pde_nl22.java running nonlinear second order, second degree, two dimension a1(x,y)*uxx(x,y)*uyy(x,y) + b1(x,y)*u(x,y)*uxx(x,y) + c1(x,y)*u(x,y)uyy(x,y) = f(x,y) f(x,y)=0.5*exp(x/2.0)*exp(y)*(6.0*x+6.0*y)* (12.0*y+8.0*x)+0.7/(x*x*y*y+0.5)* (x*x*x+2.0*y*y*y+3.0*x*x*y+4.0*x*y*y+ 5.0*x*y+6.0*x+7.0*y+8.0)*(6.0*x+6.0*y)+ (8.0-2.0*exp(x)-2.0*exp(0.5*y))* (x*x*x+2.0*y*y*y+3.0*x*x*y+4.0*x*y*y+ 5.0*x*y+6.0*x+7.0*y+8.0)*(12.0*y+8.0*x); a1(x,y) = exp(x/2.0)*exp(y)/2.0 b1(x,y) = 0.7/(x*x*y*y+0.5) c1(x,y) = (4.0 - exp(x) - exp(y/2.0))*2.0 Boundary values ub(x,y)= x^4 + 2 y^4 + 3 x^3 y + 4 x y^3 + 5 x^2 y^2 + 6 x^2 + 7 y^2 + 8 xmin=-1.0, xmax=1.0, hx=0.5, nx=5 ymin=-1.0, ymax=1.0, hy=0.5, ny=5 Dirchilet Boundary values on square x y ub(x,y) xg=-1.000, yg=-1.000, uA[0][0]=-10.000, f(x,y)=1293.012 xg=-1.000, yg=-0.500, uA[0][1]=-2.750, f(x,y)=265.982 xg=-1.000, yg=0.000, uA[0][2]=1.000, f(x,y)=-35.957 xg=-1.000, yg=0.500, uA[0][3]=2.750, f(x,y)=-30.529 xg=-1.000, yg=1.000, uA[0][4]=4.000, f(x,y)=63.469 xg=-0.500, yg=-1.000, uA[1][0]=-4.375, f(x,y)=447.550 xg=-0.500, yg=-0.500, uA[1][1]=1.500, f(x,y)=-75.469 xg=-0.500, yg=0.000, uA[1][2]=4.875, f(x,y)=-109.147 xg=-0.500, yg=0.500, uA[1][3]=7.250, f(x,y)=61.174 xg=-0.500, yg=1.000, uA[1][4]=10.125, f(x,y)=336.403 xg=0.000, yg=-1.000, uA[2][0]=-1.000, f(x,y)=79.087 xg=0.000, yg=-0.500, uA[2][1]=4.250, f(x,y)=-125.672 xg=0.000, yg=0.000, uA[2][2]=8.000, f(x,y)=0.000 xg=0.000, yg=0.500, uA[2][3]=11.750, f(x,y)=306.141 xg=0.000, yg=1.000, uA[2][4]=17.000, f(x,y)=791.980 xg=0.500, yg=-1.000, uA[3][0]=0.875, f(x,y)=-21.208 xg=0.500, yg=-0.500, uA[3][1]=6.250, f(x,y)=-39.312 xg=0.500, yg=0.000, uA[3][2]=11.125, f(x,y)=174.693 xg=0.500, yg=0.500, uA[3][3]=17.000, f(x,y)=553.309 xg=0.500, yg=1.000, uA[3][4]=25.375, f(x,y)=1034.931 xg=1.000, yg=-1.000, uA[4][0]=2.000, f(x,y)=-10.803 xg=1.000, yg=-0.500, uA[4][1]=8.250, f(x,y)=42.696 xg=1.000, yg=0.000, uA[4][2]=15.000, f(x,y)=233.182 xg=1.000, yg=0.500, uA[4][3]=23.750, f(x,y)=369.217 xg=1.000, yg=1.000, uA[4][4]=36.000, f(x,y)=210.918 dof=9, nlin=81, dof+nlin=90 solve system of equations A X = Y for X the equations are for i=0,8 A[i][0]*X11+ A[i][1]*X12+ A[i][2]*X13+ A[i][3]*X21+ A[i][4]*X22+ A[i][5]*X23+ A[i][6]*X31+ A[i][7]*X32+ A[i][8]*X33+ A[i][9]*X11*X11+ A[i][10]*X11*X12+ A[i][11]*X11*X13+ A[i][12]*X11*X21+ A[i][13]*X11*X22+ A[i][14]*X11*X23+ A[i][15]*X11*X31+ A[i][16]*X11*X32+ A[i][17]*X11*X33+ A[i][18]*X12*X11+ A[i][19]*X12*X12+ A[i][20]*X12*X13+ A[i][21]*X12*X21+ A[i][22]*X12*X22+ A[i][23]*X12*X23+ A[i][24]*X12*X31+ A[i][25]*X12*X32+ A[i][26]*X12*X33+ A[i][27]*X13*X11+ A[i][28]*X13*X12+ A[i][29]*X13*X13+ A[i][30]*X13*X21+ A[i][31]*X13*X22+ A[i][32]*X13*X23+ A[i][33]*X13*X31+ A[i][34]*X13*X32+ A[i][35]*X13*X33+ A[i][36]*X21*X11+ A[i][37]*X21*X12+ A[i][38]*X21*X13+ A[i][39]*X21*X21+ A[i][40]*X21*X22+ A[i][41]*X21*X23+ A[i][42]*X21*X31+ A[i][43]*X21*X32+ A[i][44]*X21*X33+ A[i][45]*X22*X11+ A[i][46]*X22*X12+ A[i][47]*X22*X13+ A[i][48]*X22*X21+ A[i][49]*X22*X22+ A[i][50]*X22*X23+ A[i][51]*X22*X31+ A[i][52]*X22*X32+ A[i][53]*X22*X33+ A[i][54]*X23*X11+ A[i][55]*X23*X12+ A[i][56]*X23*X13+ A[i][57]*X23*X21+ A[i][58]*X23*X22+ A[i][59]*X23*X23+ A[i][60]*X23*X31+ A[i][61]*X23*X32+ A[i][62]*X23*X33+ A[i][63]*X31*X11+ A[i][64]*X31*X12+ A[i][65]*X31*X13+ A[i][66]*X31*X21+ A[i][67]*X31*X22+ A[i][68]*X31*X23+ A[i][69]*X31*X31+ A[i][70]*X31*X32+ A[i][71]*X31*X33+ A[i][72]*X32*X11+ A[i][73]*X32*X12+ A[i][74]*X32*X13+ A[i][75]*X32*X21+ A[i][76]*X32*X22+ A[i][77]*X32*X23+ A[i][78]*X32*X31+ A[i][79]*X32*X32+ A[i][80]*X32*X33+ A[i][81]*X33*X11+ A[i][82]*X33*X12+ A[i][83]*X33*X13+ A[i][84]*X33*X21+ A[i][85]*X33*X22+ A[i][86]*X33*X23+ A[i][87]*X33*X31+ A[i][88]*X33*X32+ A[i][89]*X33*X33 = Y[i] A matrix, and Y RHS, matrix values of zero not printed A[0][0]=-66.72726158926449 at X11 A[0][1]=-6.0620374268430215 at X12 A[0][2]=-4.041358284562014 at X13 A[0][3]=-9.1717838990547 at X21 A[0][6]=-6.114522599369799 at X31 A[0][9]=-32.661509220486565 at X11*X11 A[0][10]=7.309563877257083 at X11*X12 A[0][11]=4.873042584838055 at X11*X13 A[0][12]=2.488888888888889 at X11*X21 A[0][15]=1.6592592592592592 at X11*X31 A[0][36]=-3.1491103516067644 at X21*X11 A[0][37]=0.9447331054820294 at X21*X12 A[0][38]=0.6298220703213528 at X21*X13 A[0][63]=-2.099406901071176 at X31*X11 A[0][64]=0.6298220703213528 at X31*X12 A[0][65]=0.4198813802142352 at X31*X13 Y[0]=-134.32134015318272 A[1][0]=-2.76906945092055 at X11 A[1][1]=-0.8739555810026758 at X12 A[1][2]=-2.76906945092055 at X13 A[1][4]=-1.4927015008868594 at X22 A[1][7]=-0.9951343339245728 at X32 A[1][18]=11.684992375129161 at X12*X11 A[1][19]=-31.24269403670051 at X12*X12 A[1][20]=11.684992375129161 at X12*X13 A[1][22]=2.8 at X12*X22 A[1][25]=1.8666666666666665 at X12*X32 A[1][45]=4.153604176380826 at X22*X11 A[1][46]=-7.788007830714049 at X22*X12 A[1][47]=4.153604176380826 at X22*X13 A[1][72]=2.7690694509205507 at X32*X11 A[1][73]=-5.192005220476032 at X32*X12 A[1][74]=2.7690694509205507 at X32*X13 Y[1]=-110.14263390670345 A[2][0]=1.8547033796600703 at X11 A[2][1]=2.782055069490106 at X12 A[2][2]=-8.938400032684115 at X13 A[2][5]=49.541980660535366 at X23 A[2][8]=33.02798710702358 at X33 A[2][27]=-0.08159583345762744 at X13*X11 A[2][28]=-0.12239375018644161 at X13*X12 A[2][29]=-7.888317129008154 at X13*X13 A[2][32]=2.488888888888889 at X13*X23 A[2][35]=1.6592592592592592 at X13*X33 A[2][54]=1.7120338889169888 at X23*X11 A[2][55]=2.5680508333754832 at X23*X12 A[2][56]=-8.560169444584943 at X23*X13 