pde_abc_eq.f90 running solve 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) u(x,y) = c(x,y) high order discretization, three area solution with one method boundary conditions computed using u(x) analytic solution may be given by u(x) ifcheck>0 xmin= -1.00000000000000 , xmax = 1.00000000000000 ymin= -1.00000000000000 , ymax = 1.00000000000000 nx= 7 , ny = 7 , nd= 5 hx= 0.333333333333333 , hy= 0.333333333333333 internal cells zeroed build_coef for point ix= 3, iy= 3 deriv pdxx returns bb=12, aa= -1 16 -30 16 -1 deriv pdyy returns bb=12, aa= -1 16 -30 16 -1 deriv pdx returns bb=12, aa= 1 -8 0 8 -1 deriv pdy returns bb=12, aa= 1 -8 0 8 -1 pdxx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 -0.75 0.00 0.00 i=2, 0.00 0.00 12.00 0.00 0.00 i=3, 0.00 0.00 -22.50 0.00 0.00 i=4, 0.00 0.00 12.00 0.00 0.00 i=5, 0.00 0.00 -0.75 0.00 0.00 x pdxy j=1 j=2 j=3 j=4 j=5 y i=1, 0.06 -0.50 0.00 0.50 -0.06 i=2, -0.50 4.00 -0.00 -4.00 0.50 i=3, 0.00 -0.00 0.00 0.00 -0.00 i=4, 0.50 -4.00 0.00 4.00 -0.50 i=5, -0.06 0.50 -0.00 -0.50 0.06 x pdyy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, 0.00 0.00 0.00 0.00 0.00 i=3, -0.75 12.00 -22.50 12.00 -0.75 i=4, 0.00 0.00 0.00 0.00 0.00 i=5, 0.00 0.00 0.00 0.00 0.00 x pdx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.25 0.00 0.00 i=2, 0.00 0.00 -2.00 0.00 0.00 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, 0.00 0.00 2.00 0.00 0.00 i=5, 0.00 0.00 -0.25 0.00 0.00 x pdy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, 0.00 0.00 0.00 0.00 0.00 i=3, 0.25 -2.00 0.00 2.00 -0.25 i=4, 0.00 0.00 0.00 0.00 0.00 i=5, 0.00 0.00 0.00 0.00 0.00 x working row 7, i= 3, j= 3, bi= 0, bj= 0 ii= 7, ut(ii,ii)=-118.155, uy(ii)= -58.892 working row 8, i= 3, j= 4, bi= 0, bj= 0 ii= 8, ut(ii,ii)=-113.279, uy(ii)= -15.545 working row 9, i= 3, j= 5, bi= 0, bj= 0 ii= 9, ut(ii,ii)=-108.219, uy(ii)= 56.619 working row 12, i= 4, j= 3, bi= 0, bj= 0 ii=12, ut(ii,ii)=-105.636, uy(ii)= -24.979 working row 13, i= 4, j= 4, bi= 0, bj= 0 ii=13, ut(ii,ii)=-101.250, uy(ii)= 7.000 working row 14, i= 4, j= 5, bi= 0, bj= 0 ii=14, ut(ii,ii)= -96.873, uy(ii)= 87.945 working row 17, i= 5, j= 3, bi= 0, bj= 0 ii=17, ut(ii,ii)= -88.295, uy(ii)= 9.761 working row 18, i= 5, j= 4, bi= 0, bj= 0 ii=18, ut(ii,ii)= -84.488, uy(ii)= 42.591 working row 19, i= 5, j= 5, bi= 0, bj= 0 ii=19, ut(ii,ii)= -80.918, uy(ii)= 140.198 standard central cells generated build_coef for point ix= 2, iy= 3 deriv pdxx returns bb=12, aa= 11 -20 6 4 -1 deriv pdyy returns bb=12, aa= -1 16 -30 16 -1 deriv pdx returns bb=12, aa= -3 -10 18 -6 1 deriv pdy returns bb=12, aa= 1 -8 0 8 -1 pdxx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 8.25 0.00 0.00 i=2, 0.00 0.00 -15.00 0.00 0.00 i=3, 0.00 