pde_nl22.adb running nonlinear second order, second degree, two dimension The PDE to be solved for u(x) is: 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)*exp(y)/2 b1(x,y) = 0.7/(x^2*y^2+0.5) c1(x,y) = 2*(4-exp(x)-exp(y/2)) Boundary values computed from: 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=-1.00000000000000E+00, xmax= 1.00000000000000E+00 ymin=-1.00000000000000E+00, ymax= 1.00000000000000E+00 nx= 5 points for numeric derivative, step= 5.00000000000000E-01 x grid ny= 5 points for numeric derivative, step= 5.00000000000000E-01 y grid xg= -1.00000, yg= -1.00000, Ua( 1, 1)=-10.00000, f(x)=1293.01158 xg= -1.00000, yg= -0.50000, Ua( 1, 2)= -2.75000, f(x)=265.98203 xg= -1.00000, yg= 0.00000, Ua( 1, 3)= 1.00000, f(x)=-35.95719 xg= -1.00000, yg= 0.50000, Ua( 1, 4)= 2.75000, f(x)=-30.52905 xg= -1.00000, yg= 1.00000, Ua( 1, 5)= 4.00000, f(x)= 63.46878 xg= -0.50000, yg= -1.00000, Ua( 2, 1)= -4.37500, f(x)=447.54976 xg= -0.50000, yg= -0.50000, Ua( 2, 2)= 1.50000, f(x)=-75.46906 xg= -0.50000, yg= 0.00000, Ua( 2, 3)= 4.87500, f(x)=-109.14750 xg= -0.50000, yg= 0.50000, Ua( 2, 4)= 7.25000, f(x)= 61.17387 xg= -0.50000, yg= 1.00000, Ua( 2, 5)= 10.12500, f(x)=336.40319 xg= 0.00000, yg= -1.00000, Ua( 3, 1)= -1.00000, f(x)= 79.08692 xg= 0.00000, yg= -0.50000, Ua( 3, 2)= 4.25000, f(x)=-125.67238 xg= 0.00000, yg= 0.00000, Ua( 3, 3)= 8.00000, f(x)= 0.00000 xg= 0.00000, yg= 0.50000, Ua( 3, 4)= 11.75000, f(x)=306.14091 xg= 0.00000, yg= 1.00000, Ua( 3, 5)= 17.00000, f(x)=791.97987 xg= 0.50000, yg= -1.00000, Ua( 4, 1)= 0.87500, f(x)=-21.20807 xg= 0.50000, yg= -0.50000, Ua( 4, 2)= 6.25000, f(x)=-39.31195 xg= 0.50000, yg= 0.00000, Ua( 4, 3)= 11.12500, f(x)=174.69296 xg= 0.50000, yg= 0.50000, Ua( 4, 4)= 17.00000, f(x)=553.30946 xg= 0.50000, yg= 1.00000, Ua( 4, 5)= 25.37500, f(x)=1034.93135 xg= 1.00000, yg= -1.00000, Ua( 5, 1)= 2.00000, f(x)=-10.80300 xg= 1.00000, yg= -0.50000, Ua( 5, 2)= 8.25000, f(x)= 42.69627 xg= 1.00000, yg= 0.00000, Ua( 5, 3)= 15.00000, f(x)=233.18167 xg= 1.00000, yg= 0.50000, Ua( 5, 4)= 23.75000, f(x)=369.21744 xg= 1.00000, yg= 1.00000, Ua( 5, 5)= 36.00000, f(x)=210.91823 compute non linear A matrix nonlinear matrix A, zero entries not printed i= 1, j= 1, A(i,j)=-6.67272615892645E+01 i= 1, j= 2, A(i,j)=-6.06203742684302E+00 i= 1, j= 3, A(i,j)=-4.04135828456201E+00 i= 1, j= 4, A(i,j)=-9.17178389905470E+00 i= 1, j= 7, A(i,j)=-6.11452259936980E+00 i= 1, j= 10, A(i,j)=-3.26615092204866E+01 i= 1, j= 11, A(i,j)= 7.30956387725708E+00 i= 1, j= 12, A(i,j)= 4.87304258483805E+00 i= 1, j= 13, A(i,j)= 2.48888888888889E+00 i= 1, j= 16, A(i,j)= 