##############ECHO OF PROBLEM################# ##############temp/sing2postode.ode################# diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=50 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-2.0 x_end=-1.5 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=100 ## Not Given = 0 ## No Pole = 3 ## Pole = 4 $glob_type_given_pole=4 ## Real Part $array_given_rad_poles[1][1]=0.0 ## Imag Part $array_given_rad_poles[1][2]=1.0 ## Order $array_given_ord_poles[1][1]=1.0 ## Not Used $array_given_ord_poles[1][2]=0.0 #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(arctan(x)) 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 0.5 estimated_steps 500000.0 step_error 2.0e-16 est_needed_step_err 2.0e-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 1.1229185241069579e-294 estimated_step_error 1.1229185241069579e-294 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 7.901837192668398e-281 estimated_step_error 7.901837192668398e-281 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 5.56042438355433e-267 estimated_step_error 5.56042438355433e-267 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 3.912801913190608e-253 estimated_step_error 3.912801913190608e-253 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 2.7533911215536513e-239 estimated_step_error 2.7533911215536513e-239 best_h 3.2e-05 opt_iter 6 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9375289402898288e-225 estimated_step_error 1.9375289402898288e-225 best_h 6.4e-05 opt_iter 7 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3634178594924326e-211 estimated_step_error 1.3634178594924326e-211 best_h 0.000128 opt_iter 8 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.594243547696086e-198 estimated_step_error 9.594243547696086e-198 best_h 0.000256 opt_iter 9 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.751409621872946e-184 estimated_step_error 6.751409621872946e-184 best_h 0.000512 opt_iter 10 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.750967898646189e-170 estimated_step_error 4.750967898646189e-170 best_h 0.001024 opt_iter 11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.3433170789707423e-156 estimated_step_error 3.3433170789707423e-156 best_h 0.002048 opt_iter 12 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.352819942256158e-142 estimated_step_error 2.352819942256158e-142 best_h 0.004096 opt_iter 13 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6558884660811424e-128 estimated_step_error 1.6558884660811424e-128 best_h 0.008192 opt_iter 14 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1655631511624786e-114 estimated_step_error 1.1655631511624786e-114 best_h 0.016384 opt_iter 15 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.206622748639157e-101 estimated_step_error 8.206622748639157e-101 best_h 0.032768 opt_iter 16 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.781466606566113e-87 estimated_step_error 5.781466606566113e-87 best_h 0.065536 opt_iter 17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.0774581092659855e-73 estimated_step_error 4.0774581092659855e-73 best_h 0.131072 opt_iter 18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.881707429125352e-59 estimated_step_error 2.881707429125352e-59 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] -2.0 y[1] (analytic) -1.1071487177940904 y[1] (numeric) -1.1071487177940904 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.236067977499868 Order of pole (six term test) 1.858069254012662e-12 TOP MAIN SOLVE Loop x[1] -1.99 y[1] (analytic) -1.1051406883644943 y[1] (numeric) -1.1051406883644943 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.2271281956816047 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.227128195681493 Order of pole (six term test) -2.426503442620742e-12 TOP MAIN SOLVE Loop x[1] -1.98 y[1] (analytic) -1.103116481582997 y[1] (numeric) -1.103116481582997 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.2181974664127626 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.218197466412726 Order of pole (six term test) -7.673861546209082e-13 TOP MAIN SOLVE Loop x[1] -1.97 y[1] (analytic) -1.1010759179539864 y[1] (numeric) -1.1010759179539864 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.2092758994747577 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.2092758994748674 Order of pole (six term test) 2.3021584638627246e-12 TOP MAIN SOLVE Loop x[1] -1.96 y[1] (analytic) -1.0990188156141465 y[1] (numeric) -1.0990188156141467 absolute error 2.220446049250313e-16 relative error 2.0203894762343063e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.2003636063160106 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.200363606316244 Order of pole (six term test) 4.89208673570829e-12 TOP MAIN SOLVE Loop x[1] -1.95 y[1] (analytic) -1.0969449903001363 y[1] (numeric) -1.0969449903001365 absolute error 2.220446049250313e-16 relative error 2.0242091161223813e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.191460700081113 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.1914607000812176 Order of pole (six term test) 2.2026824808563106e-12 TOP MAIN SOLVE Loop x[1] -1.94 y[1] (analytic) -1.0948542553159382 y[1] (numeric) -1.0948542553159384 absolute error 2.220446049250313e-16 relative error 2.0280745482507777e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.182567295640618 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.182567295640505 Order of pole (six term test) -2.34123831432953e-12 TOP MAIN SOLVE Loop x[1] -1.93 y[1] (analytic) -1.0927464214998852 y[1] (numeric) -1.0927464214998857 absolute error 4.440892098500626e-16 relative error 4.06397313331407e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.1736835096213984 