##############ECHO OF PROBLEM################# ##############temp/expt_lin_lin_newpostode.ode################# diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=1.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 $glob_max_h=0.00001 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(expt(2.0*x+1.0,3.0*x+2.0)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 desired_abs_gbl_error 1.0e-10 range 0.9 estimated_steps 900000.0000000001 step_error 1.111111111111111e-16 est_needed_step_err 1.111111111111111e-16 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0595270250829718e-152 estimated_step_error 1.0595270250829718e-152 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.4732301750687347e-142 estimated_step_error 1.4732301750687347e-142 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.886657497008344e-135 estimated_step_error 9.886657497008344e-135 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.634792866711539e-127 estimated_step_error 6.634792866711539e-127 best_h 1.6e-05 opt_iter 5 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.4524929614884184e-119 estimated_step_error 4.4524929614884184e-119 best_h 1.0e-05 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (analytic) 1.5209567545525315 y[1] (numeric) 1.5209567545525315 absolute error 0.0 relative error 0.0% Correct digits 16 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11000999999999612 y[1] (analytic) 1.589416016111751 y[1] (numeric) 1.5894160168779707 absolute error 7.66219754311237e-10 relative error 4.8207627615686777e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4482201977873441 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.7673247679702422 Order of pole (six term test) -97.66572363283959 TOP MAIN SOLVE Loop x[1] 0.12000999999999225 y[1] (analytic) 1.6614776780932727 y[1] (numeric) 1.6614776788595198 absolute error 7.662470657976428e-10 relative error 4.611840868527317e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.45557310231988857 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.678651756168538 Order of pole (six term test) -81.0132440571682 TOP MAIN SOLVE Loop x[1] 0.13000999999999532 y[1] (analytic) 1.737421092673896 y[1] (numeric) 1.7374210934401193 absolute error 7.662233070249158e-10 relative error 4.4101185962102944e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4629320334532111 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.6723783630455433 Order of pole (six term test) -74.56301417463197 TOP MAIN SOLVE Loop x[1] 0.14000000000000531 y[1] (analytic) 1.8173899685525425 y[1] (numeric) 1.8173899693186817 absolute error 7.661391521196492e-10 relative error 4.215601303939405e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4702912176681458 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.7148437697320666 Order of pole (six term test) -73.12852676772911 TOP MAIN SOLVE Loop x[1] 0.15000000000001532 y[1] (analytic) 1.9017841044839194 y[1] (numeric) 1.9017841052499758 absolute error 7.660563294820122e-10 relative error 4.028093029465583e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.47766745046419934 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.7969695268745927 Order of pole (six term test) -75.19515982359975 TOP MAIN SOLVE Loop x[1] 0.16000000000002532 y[1] (analytic) 1.9907803683433645 y[1] (numeric) 1.9907803691093298 absolute error 7.659652911939929e-10 relative error 3.847563012847037e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4850560355955847 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9207691585523636 Order of pole (six term test) -80.65751662389779 TOP MAIN SOLVE Loop x[1] 0.17000000000003532 y[1] (analytic) 2.0846494905002113 y[1] (numeric) 2.084649491266079 absolute error 7.658678136124308e-10 relative error 3.6738445340691826e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4912358442918479 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.098462298690942 Order of pole (six term test) -90.51650361547141 TOP MAIN SOLVE Loop x[1] 0.18000000000004532 y[1] (analytic) 2.1836791491489462 y[1] (numeric) 2.183679149914715 absolute error 7.657687817186343e-10 relative error 3.5067824960323515e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4967972038404717 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.359262604693479 Order of pole (six term test) -107.6378598278751 TOP MAIN SOLVE Loop x[1] 0.19000000000005532 y[1] (analytic) 2.288175082965221 y[1] (numeric) 2.2881750837308896 absolute error 7.656684175572082e-10 relative error 3.346196815345908e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5018411504652512 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.774520437038737 Order of pole (six term test) -140.0201018097381 TOP MAIN SOLVE Loop x[1] 0.20000000000006532 y[1] (analytic) 2.39846227969988 y[1] (numeric) 2.3984622804654383 absolute error 7.655582834331653e-10 relative error 3.19187126648896e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5062310125696882 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 3.5688015370984285 Order of pole (six term test) -217.7011309193338 TOP MAIN SOLVE Loop x[1] 0.21000000000007532 y[1] (analytic) 2.5148862460827304 y[1] (numeric) 2.5148862468481745 absolute error 7.654441525062339e-10 relative error 3.043653181922303e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5097959372048358 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 6.214820473811468 Order of pole (six term test) -619.3991184127948 TOP MAIN SOLVE Loop x[1] 0.22000000000008532 