0.00 4.50 0.00 0.00 i=4, 0.00 0.00 3.00 0.00 0.00 i=5, 0.00 0.00 -0.75 0.00 0.00 x pdxy j=1 j=2 j=3 j=4 j=5 y i=1, -0.19 1.50 -0.00 -1.50 0.19 i=2, -0.63 5.00 -0.00 -5.00 0.63 i=3, 1.13 -9.00 0.00 9.00 -1.13 i=4, -0.38 3.00 -0.00 -3.00 0.38 i=5, 0.06 -0.50 0.00 0.50 -0.06 x pdyy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, -0.75 12.00 -22.50 12.00 -0.75 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, 0.00 0.00 0.00 0.00 0.00 i=5, 0.00 0.00 0.00 0.00 0.00 x pdx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 -0.75 0.00 0.00 i=2, 0.00 0.00 -2.50 0.00 0.00 i=3, 0.00 0.00 4.50 0.00 0.00 i=4, 0.00 0.00 -1.50 0.00 0.00 i=5, 0.00 0.00 0.25 0.00 0.00 x pdy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, 0.25 -2.00 0.00 2.00 -0.25 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, 0.00 0.00 0.00 0.00 0.00 i=5, 0.00 0.00 0.00 0.00 0.00 x working row edge i= 2, j= 3 working row 2, i= 2, j= 3, bi=-1, bj= 0 ii= 2, ut(ii,ii)=-125.600, uy(ii)= -71.367 working row edge i= 2, j= 4 working row 3, i= 2, j= 4, bi=-1, bj= 0 ii= 3, ut(ii,ii)=-120.381, uy(ii)= -28.077 working row edge i= 2, j= 5 working row 4, i= 2, j= 5, bi=-1, bj= 0 ii= 4, ut(ii,ii)=-114.513, uy(ii)= 23.941 build_coef for point ix= 4, iy= 3 deriv pdxx returns bb=12, aa= -1 4 6 -20 11 deriv pdyy returns bb=12, aa= -1 16 -30 16 -1 deriv pdx returns bb=12, aa= -1 6 -18 10 3 deriv pdy returns bb=12, aa= 1 -8 0 8 -1 pdxx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 -0.75 0.00 0.00 i=2, 0.00 0.00 3.00 0.00 0.00 i=3, 0.00 0.00 4.50 0.00 0.00 i=4, 0.00 0.00 -15.00 0.00 0.00 i=5, 0.00 0.00 8.25 0.00 0.00 x pdxy j=1 j=2 j=3 j=4 j=5 y i=1, -0.06 0.50 -0.00 -0.50 0.06 i=2, 0.38 -3.00 0.00 3.00 -0.38 i=3, -1.13 9.00 -0.00 -9.00 1.13 i=4, 0.63 -5.00 0.00 5.00 -0.63 i=5, 0.19 -1.50 0.00 1.50 -0.19 x pdyy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, 0.00 0.00 0.00 0.00 0.00 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, -0.75 12.00 -22.50 12.00 -0.75 i=5, 0.00 0.00 0.00 0.00 0.00 x pdx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 -0.25 0.00 0.00 i=2, 0.00 0.00 1.50 0.00 0.00 i=3, 0.00 0.00 -4.50 0.00 0.00 i=4, 0.00 0.00 2.50 0.00 0.00 i=5, 0.00 0.00 0.75 0.00 0.00 x pdy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, 0.00 0.00 0.00 0.00 0.00 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, 0.25 -2.00 0.00 2.00 -0.25 i=5, 0.00 0.00 0.00 0.00 0.00 x working row edge i= 6, j= 3 working row 22, i= 6, j= 3, bi= 1, bj= 0 ii=22, ut(ii,ii)= -60.149, uy(ii)= -28.906 working row edge i= 6, j= 4 working row 23, i= 6, j= 4, bi= 1, bj= 0 ii=23, ut(ii,ii)= -54.708, uy(ii)= -52.636 working row edge i= 6, j= 5 working row 24, i= 6, j= 5, bi= 1, bj= 0 ii=24, ut(ii,ii)= -49.188, uy(ii)= -67.994 