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.1736835096214246 Order of pole (six term test) 5.329070518200751e-13 TOP MAIN SOLVE Loop x[1] -1.92 y[1] (analytic) -1.0906212971913698 y[1] (numeric) -1.09062129719137 absolute error 2.220446049250313e-16 relative error 2.0359459832377493e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.1648094604375694 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.007820636845693958 Order of pole (three term test) -2.8319717693865947 Radius of convergence (six term test) for eq 1 2.1648094604376213 Order of pole (six term test) 1.0764722446765518e-12 TOP MAIN SOLVE Loop x[1] -1.91 y[1] (analytic) -1.0884786881972366 y[1] (numeric) -1.088478688197237 absolute error 4.440892098500626e-16 relative error 4.079907256480817e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.1559452683219953 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.011765801714462298 Order of pole (three term test) -8.530625394241245 Radius of convergence (six term test) for eq 1 2.155945268322188 Order of pole (six term test) 3.9754866065777605e-12 TOP MAIN SOLVE Loop x[1] -1.9 y[1] (analytic) -1.0863183977578734 y[1] (numeric) -1.0863183977578739 absolute error 4.440892098500626e-16 relative error 4.088020701542463e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.1470910553583886 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.01163759957082911 Order of pole (three term test) -17.87256631118954 Radius of convergence (six term test) for eq 1 2.147091055358373 Order of pole (six term test) -3.268496584496461e-13 TOP MAIN SOLVE Loop x[1] -1.89 y[1] (analytic) -1.084140226512997 y[1] (numeric) -1.0841402265129974 absolute error 4.440892098500626e-16 relative error 4.0962340386392697e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.1382469455140116 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.007434640450767655 Order of pole (three term test) -30.57962913071991 Radius of convergence (six term test) for eq 1 2.1382469455141093 Order of pole (six term test) 2.021494083237485e-12 TOP MAIN SOLVE Loop x[1] -1.88 y[1] (analytic) -1.0819439724671487 y[1] (numeric) -1.0819439724671494 absolute error 6.661338147750939e-16 relative error 6.156823566899809e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.1294130646729865 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.1294130646743374 Order of pole (six term test) 2.7895907805941533e-11 TOP MAIN SOLVE Loop x[1] -1.8699999999999999 y[1] (analytic) -1.0797294309549066 y[1] (numeric) -1.079729430954907 absolute error 4.440892098500626e-16 relative error 4.112967537221919e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.1205895406702355 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 0.9080261154396462 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 2.120589540669829 Order of pole (six term test) -8.391509709326783e-12 TOP MAIN SOLVE Loop x[1] -1.8599999999999999 y[1] (analytic) -1.0774963946058176 y[1] (numeric) -1.077496394605818 absolute error 4.440892098500626e-16 relative error 4.1214913764284525e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.1117765033260505 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 0.5939466670289647 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 2.111776503325885 Order of pole (six term test) -3.417710559006082e-12 TOP MAIN SOLVE Loop x[1] -1.8499999999999999 y[1] (analytic) -1.075244653309068 y[1] (numeric) -1.0752446533090685 absolute error 4.440892098500626e-16 relative error 4.1301224654628787e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.1029740844813087 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.1029740844813207 Order of pole (six term test) 2.4158453015843406e-13 TOP MAIN SOLVE Loop x[1] -1.8399999999999999 y[1] (analytic) -1.0729739941778953 y[1] (numeric) -1.0729739941778957 absolute error 4.440892098500626e-16 relative error 4.1388627521240205e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.094182418033348 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.0941824180335122 Order of pole (six term test) 3.396394276933279e-12 TOP MAIN SOLVE Loop x[1] -1.8299999999999998 y[1] (analytic) -1.0706842015137568 y[1] (numeric) -1.0706842015137572 absolute error 4.440892098500626e-16 relative error 4.147714230042804e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.0854016399725017 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.0854016399725266 Order of pole (six term test) 5.186961971048731e-13 TOP MAIN SOLVE Loop x[1] -1.8199999999999998 y[1] (analytic) -1.068375056770266 y[1] (numeric) -1.0683750567702661 absolute error 2.220446049250313e-16 relative error 2.0783394700011033e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.076631888419322 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.0766318884190746 Order of pole (six term test) -5.098144129078719e-12 TOP MAIN SOLVE Loop x[1] -1.8099999999999998 y[1] (analytic) -1.066046338516909 y[1] (numeric) -1.0660463385169094 absolute error 4.440892098500626e-16 relative error 4.1657589713021535e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.067873303662485 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 0.9296890689377629 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 2.0678733036626653 Order of pole (six term test) 3.723243935382925e-12 TOP MAIN SOLVE Loop x[1] -1.7999999999999998 y[1] (analytic) -1.0636978224025597 y[1] (numeric) -1.06369782240256 absolute error 2.220446049250313e-16 relative error 2.0874782315855663e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.0591260281974 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.0591260281975123 Order of pole (six term test) 2.3234747459355276e-12 TOP MAIN SOLVE Loop x[1] -1.7899999999999998 y[1] (analytic) -1.0613292811188 