A[2][81]=1.141355925944659 at X33*X11 A[2][82]=1.7120338889169888 at X33*X12 A[2][83]=-5.706779629723296 at X33*X13 Y[2]=7.503394735475837 A[3][0]=-15.095874197292208 at X11 A[3][3]=-12.017711675611451 at X21 A[3][4]=-1.111972876139828 at X22 A[3][5]=-0.7413152507598851 at X23 A[3][6]=-15.095874197292208 at X31 A[3][12]=-10.782767283780148 at X11*X21 A[3][13]=3.2348301851340446 at X11*X22 A[3][14]=2.1565534567560296 at X11*X23 A[3][36]=7.466666666666666 at X21*X11 A[3][39]=-23.398300901960155 at X21*X21 A[3][40]=2.8194902705880462 at X21*X22 A[3][41]=1.8796601803920305 at X21*X23 A[3][42]=7.466666666666666 at X21*X31 A[3][66]=-10.782767283780148 at X31*X21 A[3][67]=3.2348301851340446 at X31*X22 A[3][68]=2.1565534567560296 at X31*X23 Y[3]=-130.86159088126385 A[4][1]=-14.22222222222222 at X12 A[4][3]=-14.222222222222221 at X21 A[4][4]=24.53333333333333 at X22 A[4][5]=-14.222222222222221 at X23 A[4][7]=-14.22222222222222 at X32 A[4][21]=14.222222222222221 at X12*X21 A[4][22]=-26.666666666666664 at X12*X22 A[4][23]=14.222222222222221 at X12*X23 A[4][46]=7.466666666666666 at X22*X12 A[4][48]=-5.333333333333332 at X22*X21 A[4][49]=-4.0 at X22*X22 A[4][50]=-5.333333333333332 at X22*X23 A[4][52]=7.466666666666666 at X22*X32 A[4][75]=14.222222222222221 at X32*X21 A[4][76]=-26.666666666666664 at X32*X22 A[4][77]=14.222222222222221 at X32*X23 Y[4]=-14.22222222222222 A[5][2]=275.5196434592214 at X13 A[5][3]=-9.709136371900755 at X21 A[5][4]=-14.563704557851132 at X22 A[5][5]=-265.35150185140003 at X23 A[5][8]=275.5196434592214 at X33 A[5][30]=5.8621200736004555 at X13*X21 A[5][31]=8.793180110400684 at X13*X22 A[5][32]=-29.310600368002277 at X13*X23 A[5][56]=7.466666666666666 at X23*X13 A[5][57]=-6.415542915834832 at X23*X21 A[5][58]=-9.62331437375225 at X23*X22 A[5][59]=18.077714579174163 at X23*X23 A[5][62]=7.466666666666666 at X23*X33 A[5][84]=5.8621200736004555 at X33*X21 A[5][85]=8.793180110400684 at X33*X22 A[5][86]=-29.310600368002277 at X33*X23 Y[5]=762.470317162665 A[6][0]=-2.7258027407499164 at X11 A[6][3]=-4.0887041111248745 at X21 A[6][6]=-45.00556756554896 at X31 A[6][7]=24.27262440572545 at X32 A[6][8]=16.181749603816964 at X33 A[6][15]=-3.4613368136506875 at X11*X31 A[6][16]=1.0384010440952063 at X11*X32 A[6][17]=0.6922673627301374 at X11*X33 A[6][42]=-5.192005220476031 at X21*X31 A[6][43]=1.5576015661428095 at X21*X32 A[6][44]=1.0384010440952063 at X21*X33 A[6][63]=1.6592592592592592 at X31*X11 A[6][66]=2.488888888888889 at X31*X21 A[6][69]=-11.955984844422415 at X31*X31 A[6][70]=1.097906564437836 at X31*X32 A[6][71]=0.7319377096252238 at X31*X33 Y[6]=24.40369040931762 A[7][1]=-7.4901482640118235 at X12 A[7][4]=-11.235222396017736 at X22 A[7][6]=187.18237185492407 at X31 A[7][7]=-260.63025033733794 at X32 