build_coef for point ix= 3, iy= 2 deriv pdxx returns bb=12, aa= -1 16 -30 16 -1 deriv pdyy returns bb=12, aa= 11 -20 6 4 -1 deriv pdx returns bb=12, aa= 1 -8 0 8 -1 deriv pdy returns bb=12, aa= -3 -10 18 -6 1 pdxx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 -0.75 0.00 0.00 0.00 i=2, 0.00 12.00 0.00 0.00 0.00 i=3, 0.00 -22.50 0.00 0.00 0.00 i=4, 0.00 12.00 0.00 0.00 0.00 i=5, 0.00 -0.75 0.00 0.00 0.00 x pdxy j=1 j=2 j=3 j=4 j=5 y i=1, -0.19 -0.63 1.13 -0.38 0.06 i=2, 1.50 5.00 -9.00 3.00 -0.50 i=3, -0.00 -0.00 0.00 -0.00 0.00 i=4, -1.50 -5.00 9.00 -3.00 0.50 i=5, 0.19 0.63 -1.13 0.38 -0.06 x pdyy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, 0.00 0.00 0.00 0.00 0.00 i=3, 8.25 -15.00 4.50 3.00 -0.75 i=4, 0.00 0.00 0.00 0.00 0.00 i=5, 0.00 0.00 0.00 0.00 0.00 x pdx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.25 0.00 0.00 0.00 i=2, 0.00 -2.00 0.00 0.00 0.00 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, 0.00 2.00 0.00 0.00 0.00 i=5, 0.00 -0.25 0.00 0.00 0.00 x pdy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, 0.00 0.00 0.00 0.00 0.00 i=3, -0.75 -2.50 4.50 -1.50 0.25 i=4, 0.00 0.00 0.00 0.00 0.00 i=5, 0.00 0.00 0.00 0.00 0.00 x working row edge i= 3, j= 2 working row 6, i= 3, j= 2, bi= 0, bj=-1 ii= 6, ut(ii,ii)= -83.860, uy(ii)= 66.541 working row edge i= 4, j= 2 working row 11, i= 4, j= 2, bi= 0, bj=-1 ii=11, ut(ii,ii)= -75.613, uy(ii)= -1.719 working row edge i= 5, j= 2 working row 16, i= 5, j= 2, bi= 0, bj=-1 ii=16, ut(ii,ii)= -64.163, uy(ii)= -23.770 build_coef for point ix= 3, iy= 4 deriv pdxx returns bb=12, aa= -1 16 -30 16 -1 deriv pdyy returns bb=12, aa= -1 4 6 -20 11 deriv pdx returns bb=12, aa= 1 -8 0 8 -1 deriv pdy returns bb=12, aa= -1 6 -18 10 3 pdxx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 -0.75 0.00 i=2, 0.00 0.00 0.00 12.00 0.00 i=3, 0.00 0.00 0.00 -22.50 0.00 i=4, 0.00 0.00 0.00 12.00 0.00 i=5, 0.00 0.00 0.00 -0.75 0.00 x pdxy j=1 j=2 j=3 j=4 j=5 y i=1, -0.06 0.38 -1.13 0.63 0.19 i=2, 0.50 -3.00 9.00 -5.00 -1.50 i=3, -0.00 0.00 -0.00 0.00 0.00 i=4, -0.50 3.00 -9.00 5.00 1.50 i=5, 0.06 -0.38 1.13 -0.63 -0.19 x pdyy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, 0.00 0.00 0.00 0.00 0.00 i=3, -0.75 3.00 4.50 -15.00 8.25 i=4, 0.00 0.00 0.00 0.00 0.00 i=5, 0.00 0.00 0.00 0.00 0.00 x pdx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.25 0.00 i=2, 0.00 0.00 0.00 -2.00 0.00 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, 0.00 0.00 0.00 2.00 0.00 i=5, 0.00 0.00 0.00 -0.25 0.00 x pdy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, 0.00 0.00 0.00 0.00 0.00 i=3, -0.25 1.50 -4.50 2.50 0.75 i=4, 0.00 0.00 0.00 0.00 0.00 i=5, 0.00 0.00 0.00 0.00 0.00 x working row edge i= 3, j= 6 