1.65925925925926E+00 i= 1, j= 37, A(i,j)=-3.14911035160676E+00 i= 1, j= 38, A(i,j)= 9.44733105482029E-01 i= 1, j= 39, A(i,j)= 6.29822070321353E-01 i= 1, j= 64, A(i,j)=-2.09940690107118E+00 i= 1, j= 65, A(i,j)= 6.29822070321353E-01 i= 1, j= 66, A(i,j)= 4.19881380214235E-01 i= 2, j= 1, A(i,j)=-2.76906945092055E+00 i= 2, j= 2, A(i,j)=-8.73955581002674E-01 i= 2, j= 3, A(i,j)=-2.76906945092055E+00 i= 2, j= 5, A(i,j)=-1.49270150088686E+00 i= 2, j= 8, A(i,j)=-9.95134333924573E-01 i= 2, j= 19, A(i,j)= 1.16849923751292E+01 i= 2, j= 20, A(i,j)=-3.12426940367005E+01 i= 2, j= 21, A(i,j)= 1.16849923751292E+01 i= 2, j= 23, A(i,j)= 2.80000000000000E+00 i= 2, j= 26, A(i,j)= 1.86666666666667E+00 i= 2, j= 46, A(i,j)= 4.15360417638083E+00 i= 2, j= 47, A(i,j)=-7.78800783071405E+00 i= 2, j= 48, A(i,j)= 4.15360417638083E+00 i= 2, j= 73, A(i,j)= 2.76906945092055E+00 i= 2, j= 74, A(i,j)=-5.19200522047603E+00 i= 2, j= 75, A(i,j)= 2.76906945092055E+00 i= 3, j= 1, A(i,j)= 1.85470337966007E+00 i= 3, j= 2, A(i,j)= 2.78205506949011E+00 i= 3, j= 3, A(i,j)=-8.93840003268415E+00 i= 3, j= 6, A(i,j)= 4.95419806605354E+01 i= 3, j= 9, A(i,j)= 3.30279871070236E+01 i= 3, j= 28, A(i,j)=-8.15958334576283E-02 i= 3, j= 29, A(i,j)=-1.22393750186443E-01 i= 3, j= 30, A(i,j)=-7.88831712900815E+00 i= 3, j= 33, A(i,j)= 2.48888888888889E+00 i= 3, j= 36, A(i,j)= 1.65925925925926E+00 i= 3, j= 55, A(i,j)= 1.71203388891699E+00 i= 3, j= 56, A(i,j)= 2.56805083337548E+00 i= 3, j= 57, A(i,j)=-8.56016944458494E+00 i= 3, j= 82, A(i,j)= 1.14135592594466E+00 i= 3, j= 83, A(i,j)= 1.71203388891699E+00 i= 3, j= 84, A(i,j)=-5.70677962972330E+00 i= 4, j= 1, A(i,j)=-1.50958741972922E+01 i= 4, j= 4, A(i,j)=-1.20177116756115E+01 i= 4, j= 5, A(i,j)=-1.11197287613983E+00 i= 4, j= 6, A(i,j)=-7.41315250759885E-01 i= 4, j= 7, A(i,j)=-1.50958741972922E+01 i= 4, j= 13, A(i,j)=-1.07827672837801E+01 i= 4, j= 14, A(i,j)= 3.23483018513404E+00 i= 4, j= 15, A(i,j)= 2.15655345675603E+00 i= 4, j= 37, A(i,j)= 7.46666666666667E+00 i= 4, j= 40, A(i,j)=-2.33983009019602E+01 i= 4, j= 41, A(i,j)= 2.81949027058805E+00 i= 4, j= 42, A(i,j)= 1.87966018039203E+00 i= 4, j= 43, A(i,j)= 7.46666666666667E+00 i= 4, j= 67, A(i,j)=-1.07827672837801E+01 i= 4, j= 68, A(i,j)= 3.23483018513404E+00 i= 4, j= 69, A(i,j)= 2.15655345675603E+00 i= 5, j= 2, A(i,j)=-1.42222222222222E+01 i= 5, j= 4, A(i,j)=-1.42222222222222E+01 i= 5, j= 5, A(i,j)= 2.45333333333333E+01 i= 5, j= 6, A(i,j)=-1.42222222222222E+01 i= 5, j= 8, A(i,j)=-1.42222222222222E+01 i= 5, j= 22, A(i,j)= 1.42222222222222E+01 i= 5, j= 23, A(i,j)=-2.66666666666667E+01 i= 5, j= 24, A(i,j)= 1.42222222222222E+01 i= 