y[1] (analytic) 2.637814364797841 y[1] (numeric) 2.6378143655631643 absolute error 7.653233602411547e-10 relative error 2.9013541303533244e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.512323144379158 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.23000000000009532 y[1] (analytic) 2.7676373447114426 y[1] (numeric) 2.767637345476637 absolute error 7.651945743702981e-10 relative error 2.764793500971054e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5135488288355917 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.24000000000010532 y[1] (analytic) 2.904770770984286 y[1] (numeric) 2.904770771749338 absolute error 7.650520217339363e-10 relative error 2.6337776094968668e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5131476979405947 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2500000000001153 y[1] (analytic) 3.049656762184943 y[1] (numeric) 3.0496567629498417 absolute error 7.64898810956538e-10 relative error 2.5081472132900693e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5107212903126277 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2600000000001253 y[1] (analytic) 3.2027657420416396 y[1] (numeric) 3.2027657428063856 absolute error 7.647460442683496e-10 relative error 2.3877676541552285e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.5057854783681172 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2700000000001353 y[1] (analytic) 3.3645983340305223 y[1] (numeric) 3.364598334795104 absolute error 7.645817312607051e-10 relative error 2.2724309274230564e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.49775795894538655 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2800000000001453 y[1] (analytic) 3.5356873876009005 y[1] (numeric) 3.5356873883653126 absolute error 7.644120891825423e-10 relative error 2.1619900330080516e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4859471216829068 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2900000000001553 y[1] (analytic) 3.716600145486073 y[1] (numeric) 3.7166001462503058 absolute error 7.642326771417629e-10 relative error 2.0562682215625142e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3000000000001653 y[1] (analytic) 3.907940562245493 y[1] (numeric) 3.9079405630095385 absolute error 7.64045715584416e-10 relative error 1.9551108913115026e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3100000000001753 y[1] (analytic) 4.110351784933933 y[1] (numeric) 4.110351785697781 absolute error 7.638485399752426e-10 relative error 1.8583532017260665e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3200000000001853 y[1] (analytic) 4.324518807600128 y[1] (numeric) 4.324518808363764 absolute error 7.636353771545146e-10 relative error 1.7658273928938938e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3300000000001953 y[1] (analytic) 4.551171312185456 y[1] (numeric) 4.551171312948849 absolute error 7.633929044459364e-10 relative error 1.6773547996358718e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3400000000002053 y[1] (analytic) 4.791086709327331 y[1] (numeric) 4.791086710090491 absolute error 7.63160201699975e-10 relative error 1.592874953012743e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3500000000002153 y[1] (analytic) 5.04509339357734 y[1] (numeric) 5.0450933943402365 absolute error 7.628964127093241e-10 relative error 1.512155183649385e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3600000000002253 y[1] (analytic) 5.314074228626133 y[1] (numeric) 5.314074229388753 absolute error 7.626201892207973e-10 relative error 1.4350951010670401e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3700000000002353 y[1] (analytic) 5.598970279291816 y[1] (numeric) 5.598970280054158 absolute error 7.623421893754312e-10 relative error 1.3615757029377478e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3800000000002453 y[1] (analytic) 5.900784808282486 y[1] (numeric) 5.900784809044536 absolute error 7.620499786753498e-10 relative error 1.2914383483459993e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3900000000002553 y[1] (analytic) 6.220587557093526 y[1] (numeric) 6.220587557855246 absolute error 7.617195763032214e-10 relative error 1.2245138731864795e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4000000000002653 y[1] (analytic) 6.559519331853952 y[1] (numeric) 6.5595193326153325 absolute error 7.61380292146896e-10 relative error 1.1607257386216179e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4100000000002753 y[1] (analytic) 6.918796916501542 y[1] (numeric) 6.918796917262559 absolute error 7.610170271732386e-10 relative error 1.0999268172739538e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4200000000002853 y[1] (analytic) 7.299718337352473 y[1] (numeric) 7.299718338113111 absolute error 7.606377749880266e-10 relative error 1.0420097596038226e-08% Correct digits 10 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4300000000002953 y[1] (analytic) 7.703668504947269 y[1] (numeric) 7.703668505707514 absolute error 7.602443119480995e-10 relative error 9.868601062725806e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4400000000003053 y[1] (analytic) 8.13212526101118 y[1] (numeric) 8.132125261771002 absolute error 7.598224271987419e-10 relative error 9.343466840601306e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4500000000003153 y[1] (analytic) 8.58666586047486 y[1] (numeric) 8.586665861234213 absolute error 7.593534689931403e-10 relative error 8.843403031303545e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4600000000003253 