working row 10, i= 3, j= 6, bi= 0, bj= 1 ii=10, ut(ii,ii)= -75.221, uy(ii)=-350.310 working row edge i= 4, j= 6 working row 15, i= 4, j= 6, bi= 0, bj= 1 ii=15, ut(ii,ii)= -68.710, uy(ii)=-396.662 working row edge i= 5, j= 6 working row 20, i= 5, j= 6, bi= 0, bj= 1 ii=20, ut(ii,ii)= -59.446, uy(ii)=-337.037 four sides, one element in, special case, generated build_coef for point ix= 2, iy= 2 deriv pdxx returns bb=12, aa= 11 -20 6 4 -1 deriv pdyy returns bb=12, aa= 11 -20 6 4 -1 deriv pdx returns bb=12, aa= -3 -10 18 -6 1 deriv pdy returns bb=12, aa= -3 -10 18 -6 1 pdxx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 8.25 0.00 0.00 0.00 i=2, 0.00 -15.00 0.00 0.00 0.00 i=3, 0.00 4.50 0.00 0.00 0.00 i=4, 0.00 3.00 0.00 0.00 0.00 i=5, 0.00 -0.75 0.00 0.00 0.00 x pdxy j=1 j=2 j=3 j=4 j=5 y i=1, 0.56 1.88 -3.38 1.13 -0.19 i=2, 1.88 6.25 -11.25 3.75 -0.63 i=3, -3.38 -11.25 20.25 -6.75 1.13 i=4, 1.13 3.75 -6.75 2.25 -0.38 i=5, -0.19 -0.63 1.13 -0.38 0.06 x pdyy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, 8.25 -15.00 4.50 3.00 -0.75 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, 0.00 0.00 0.00 0.00 0.00 i=5, 0.00 0.00 0.00 0.00 0.00 x pdx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 -0.75 0.00 0.00 0.00 i=2, 0.00 -2.50 0.00 0.00 0.00 i=3, 0.00 4.50 0.00 0.00 0.00 i=4, 0.00 -1.50 0.00 0.00 0.00 i=5, 0.00 0.25 0.00 0.00 0.00 x pdy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, -0.75 -2.50 4.50 -1.50 0.25 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, 0.00 0.00 0.00 0.00 0.00 i=5, 0.00 0.00 0.00 0.00 0.00 x working row 1, i= 2, j= 2, bi=-1, bj=-1 ii= 1, ut(ii,ii)= -81.626, uy(ii)= 213.508 build_coef for point ix= 2, iy= 4 deriv pdxx returns bb=12, aa= 11 -20 6 4 -1 deriv pdyy returns bb=12, aa= -1 4 6 -20 11 deriv pdx returns bb=12, aa= -3 -10 18 -6 1 deriv pdy returns bb=12, aa= -1 6 -18 10 3 pdxx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 8.25 0.00 i=2, 0.00 0.00 0.00 -15.00 0.00 i=3, 0.00 0.00 0.00 4.50 0.00 i=4, 0.00 0.00 0.00 3.00 0.00 i=5, 0.00 0.00 0.00 -0.75 0.00 x pdxy j=1 j=2 j=3 j=4 j=5 y i=1, 0.19 -1.13 3.38 -1.88 -0.56 i=2, 0.63 -3.75 11.25 -6.25 -1.88 i=3, -1.13 6.75 -20.25 11.25 3.38 i=4, 0.38 -2.25 6.75 -3.75 -1.13 i=5, -0.06 0.38 -1.13 0.63 0.19 x pdyy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, -0.75 3.00 4.50 -15.00 8.25 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, 0.00 0.00 0.00 0.00 0.00 i=5, 0.00 0.00 0.00 0.00 0.00 x pdx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 -0.75 0.00 i=2, 0.00 0.00 0.00 -2.50 0.00 i=3, 0.00 0.00 0.00 4.50 0.00 i=4, 0.00 0.00 0.00 -1.50 0.00 i=5, 0.00 0.00 0.00 0.25 0.00 x pdy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, -0.25 1.50 -4.50 2.50 0.75 