5, j= 47, A(i,j)= 7.46666666666667E+00 i= 5, j= 49, A(i,j)=-5.33333333333333E+00 i= 5, j= 50, A(i,j)=-4.00000000000000E+00 i= 5, j= 51, A(i,j)=-5.33333333333333E+00 i= 5, j= 53, A(i,j)= 7.46666666666667E+00 i= 5, j= 76, A(i,j)= 1.42222222222222E+01 i= 5, j= 77, A(i,j)=-2.66666666666667E+01 i= 5, j= 78, A(i,j)= 1.42222222222222E+01 i= 6, j= 3, A(i,j)= 2.75519643459221E+02 i= 6, j= 4, A(i,j)=-9.70913637190075E+00 i= 6, j= 5, A(i,j)=-1.45637045578511E+01 i= 6, j= 6, A(i,j)=-2.65351501851400E+02 i= 6, j= 9, A(i,j)= 2.75519643459221E+02 i= 6, j= 31, A(i,j)= 5.86212007360046E+00 i= 6, j= 32, A(i,j)= 8.79318011040068E+00 i= 6, j= 33, A(i,j)=-2.93106003680023E+01 i= 6, j= 57, A(i,j)= 7.46666666666667E+00 i= 6, j= 58, A(i,j)=-6.41554291583483E+00 i= 6, j= 59, A(i,j)=-9.62331437375225E+00 i= 6, j= 60, A(i,j)= 1.80777145791742E+01 i= 6, j= 63, A(i,j)= 7.46666666666667E+00 i= 6, j= 85, A(i,j)= 5.86212007360046E+00 i= 6, j= 86, A(i,j)= 8.79318011040068E+00 i= 6, j= 87, A(i,j)=-2.93106003680023E+01 i= 7, j= 1, A(i,j)=-2.72580274074992E+00 i= 7, j= 4, A(i,j)=-4.08870411112487E+00 i= 7, j= 7, A(i,j)=-4.50055675655490E+01 i= 7, j= 8, A(i,j)= 2.42726244057254E+01 i= 7, j= 9, A(i,j)= 1.61817496038170E+01 i= 7, j= 16, A(i,j)=-3.46133681365069E+00 i= 7, j= 17, A(i,j)= 1.03840104409521E+00 i= 7, j= 18, A(i,j)= 6.92267362730137E-01 i= 7, j= 43, A(i,j)=-5.19200522047603E+00 i= 7, j= 44, A(i,j)= 1.55760156614281E+00 i= 7, j= 45, A(i,j)= 1.03840104409521E+00 i= 7, j= 64, A(i,j)= 1.65925925925926E+00 i= 7, j= 67, A(i,j)= 2.48888888888889E+00 i= 7, j= 70, A(i,j)=-1.19559848444224E+01 i= 7, j= 71, A(i,j)= 1.09790656443784E+00 i= 7, j= 72, A(i,j)= 7.31937709625223E-01 i= 8, j= 2, A(i,j)=-7.49014826401182E+00 i= 8, j= 5, A(i,j)=-1.12352223960177E+01 i= 8, j= 7, A(i,j)= 1.87182371854924E+02 i= 8, j= 8, A(i,j)=-2.60630250337338E+02 i= 8, j= 9, A(i,j)= 1.87182371854924E+02 i= 8, j= 25, A(i,j)= 4.56542370377864E+00 i= 8, j= 26, A(i,j)=-8.56016944458494E+00 i= 8, j= 27, A(i,j)= 4.56542370377864E+00 i= 8, j= 52, A(i,j)= 6.84813555566795E+00 i= 8, j= 53, A(i,j)=-1.28402541668774E+01 i= 8, j= 54, A(i,j)= 6.84813555566795E+00 i= 8, j= 74, A(i,j)= 1.86666666666667E+00 i= 8, j= 77, A(i,j)= 2.80000000000000E+00 i= 8, j= 79, A(i,j)=-8.41347873969455E+00 i= 8, j= 80, A(i,j)= 6.44193930359394E+00 i= 8, j= 81, A(i,j)=-8.41347873969455E+00 i= 9, j= 3, A(i,j)= 1.30901167693884E+02 i= 9, j= 6, A(i,j)= 1.96351751540826E+02 i= 9, j= 7, A(i,j)= 1.21609889843195E+02 i= 9, j= 8, A(i,j)= 1.82414834764792E+02 i= 9, j= 9, A(i,j)=-9.57350168566212E+02 i= 9, j= 34, A(i,j)= 1.88177779254460E+00 i= 9, j= 35, A(i,j)= 