y[1] (analytic) 9.068973920772217 y[1] (numeric) 9.068973921531104 absolute error 7.58886287144378e-10 relative error 8.367939898979876e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.1233036071493805 Order of pole (three term test) -3982.4225187196957 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4700000000003353 y[1] (analytic) 9.5808468730796 y[1] (numeric) 9.580846873837988 absolute error 7.583871308725065e-10 relative error 7.91565861472469e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3425988148239785 Order of pole (three term test) -1295.932834568414 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4800000000003453 y[1] (analytic) 10.124203952797949 y[1] (numeric) 10.124203953555796 absolute error 7.578471183933289e-10 relative error 7.485498335737186e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7245984809671917 Order of pole (three term test) -700.9572970525365 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4900000000003553 y[1] (analytic) 10.701094769422355 y[1] (numeric) 10.701094770179628 absolute error 7.572733551342026e-10 relative error 7.0765970347076945e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4573100894501516 Order of pole (three term test) -444.955332545388 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5000000000003653 y[1] (analytic) 11.313708499007818 y[1] (numeric) 11.313708499764461 absolute error 7.566427484562155e-10 relative error 6.687840229599084e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.31097781691657 Order of pole (three term test) -305.72256619122436 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5100000000003198 y[1] (analytic) 11.964383745739962 y[1] (numeric) 11.964383746499589 absolute error 7.596270279464079e-10 relative error 6.349069405408203e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.220475026441264 Order of pole (three term test) -220.28674122902913 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5200000000002742 y[1] (analytic) 12.655619122703198 y[1] (numeric) 12.655619123465927 absolute error 7.627285469880007e-10 relative error 6.026797579738513e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.16022279571866826 Order of pole (three term test) -163.92934817167136 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5300000000002287 y[1] (analytic) 13.390084605726244 y[1] (numeric) 13.39008460649232 absolute error 7.660752032734308e-10 relative error 5.7212125675876626e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11810955768415125 Order of pole (three term test) -124.96077881007768 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5400000000001832 y[1] (analytic) 14.170633718396827 y[1] (numeric) 14.170633719166453 absolute error 7.696261405953919e-10 relative error 5.431134244873153e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.08764734072681847 Order of pole (three term test) -97.13396532119393 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5500000000001377 y[1] (analytic) 15.000316610753403 y[1] (numeric) 15.00031661152679 absolute error 7.733866880244022e-10 relative error 5.155802427996607e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.06503984482374281 Order of pole (three term test) -76.80890606768858 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5600000000000922 y[1] (analytic) 15.882394099000607 y[1] (numeric) 15.882394099778027 absolute error 7.774207944066802e-10 relative error 4.894858983858102e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.04791242969693062 Order of pole (three term test) -61.724824464531515 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5700000000000467 y[1] (analytic) 16.820352738790113 y[1] (numeric) 16.820352739571845 absolute error 7.817320124559046e-10 relative error 4.647536378075592e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.034699182205941294 Order of pole (three term test) -50.408154112813364 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5800000000000012 y[1] (analytic) 17.81792101021699 y[1] (numeric) 17.81792101100329 absolute error 7.863008022468421e-10 relative error 4.412977259221032e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.02432121204710487 Order of pole (three term test) -41.86257130382011 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5900099999999556 y[1] (analytic) 18.88018109482638 y[1] (numeric) 18.880181095617548 absolute error 7.911680199867988e-10 relative error 4.1904683859393575e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.5649948928198492 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.015998348137237602 Order of pole (three term test) -35.390145731774226 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6000099999999101 y[1] (analytic) 20.00928005473505 y[1] (numeric) 20.009280055531292 absolute error 7.962412951201259e-10 relative error 3.97936004165078e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.6257003547493236 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.009172536160311148 Order of pole (three term test) -30.513077025783886 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6100099999998646 y[1] (analytic) 21.210810693386605 y[1] (numeric) 21.210810694188282 absolute error 8.016769470486906e-10 relative error 3.779567686673326e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.677774921973498 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.003390922388951256 Order of pole (three term test) -26.872851066087062 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6200099999998191 