A[7][8]=187.18237185492407 at X33 A[7][24]=4.565423703778635 at X12*X31 A[7][25]=-8.560169444584941 at X12*X32 A[7][26]=4.565423703778635 at X12*X33 A[7][51]=6.8481355556679535 at X22*X31 A[7][52]=-12.840254166877415 at X22*X32 A[7][53]=6.8481355556679535 at X22*X33 A[7][73]=1.8666666666666665 at X32*X12 A[7][76]=2.8 at X32*X22 A[7][78]=-8.413478739694543 at X32*X31 A[7][79]=6.441939303593937 at X32*X32 A[7][80]=-8.413478739694543 at X32*X33 Y[7]=481.78903823229984 A[8][2]=130.9011676938837 at X13 A[8][5]=196.35175154082557 at X23 A[8][6]=121.60988984319475 at X31 A[8][7]=182.41483476479212 at X32 A[8][8]=-957.3501685662122 at X33 A[8][33]=1.8817777925445995 at X13*X31 A[8][34]=2.8226666888168994 at X13*X32 A[8][35]=-9.408888962722997 at X13*X33 A[8][60]=2.8226666888168994 at X23*X31 A[8][61]=4.23400003322535 at X23*X32 A[8][62]=-14.113333444084498 at X23*X33 A[8][83]=1.6592592592592592 at X33*X13 A[8][86]=2.488888888888889 at X33*X23 A[8][87]=-6.56288012909065 at X33*X31 A[8][88]=-9.844320193635976 at X33*X32 A[8][89]=24.51810434915695 at X33*X33 Y[8]=-7906.178502097397 Check by giving solution as initial guess no output expected from SN.simeq at 1,1 expected 1.500 got 1.500 at 1,2 expected 4.875 got 4.875 at 1,3 expected 7.250 got 7.250 at 2,1 expected 4.250 got 4.250 at 2,2 expected 8.000 got 8.000 at 2,3 expected 11.750 got 11.750 at 3,1 expected 6.250 got 6.250 at 3,2 expected 11.125 got 11.125 at 3,3 expected 17.000 got 17.000 initial guess, all=5.0 simeq_newton5 itr 1, prev=8396.620431248135, residual=4956.068069763331 simeq_newton5 itr 2, prev=4956.068069763331, residual=398.9351974750618 simeq_newton5 itr 3, prev=398.9351974750618, residual=15.498223123233027 simeq_newton5 itr 4, prev=15.498223123233027, residual=0.04372263661564979 simeq_newton5 itr 5, prev=0.04372263661564979, residual=2.7381453016062096E-7 at 1,1 computed 1.500 exact=1.500 error=-1.3028689238581137E-11 at 1,2 computed 4.875 exact=4.875 error=-2.3000090720870503E-10 at 1,3 computed 7.250 exact=7.250 error=-6.065468127758322E-10 at 2,1 computed 4.250 exact=4.250 error=-9.538059231317675E-11 at 2,2 computed 8.000 exact=8.000 error=-2.8204283353261417E-10 at 2,3 computed 11.750 exact=11.750 error=-4.4011905231400306E-10 at 3,1 computed 6.250 exact=6.250 error=-6.52162768233211E-11 at 3,2 computed 11.125 exact=11.125 error=-1.4173018314522778E-10 at 3,3 computed 17.000 exact=17.000 error=-1.8519941136219131E-10 check solution against PDE maxerr=1.340212634204363E-7, rmserr=5.421556541610609E-8, avgerr=3.0423931857799394E-8 check check_soln using expected solution check solution against PDE maxerr=3.126388037344441E-13, rmserr=1.2318351256554027E-13, avgerr=7.500173321912168E-14 pde_nl22.java finished in 0.10299992561340332 seconds