2.82266668881690E+00 i= 9, j= 36, A(i,j)=-9.40888896272300E+00 i= 9, j= 61, A(i,j)= 2.82266668881690E+00 i= 9, j= 62, A(i,j)= 4.23400003322535E+00 i= 9, j= 63, A(i,j)=-1.41133334440845E+01 i= 9, j= 84, A(i,j)= 1.65925925925926E+00 i= 9, j= 87, A(i,j)= 2.48888888888889E+00 i= 9, j= 88, A(i,j)=-6.56288012909065E+00 i= 9, j= 89, A(i,j)=-9.84432019363598E+00 i= 9, j= 90, A(i,j)= 2.45181043491570E+01 Y computed RHS Y( 1)=-1.34321340153183E+02 Y( 2)=-1.10142633906703E+02 Y( 3)= 7.50339473547582E+00 Y( 4)=-1.30861590881264E+02 Y( 5)=-1.42222222222222E+01 Y( 6)= 7.62470317162665E+02 Y( 7)= 2.44036904093176E+01 Y( 8)= 4.81789038232300E+02 Y( 9)=-7.90617850209740E+03 system of equations to be solved, i=1.. 9 A(i, 1)*X11+ A(i, 2)*X12+ A(i, 3)*X13+ A(i, 4)*X21+ A(i, 5)*X22+ A(i, 6)*X23+ A(i, 7)*X31+ A(i, 8)*X32+ A(i, 9)*X33+ A(i, 10)*X11*X11+ A(i, 11)*X11*X12+ A(i, 12)*X11*X13+ A(i, 13)*X11*X21+ A(i, 14)*X11*X22+ A(i, 15)*X11*X23+ A(i, 16)*X11*X31+ A(i, 17)*X11*X32+ A(i, 18)*X11*X33+ A(i, 19)*X12*X11+ A(i, 20)*X12*X12+ A(i, 21)*X12*X13+ A(i, 22)*X12*X21+ A(i, 23)*X12*X22+ A(i, 24)*X12*X23+ A(i, 25)*X12*X31+ A(i, 26)*X12*X32+ A(i, 27)*X12*X33+ A(i, 28)*X13*X11+ A(i, 29)*X13*X12+ A(i, 30)*X13*X13+ A(i, 31)*X13*X21+ A(i, 32)*X13*X22+ A(i, 33)*X13*X23+ A(i, 34)*X13*X31+ A(i, 35)*X13*X32+ A(i, 36)*X13*X33+ A(i, 37)*X21*X11+ A(i, 38)*X21*X12+ A(i, 39)*X21*X13+ A(i, 40)*X21*X21+ A(i, 41)*X21*X22+ A(i, 42)*X21*X23+ A(i, 43)*X21*X31+ A(i, 44)*X21*X32+ A(i, 45)*X21*X33+ A(i, 46)*X22*X11+ A(i, 47)*X22*X12+ A(i, 48)*X22*X13+ A(i, 49)*X22*X21+ A(i, 50)*X22*X22+ A(i, 51)*X22*X23+ A(i, 52)*X22*X31+ A(i, 53)*X22*X32+ A(i, 54)*X22*X33+ A(i, 55)*X23*X11+ A(i, 56)*X23*X12+ A(i, 57)*X23*X13+ A(i, 58)*X23*X21+ A(i, 59)*X23*X22+ A(i, 60)*X23*X23+ A(i, 61)*X23*X31+ A(i, 62)*X23*X32+ A(i, 63)*X23*X33+ A(i, 64)*X31*X11+ A(i, 65)*X31*X12+ A(i, 66)*X31*X13+ A(i, 67)*X31*X21+ A(i, 68)*X31*X22+ A(i, 69)*X31*X23+ A(i, 70)*X31*X31+ A(i, 71)*X31*X32+ A(i, 72)*X31*X33+ A(i, 73)*X32*X11+ A(i, 74)*X32*X12+ A(i, 75)*X32*X13+ A(i, 76)*X32*X21+ A(i, 77)*X32*X22+ A(i, 78)*X32*X23+ A(i, 79)*X32*X31+ A(i, 80)*X32*X32+ A(i, 81)*X32*X33+ A(i, 82)*X33*X11+ A(i, 83)*X33*X12+ A(i, 84)*X33*X13+ A(i, 85)*X33*X21+ A(i, 86)*X33*X22+ A(i, 87)*X33*X23+ A(i, 88)*X33*X31+ A(i, 89)*X33*X32+ A(i, 90)*X33*X33 = Y(i) test, giving exact solution X11 = 1.50000000000000E+00 X12 = 4.87500000000000E+00 X13 = 7.25000000000000E+00 X21 = 4.25000000000000E+00 X22 = 8.00000000000000E+00 X23 = 1.17500000000000E+01 X31 = 6.25000000000000E+00 X32 = 1.11250000000000E+01 X33 = 1.70000000000000E+01 Check_Equation residual = 