y[1] (analytic) 22.489656691641862 y[1] (numeric) 22.489656692449362 absolute error 8.074998447682447e-10 relative error 3.5905387789594265e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.7223069271643814 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6300099999997736 y[1] (analytic) 23.8510444662709 y[1] (numeric) 23.8510444670846 absolute error 8.136993301377515e-10 relative error 3.411587829155446e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.76034433067335 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6400099999997281 y[1] (analytic) 25.300568042825667 y[1] (numeric) 25.30056804364595 absolute error 8.202825085845689e-10 relative error 3.2421505603988665e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.7928542736587798 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6500099999996826 y[1] (analytic) 26.844215786551626 y[1] (numeric) 26.84421578737896 absolute error 8.273346452369879e-10 relative error 3.0819847814346086e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.7987674212586335 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.660009999999637 y[1] (analytic) 28.48839913371492 y[1] (numeric) 28.488399134549756 absolute error 8.348344238129357e-10 relative error 2.9304364204338226e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8025094917365856 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6700099999995915 y[1] (analytic) 30.239983476882387 y[1] (numeric) 30.239983477725193 absolute error 8.42806713308164e-10 relative error 2.787060759978477e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8064236255169037 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.680009999999546 y[1] (analytic) 32.10632136974571 y[1] (numeric) 32.10632137059702 absolute error 8.513154625688912e-10 relative error 2.651550929067505e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8104597323830083 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6900099999995005 y[1] (analytic) 34.09528823010088 y[1] (numeric) 34.09528823096118 absolute error 8.603038281762565e-10 relative error 2.52323377462092e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8145772186391413 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.700009999999455 y[1] (analytic) 36.21532073365865 y[1] (numeric) 36.215320734528625 absolute error 8.699743148099515e-10 relative error 2.4022272816747253e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8187431877383857 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7100099999994095 y[1] (analytic) 38.47545810655649 y[1] (numeric) 38.475458107436836 absolute error 8.803482387520489e-10 relative error 2.288077340921982e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8229309924121293 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.720009999999364 y[1] (analytic) 40.88538654085972 y[1] (numeric) 40.885386541750975 absolute error 8.912550697459665e-10 relative error 2.179886617569999e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8271190666556494 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7300099999993185 y[1] (analytic) 43.4554869750801 y[1] (numeric) 43.455486975983064 absolute error 9.029648140312929e-10 relative error 2.0779074793227044e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8312899814134254 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.740009999999273 y[1] (analytic) 46.19688650091138 y[1] (numeric) 46.19688650182671 absolute error 9.153282576335187e-10 relative error 1.981363522443143e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8354296796814666 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7500099999992275 y[1] (analytic) 49.12151367810231 y[1] (numeric) 49.12151367903087 absolute error 9.285585633733717e-10 relative error 1.890329702497157e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8395268559247604 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.760009999999182 y[1] (analytic) 52.242158061784636 y[1] (numeric) 52.2421580627273 absolute error 9.426628366782097e-10 relative error 1.8044102151434124e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.843572451861351 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7700099999991364 y[1] (analytic) 55.57253427078553 y[1] (numeric) 55.57253427174334 absolute error 9.57811607804615e-10 relative error 1.7235341529280165e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8475592462752852 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7800099999990909 y[1] (analytic) 59.12735095162966 y[1] (numeric) 59.127350952603614 absolute error 9.739551387610845e-10 relative error 1.6472159213725785e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8514815209465187 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7900099999990454 y[1] (analytic) 62.922385021239116 y[1] (numeric) 62.92238502223034 absolute error 9.91221327240055e-10 relative error 1.5753079399413634e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.855334788294685 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8000099999989999 y[1] (analytic) 66.9745616019439 y[1] (numeric) 66.97456160295363 absolute error 1.009723860079248e-09 relative error 1.507622948068601e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8591155691273196 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8100099999989544 y[1] (analytic) 71.30204009551397 y[1] (numeric) 71.30204009654338 absolute error 1.0294058938598027e-09 relative error 1.4437257229678743e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8628212111157034 