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, 0.00 0.00 0.00 0.00 0.00 i=5, 0.00 0.00 0.00 0.00 0.00 x working row 5, i= 2, j= 6, bi=-1, bj= 1 ii= 5, ut(ii,ii)= -83.654, uy(ii)=-277.927 build_coef for point ix= 4, iy= 2 deriv pdxx returns bb=12, aa= -1 4 6 -20 11 deriv pdyy returns bb=12, aa= 11 -20 6 4 -1 deriv pdx returns bb=12, aa= -1 6 -18 10 3 deriv pdy returns bb=12, aa= -3 -10 18 -6 1 pdxx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 -0.75 0.00 0.00 0.00 i=2, 0.00 3.00 0.00 0.00 0.00 i=3, 0.00 4.50 0.00 0.00 0.00 i=4, 0.00 -15.00 0.00 0.00 0.00 i=5, 0.00 8.25 0.00 0.00 0.00 x pdxy j=1 j=2 j=3 j=4 j=5 y i=1, 0.19 0.63 -1.13 0.38 -0.06 i=2, -1.13 -3.75 6.75 -2.25 0.38 i=3, 3.38 11.25 -20.25 6.75 -1.13 i=4, -1.88 -6.25 11.25 -3.75 0.63 i=5, -0.56 -1.88 3.38 -1.13 0.19 x pdyy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, 0.00 0.00 0.00 0.00 0.00 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, 8.25 -15.00 4.50 3.00 -0.75 i=5, 0.00 0.00 0.00 0.00 0.00 x pdx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 -0.25 0.00 0.00 0.00 i=2, 0.00 1.50 0.00 0.00 0.00 i=3, 0.00 -4.50 0.00 0.00 0.00 i=4, 0.00 2.50 0.00 0.00 0.00 i=5, 0.00 0.75 0.00 0.00 0.00 x pdy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, 0.00 0.00 0.00 0.00 0.00 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, -0.75 -2.50 4.50 -1.50 0.25 i=5, 0.00 0.00 0.00 0.00 0.00 x working row 21, i= 6, j= 2, bi= 1, bj=-1 ii=21, ut(ii,ii)= -52.348, uy(ii)= -51.723 build_coef for point ix= 4, iy= 4 deriv pdxx returns bb=12, aa= -1 4 6 -20 11 deriv pdyy returns bb=12, aa= -1 4 6 -20 11 deriv pdx returns bb=12, aa= -1 6 -18 10 3 deriv pdy returns bb=12, aa= -1 6 -18 10 3 pdxx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 -0.75 0.00 i=2, 0.00 0.00 0.00 3.00 0.00 i=3, 0.00 0.00 0.00 4.50 0.00 i=4, 0.00 0.00 0.00 -15.00 0.00 i=5, 0.00 0.00 0.00 8.25 0.00 x pdxy j=1 j=2 j=3 j=4 j=5 y i=1, 0.06 -0.38 1.13 -0.63 -0.19 i=2, -0.38 2.25 -6.75 3.75 1.13 i=3, 1.13 -6.75 20.25 -11.25 -3.38 i=4, -0.63 3.75 -11.25 6.25 1.88 i=5, -0.19 1.13 -3.38 1.88 0.56 x pdyy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, 0.00 0.00 0.00 0.00 0.00 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, -0.75 3.00 4.50 -15.00 8.25 i=5, 0.00 0.00 0.00 0.00 0.00 x pdx j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 -0.25 0.00 i=2, 0.00 0.00 0.00 1.50 0.00 i=3, 0.00 0.00 0.00 -4.50 0.00 i=4, 0.00 0.00 0.00 2.50 0.00 i=5, 0.00 0.00 0.00 0.75 0.00 x pdy j=1 j=2 j=3 j=4 j=5 y i=1, 0.00 0.00 0.00 0.00 0.00 i=2, 0.00 0.00 0.00 0.00 0.00 i=3, 0.00 0.00 0.00 0.00 0.00 i=4, -0.25 1.50 -4.50 2.50 0.75 i=5, 0.00 0.00 0.00 0.00 0.00 x working row 25, i= 6, j= 6, bi= 1, bj= 1 ii=25, ut(ii,ii)= -26.963, uy(ii)=-520.864 matrix initialized initial matrix i= 1, j= 1 .. 