8.18545231595635E-12 simeq_newton5.adb running itr 0, initial residual= 1.03845820831339E-11 simeq_newton5 found solution expected= 1.500 got= 1.500 expected= 4.875 got= 4.875 expected= 7.250 got= 7.250 expected= 4.250 got= 4.250 expected= 8.000 got= 8.000 expected= 11.750 got= 11.750 expected= 6.250 got= 6.250 expected= 11.125 got= 11.125 expected= 17.000 got= 17.000 initial guess, all 5.00000000000000E+00 simeq_newton5.adb running itr 0, initial residual= 8.39662043124813E+03 itr 1, prev= 8.39662043124813E+03, residual= 4.95606806976332E+03 itr 2, prev= 4.95606806976332E+03, residual= 3.98935197475062E+02 itr 3, prev= 3.98935197475062E+02, residual= 1.54982231232335E+01 itr 4, prev= 1.54982231232335E+01, residual= 4.37226366162697E-02 itr 5, prev= 4.37226366162697E-02, residual= 2.73813380857746E-07 simeq_newton5 found solution U computed from nonlinear equations, Ua analytic, error ug( 1, 1)= -10.00000000, Ua= -10.00000000, err= 0.00000000 ug( 1, 2)= -2.75000000, Ua= -2.75000000, err= 0.00000000 ug( 1, 3)= 1.00000000, Ua= 1.00000000, err= 0.00000000 ug( 1, 4)= 2.75000000, Ua= 2.75000000, err= 0.00000000 ug( 1, 5)= 4.00000000, Ua= 4.00000000, err= 0.00000000 ug( 2, 1)= -4.37500000, Ua= -4.37500000, err= 0.00000000 ug( 2, 2)= 1.50000000, Ua= 1.50000000, err= 0.00000000 ug( 2, 3)= 4.87500000, Ua= 4.87500000, err= 0.00000000 ug( 2, 4)= 7.25000000, Ua= 7.25000000, err= 0.00000000 ug( 2, 5)= 10.12500000, Ua= 10.12500000, err= 0.00000000 ug( 3, 1)= -1.00000000, Ua= -1.00000000, err= 0.00000000 ug( 3, 2)= 4.25000000, Ua= 4.25000000, err= 0.00000000 ug( 3, 3)= 8.00000000, Ua= 8.00000000, err= 0.00000000 ug( 3, 4)= 11.75000000, Ua= 11.75000000, err= 0.00000000 ug( 3, 5)= 17.00000000, Ua= 17.00000000, err= 0.00000000 ug( 4, 1)= 0.87500000, Ua= 0.87500000, err= 0.00000000 ug( 4, 2)= 6.25000000, Ua= 6.25000000, err= 0.00000000 ug( 4, 3)= 11.12500000, Ua= 11.12500000, err= 0.00000000 ug( 4, 4)= 17.00000000, Ua= 17.00000000, err= 0.00000000 ug( 4, 5)= 25.37500000, Ua= 25.37500000, err= 0.00000000 ug( 5, 1)= 2.00000000, Ua= 2.00000000, err= 0.00000000 ug( 5, 2)= 8.25000000, Ua= 8.25000000, err= 0.00000000 ug( 5, 3)= 15.00000000, Ua= 15.00000000, err= 0.00000000 ug( 5, 4)= 23.75000000, Ua= 23.75000000, err= 0.00000000 ug( 5, 5)= 36.00000000, Ua= 36.00000000, err= 0.00000000 maxerr= 6.06545036418993E-10, avgerr= 2.28808108262671E-10 check_soln on computed solution against PDE check_soln check_soln max error= 1.34021242104154E-07 just checking check_soln when given correct solution check_soln check_soln max error= 1.64845914696343E-12 pde_nl22.adb finished in 0.012911000 seconds