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8200099999989089 y[1] (analytic) 75.92430687872115 y[1] (numeric) 75.9243068797716 absolute error 1.050452169693017e-09 relative error 1.3835518727500175e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.866449740411027 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8300099999988634 y[1] (analytic) 80.86227514166106 y[1] (numeric) 80.86227514273413 absolute error 1.0730758503996185e-09 relative error 1.3270413780959263e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8699997402522546 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8400099999988179 y[1] (analytic) 86.13839243195277 y[1] (numeric) 86.13839243304976 absolute error 1.0969927188853035e-09 relative error 1.2735235565858754e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8734702515763053 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8500099999987724 y[1] (analytic) 91.77675651325319 y[1] (numeric) 91.77675651437583 absolute error 1.122643311646243e-09 relative error 1.2232327163186745e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8768606915766444 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8600099999987268 y[1] (analytic) 97.80324019555707 y[1] (numeric) 97.80324019670728 absolute error 1.150212369793735e-09 relative error 1.17604730425484e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8801707869138045 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8700099999986813 y[1] (analytic) 104.24562584781485 y[1] (numeric) 104.24562584899452 absolute error 1.1796714716183487e-09 relative error 1.1316268304058308e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8834005188938274 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8800099999986358 y[1] (analytic) 111.13375036082354 y[1] (numeric) 111.1337503620349 absolute error 1.2113616776332492e-09 relative error 1.0900034181337894e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8865500784283729 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8900099999985903 y[1] (analytic) 118.4996613904961 y[1] (numeric) 118.4996613917408 absolute error 1.244700342795113e-09 relative error 1.0503830375459118e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8896198289939203 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9000099999985448 y[1] (analytic) 126.37778577888882 y[1] (numeric) 126.37778578016905 absolute error 1.2802274795831181e-09 relative error 1.0130162288355092e-09% Correct digits 11 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.892610276135651 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 69.1551003249949 Order of pole (three term test) 20327.68132564514 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9100099999984993 y[1] (analytic) 134.80511112319144 y[1] (numeric) 134.80511112450932 absolute error 1.3178862445784034e-09 relative error 9.77623350923286e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8955220423289885 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 18.06931946083065 Order of pole (three term test) 5291.358800314116 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9200099999984538 y[1] (analytic) 143.8213815417301 y[1] (numeric) 143.82138154308868 absolute error 1.358586132482742e-09 relative error 9.446343220451857e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.8983558462291048 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 11.426913125029591 Order of pole (three term test) 3334.5634357889003 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9300099999984083 y[1] (analytic) 153.46930877140187 y[1] (numeric) 153.46930877280403 absolute error 1.4021566130395513e-09 relative error 9.136397526414318e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.9011124855161308 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 8.868190578275122 Order of pole (three term test) 2579.4765754629716 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9400099999983628 y[1] (analytic) 163.7947998234018 y[1] (numeric) 163.79479982485103 absolute error 1.4492229638563003e-09 relative error 8.847795933807454e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.9037928226884053 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 7.546364270665267 Order of pole (three term test) 2188.2952378025766 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9500099999983173 y[1] (analytic) 174.84720252421488 y[1] (numeric) 174.84720252571435 absolute error 1.4994725461292546e-09 relative error 8.575902413546423e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.906397773274051 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 6.761491963882528 Order of pole (three term test) 1955.0319853926017 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9600099999982717 y[1] (analytic) 186.67957037727336 y[1] (numeric) 186.6795703788268 absolute error 1.5534453723375918e-09 relative error 8.32145354308524e-10% Correct digits 12 h 1.0e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 1.9089282960276104 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 6.257603194025015 Order of pole (three term test) 1804.3605883523617 NO COMPLEX POLE (six term test) for Equation 1 Finished! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ; Iterations 86015 Total Elapsed Time 3 Minutes 0.0 Seconds Elapsed Time(since restart) 3 Minutes 0.0 Seconds Expected Time Remaining 8.337053571807132 Seconds Optimized Time Remaining 8.337053571807132 Seconds Expected Total Time 3 Minutes 8.337053571807132 Seconds Time to Timeout 0.0 Seconds Percent Done 95.57333333314122%