= 1.000, u= 0.64024, us= 0.64024, err= 0.00000000000000E+00 xg( 8)= 0.400, yg( 1)= -1.000, u= 0.58182, us= 0.58182, err= 0.00000000000000E+00 xg( 8)= 0.400, yg( 2)= -0.800, u= 0.49721, us= 0.53410, err= 3.68988938052634E-02 xg( 8)= 0.400, yg( 3)= -0.600, u= 0.40069, us= 0.50571, err= 1.05011805225261E-01 xg( 8)= 0.400, yg( 4)= -0.400, u= 0.28782, us= 0.48336, err= 1.95537626619553E-01 xg( 8)= 0.400, yg( 5)= -0.200, u= 0.15365, us= 0.46699, err= 3.13346098723579E-01 xg( 8)= 0.400, yg( 6)= 0.000, u= 0.00000, us= 0.46073, err= 4.60733575146199E-01 xg( 8)= 0.400, yg( 7)= 0.200, u= 0.15365, us= 0.46699, err= 3.13346098723565E-01 xg( 8)= 0.400, yg( 8)= 0.400, u= 0.28782, us= 0.48336, err= 1.95537626619523E-01 xg( 8)= 0.400, yg( 9)= 0.600, u= 0.40069, us= 0.50571, err= 1.05011805225207E-01 xg( 8)= 0.400, yg( 10)= 0.800, u= 0.49721, us= 0.53410, err= 3.68988938051978E-02 xg( 8)= 0.400, yg( 11)= 1.000, u= 0.58182, us= 0.58182, err= 0.00000000000000E+00 xg( 9)= 0.600, yg( 1)= -1.000, u= 0.53207, us= 0.53207, err= 0.00000000000000E+00 xg( 9)= 0.600, yg( 2)= -0.800, u= 0.44721, us= 0.43727, err= 9.94183097626983E-03 xg( 9)= 0.600, yg( 3)= -0.600, u= 0.35251, us= 0.41498, err= 6.24655910565157E-02 xg( 9)= 0.600, yg( 4)= -0.400, u= 0.24608, us= 0.38677, err= 1.40688308163894E-01 xg( 9)= 0.600, yg( 5)= -0.200, u= 0.12739, us= 0.36061, err= 2.33222174332220E-01 xg( 9)= 0.600, yg( 6)= 0.000, u= 0.00000, us= 0.34926, err= 3.49263466145404E-01 xg( 9)= 0.600, yg( 7)= 0.200, u= 0.12739, us= 0.36061, err= 2.33222174332211E-01 xg( 9)= 0.600, yg( 8)= 0.400, u= 0.24608, us= 0.38677, err= 1.40688308163875E-01 xg( 9)= 0.600, yg( 9)= 0.600, u= 0.35251, us= 0.41498, err= 6.24655910564766E-02 xg( 9)= 0.600, yg( 10)= 0.800, u= 0.44721, us= 0.43727, err= 9.94183097632639E-03 xg( 9)= 0.600, yg( 11)= 1.000, u= 0.53207, us= 0.53207, err= 0.00000000000000E+00 xg( 10)= 0.800, yg( 1)= -1.000, u= 0.49022, us= 0.49022, err= 0.00000000000000E+00 xg( 10)= 0.800, yg( 2)= -0.800, u= 0.40704, us= 0.32370, err= 8.33443601315420E-02 xg( 10)= 0.800, yg( 3)= -0.600, u= 0.31623, us= 0.33401, err= 1.77815490844944E-02 xg( 10)= 0.800, yg( 4)= -0.400, u= 0.21729, us= 0.28892, err= 7.16326371203463E-02 xg( 10)= 0.800, yg( 5)= -0.200, u= 0.11095, us= 0.23904, err= 1.28082898311983E-01 xg( 10)= 0.800, yg( 6)= 0.000, u= 0.00000, us= 0.21119, err= 2.11193028341388E-01 xg( 10)= 0.800, yg( 7)= 0.200, u= 0.11095, us= 0.23904, err= 1.28082898311987E-01 xg( 10)= 0.800, yg( 8)= 0.400, u= 0.21729, us= 0.28892, err= 7.16326371203516E-02 xg( 10)= 0.800, yg( 9)= 0.600, u= 0.31623, us= 0.33401, err= 1.77815490844808E-02 xg( 10)= 0.800, yg( 10)= 0.800, u= 0.40704, us= 0.32370, err= 8.33443601316031E-02 xg( 10)= 0.800, yg( 11)= 1.000, u= 0.49022, us= 0.49022, err= 0.00000000000000E+00 xg( 11)= 1.000, yg( 1)= -1.000, u= 0.45509, us= 0.45509, err= 0.00000000000000E+00 xg( 11)= 1.000, yg( 2)= -0.800, u= 0.37458, us= 0.37458, err= 0.00000000000000E+00 xg( 11)= 1.000, yg( 3)= -0.600, u= 0.28826, us= 0.28826, err= 0.00000000000000E+00 xg( 11)= 1.000, yg( 4)= -0.400, u= 0.19626, us= 0.19626, err= 0.00000000000000E+00 xg( 11)= 1.000, yg( 5)= -0.200, u= 0.09951, us= 0.09951, err= 0.00000000000000E+00 xg( 11)= 1.000, yg( 6)= 0.000, u= 0.00000, us= 0.00000, err= 0.00000000000000E+00 xg( 11)= 1.000, yg( 7)= 0.200, u= 0.09951, us= 0.09951, err= 0.00000000000000E+00 xg( 11)= 1.000, yg( 8)= 0.400, u= 0.19626, us= 0.19626, err= 0.00000000000000E+00 xg( 11)= 1.000, yg( 9)= 0.600, u= 0.28826, us= 0.28826, err= 0.00000000000000E+00 xg( 11)= 1.000, yg( 10)= 0.800, u= 0.37458, us= 0.37458, err= 0.00000000000000E+00 xg( 11)= 1.000, yg( 11)= 1.000, u= 0.45509, us= 0.45509, err= 0.00000000000000E+00 avg_error= 1.39893580505429E-01, max_error= 6.47820656616987E-01 writing corner0_ada.dat finished writing corner0_ada.dat finished corner0.adb in 0.101951000 seconds