25 -81.626 12.307 20.828 -4.856 0.000 -11.462 20.322 -6.774 1.129 0.000 4.648 -6.774 2.258 -0.376 0.000 -0.821 1.129 -0.376 0.063 0.000 0.000 0.000 0.000 0.000 0.000 213.508 i= 2, j= 1 .. 25 69.881 -125.600 56.843 -3.145 0.000 -11.467 1.655 11.467 -1.433 0.000 3.822 0.603 -3.822 0.478 0.000 -0.637 -0.165 0.637 -0.080 0.000 0.000 0.000 0.000 0.000 0.000 -71.367 i= 3, j= 1 .. 25 -4.605 66.678 -120.381 52.678 -2.855 1.575 -12.600 3.612 12.600 -1.575 -0.525 4.200 0.408 -4.200 0.525 0.087 -0.700 -0.158 0.700 -0.087 0.000 0.000 0.000 0.000 0.000 -28.077 i= 4, j= 1 .. 25 0.000 -4.273 61.844 -114.513 48.806 0.000 1.433 -11.467 5.750 11.467 0.000 -0.478 3.822 0.333 -3.822 0.000 0.080 -0.637 -0.181 0.637 0.000 0.000 0.000 0.000 0.000 23.941 i= 5, j= 1 .. 25 0.000 -2.435 8.338 31.442 -83.654 0.000 -1.129 6.774 -20.322 19.430 0.000 0.376 -2.258 6.774 -3.337 0.000 -0.063 0.376 -1.129 0.382 0.000 0.000 0.000 0.000 0.000 -277.927 i= 6, j= 1 .. 25 10.089 -11.467 3.822 -0.637 0.000 -83.860 22.436 15.624 -3.887 0.000 -4.874 11.467 -3.822 0.637 0.000 0.772 -1.433 0.478 -0.080 0.000 0.000 0.000 0.000 0.000 0.000 66.541 i= 7, j= 1 .. 25 5.465 4.084 -5.465 0.683 0.000 58.562 -118.155 58.414 -3.646 0.000 -5.465 3.195 5.465 -0.683 0.000 0.683 -0.172 -0.683 0.085 0.000 0.000 0.000 0.000 0.000 0.000 -58.892 i= 8, j= 1 .. 25 -0.700 5.600 4.857 -5.600 0.700 -3.425 54.803 -113.279 54.803 -3.425 0.700 -5.600 5.301 5.600 -0.700 -0.087 0.700 -0.345 -0.700 0.087 0.000 0.000 0.000 0.000 0.000 -15.545 i= 9, j= 1 .. 25 0.000 -0.683 5.465 6.199 -5.465 0.000 -3.162 50.525 -108.219 50.377 0.000 0.683 -5.465 7.977 5.465 0.000 -0.085 0.683 -0.554 -0.683 0.000 0.000 0.000 0.000 0.000 56.619 i= 10, j= 1 .. 25 0.000 0.637 -3.822 11.467 1.966 0.000 -2.795 11.105 17.657 -75.221 0.000 -0.637 3.822 -11.467 17.819 0.000 0.080 -0.478 1.433 -1.609 0.000 0.000 0.000 0.000 0.000 -350.310 i= 11, j= 1 .. 25 -1.234 1.575 -0.525 0.087 0.000 11.414 -12.600 4.200 -0.700 0.000 -75.613 20.551 13.701 -3.425 0.000 -5.253 12.600 -4.200 0.700 0.000 0.849 -1.575 0.525 -0.087 0.000 -1.719 i= 12, j= 1 .. 25 -0.700 -0.352 0.700 -0.087 0.000 5.600 4.966 -5.600 0.700 0.000 51.684 -105.636 51.684 -3.230 0.000 -5.600 3.633 5.600 -0.700 0.000 0.700 -0.185 -0.700 0.087 0.000 -24.979 i= 13, j= 1 .. 25 0.087 -0.700 -0.375 0.700 -0.087 -0.700 5.600 6.000 -5.600 0.700 -3.000 48.000 -101.250 48.000 -3.000 0.700 -5.600 6.000 5.600 -0.700 -0.087 0.700 -0.375 -0.700 0.087 7.000 i= 14, j= 1 .. 25 0.000 0.087 -0.700 -0.440 0.700 0.000 -0.700 5.600 7.707 -5.600 0.000 -2.728 43.647 -96.873 43.647 0.000 0.700 -5.600 9.040 5.600 0.000 -0.087 0.700 -0.607 -0.700 87.945 i= 15, j= 1 .. 25 0.000 -0.087 0.525 -1.575 0.311 0.000 0.700 -4.200 12.600 3.353 0.000 -2.407 9.626 14.439 -68.710 0.000 -0.700 4.200 -12.600 20.020 0.000 0.087 -0.525 1.575 -1.772 -396.662 i= 16, j= 1 .. 25 0.000 0.000 0.000 0.000 0.000 -1.163 1.433 -0.478 0.080 0.000 11.121 -11.467 3.822 -0.637 0.000 -64.163 17.657 11.105 -2.795 0.000 -3.843 11.467 -3.822 0.637 0.000 -23.770 i= 17, j= 1 .. 25 0.000 0.000 0.000 0.000 0.000 -0.683 -0.373 0.683 -0.085 0.000 5.465 5.523 -5.465 0.683 0.000 42.116 -88.295 42.264 -2.646 0.000 -5.465 4.634 5.465 -0.683 0.000 9.761 i= 18, j= 1 .. 25 0.000 0.000 0.000 0.000 0.000 0.087 -0.700 -0.415 0.700 -0.087 -0.700 5.600 6.866 -5.600 0.700 -2.407 38.505 -84.488 38.505 -2.407 0.700 -5.600 7.310 5.600 -0.700 42.591 i= 19, j= 1 .. 25 0.000 0.000 0.000 0.000 0.000 0.000 0.085 -0.683 -0.507 0.683 0.000 -0.683 5.465 9.003 -5.465 0.000 -2.125 34.079 -80.918 34.227 0.000 0.683 -5.465 10.781 5.465 140.198 i= 20, j= 1 .. 25 0.000 0.000 0.000 0.000 0.000 0.000 -0.080 0.478 -1.433 0.128 0.000 0.637 -3.822 11.467 5.880 0.000 -1.850 7.475 10.212 -59.446 0.000 -0.637 3.822 -11.467 21.732 -337.037 i= 21, j= 1 .. 25 0.000 0.000 0.000 0.000 0.000 0.414 -1.129 0.376 -0.063 0.000 -3.022 6.774 -2.258 0.376 0.000 13.902 -20.322 6.774 -1.129 0.000 -52.348 24.645 3.807 -1.302 0.000 -51.723 i= 22, j= 1 .. 25 0.000 0.000 0.000 0.000 0.000 0.637 -0.403 -0.637 0.080 0.000 -3.822 1.667 3.822 -0.478 0.000 11.467 1.750 -11.467 1.433 0.000 22.420 -60.149 35.458 -2.624 0.000 -28.906 i= 23, j= 1 .. 25 0.000 0.000 0.000 0.000 0.000 -0.087 0.700 -0.634 -0.700 0.087 0.525 -4.200 2.760 4.200 -0.525 -1.575 12.600 1.140 -12.600 1.575 -0.703 18.254 -54.708 32.254 -2.453 -52.636 i= 24, j= 1 .. 25 0.000 0.000 0.000 0.000 0.000 0.000 -0.080 0.637 -0.925 -0.637 0.000 0.478 -3.822 4.088 3.822 0.000 -1.433 11.467 0.882 -11.467 0.000 -0.491 14.383 -49.188 27.421 -67.994 i= 25, j= 1 .. 25 0.000 0.000 0.000 0.000 0.000 0.000 0.063 -0.376 1.129 -1.924 0.000 -0.376 2.258 -6.774 9.507 0.000 1.129 -6.774 20.322 -10.174 0.000 -1.686 8.148 -6.713 -26.963 -520.864 computed solution us(x,y) -1.407 1.667 3.704 5.148 6.444 1.000 3.852 5.963 7.778 9.741 2.741 5.593 8.000 10.407 13.259 4.037 7.111 10.037 13.259 17.222 5.111 8.630 12.296 16.556 21.852 exact solution u(x,y) -1.407 1.667 3.704 5.148 6.444 1.000 3.852 5.963 7.778 9.741 2.741 5.593 8.000 10.407 13.259 4.037 7.111 10.037 13.259 17.222 5.111 8.630 12.296 16.556 21.852 difference exact-computed solution u(x,y)-us(x,y) -0.0000 -0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0000 error= 0.60507155E-13 avg= 0.16807543E-14 max= 0.88817842E-14 check solution against PDE check_soln values against PDE maxerr= 0.490274E-12, rmserr= 0.227299E-12, avgerr= 0.174047E-12