y[1] (numeric) -1.0613292811188002 absolute error 2.220446049250313e-16 relative error 2.0921368031131964e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.0503902067655315 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.050390206765712 Order of pole (six term test) 3.716138508025324e-12 TOP MAIN SOLVE Loop x[1] -1.7799999999999998 y[1] (analytic) -1.0589404843630723 y[1] (numeric) -1.0589404843630728 absolute error 4.440892098500626e-16 relative error 4.193712643984631e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.0416659863944444 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.0416659863945315 Order of pole (six term test) 1.7976731214730535e-12 TOP MAIN SOLVE Loop x[1] -1.7699999999999998 y[1] (analytic) -1.056531198801675 y[1] (numeric) -1.0565311988016752 absolute error 2.220446049250313e-16 relative error 2.101637937212605e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.032953516438583 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.4255623670151267 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 2.032953516438468 Order of pole (six term test) -2.3447910280083306e-12 TOP MAIN SOLVE Loop x[1] -1.7599999999999998 y[1] (analytic) -1.0541011880326194 y[1] (numeric) -1.0541011880326197 absolute error 2.220446049250313e-16 relative error 2.106482825804007e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.0242529486207994 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 1.5231120840191432 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 2.0242529486208456 Order of pole (six term test) 9.521272659185342e-13 TOP MAIN SOLVE Loop x[1] -1.7499999999999998 y[1] (analytic) -1.0516502125483735 y[1] (numeric) -1.051650212548374 absolute error 4.440892098500626e-16 relative error 4.222784387348141e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.0155644370746373 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.0155644370747026 Order of pole (six term test) 1.3606893389805919e-12 TOP MAIN SOLVE Loop x[1] -1.7399999999999998 y[1] (analytic) -1.04917802969851 y[1] (numeric) -1.0491780296985105 absolute error 4.440892098500626e-16 relative error 4.232734552949754e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.006888138387389 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.0068881383874024 Order of pole (six term test) 2.5934809855243657e-13 TOP MAIN SOLVE Loop x[1] -1.7299999999999998 y[1] (analytic) -1.0466843936522807 y[1] (numeric) -1.0466843936522812 absolute error 4.440892098500626e-16 relative error 4.242818681001502e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9982242116439284 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9982242116439788 Order of pole (six term test) 9.805489753489383e-13 TOP MAIN SOLVE Loop x[1] -1.7199999999999998 y[1] (analytic) -1.0441690553611458 y[1] (numeric) -1.0441690553611465 absolute error 6.661338147750939e-16 relative error 6.379559050854067e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.989572818471342 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9895728184713846 Order of pole (six term test) 7.709388682997087e-13 TOP MAIN SOLVE Loop x[1] -1.7099999999999997 y[1] (analytic) -1.0416317625212812 y[1] (numeric) -1.0416317625212819 absolute error 6.661338147750939e-16 relative error 6.395098908684483e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9809341230843591 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9809341230843556 Order of pole (six term test) -1.4210854715202004e-13 TOP MAIN SOLVE Loop x[1] -1.6999999999999997 y[1] (analytic) -1.039072259536091 y[1] (numeric) -1.0390722595360915 absolute error 4.440892098500626e-16 relative error 4.273901124531346e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9723082923316018 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9723082923316244 Order of pole (six term test) 6.181721801112872e-13 TOP MAIN SOLVE Loop x[1] -1.6899999999999997 y[1] (analytic) -1.036490287478756 y[1] (numeric) -1.0364902874787567 absolute error 6.661338147750939e-16 relative error 6.426821580696645e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.963695495742657 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.963695495742593 Order of pole (six term test) -1.680433570072637e-12 TOP MAIN SOLVE Loop x[1] -1.6799999999999997 y[1] (analytic) -1.0338855840548509 y[1] (numeric) -1.0338855840548515 absolute error 6.661338147750939e-16 relative error 6.443012892805297e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9550959055759898 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9550959055759805 Order of pole (six term test) -2.0961010704922955e-13 TOP MAIN SOLVE Loop x[1] -1.6699999999999997 y[1] (analytic) -1.0312578835650579 y[1] (numeric) -1.0312578835650585 absolute error 6.661338147750939e-16 relative error 6.459430035795409e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9465096968677036 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9465096968676454 Order of pole (six term test) -1.3749001936957939e-12 TOP MAIN SOLVE Loop x[1] -1.6599999999999997 y[1] (analytic) -1.0286069168680179 y[1] (numeric) -1.0286069168680185 absolute error 6.661338147750939e-16 relative error 6.476077536046421e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9379370474811608 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9379370474809494 Order of pole (six term test) -5.002220859751105e-12 TOP MAIN SOLVE Loop x[1] -1.6499999999999997 y[1] (analytic) -1.0259324113433528 y[1] (numeric) -1.0259324113433534 absolute error 6.661338147750939e-16 relative error 6.492960037229551e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9293781381574735 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.929378138157553 Order of pole (six term test) 1.8687273950490635e-12 TOP MAIN SOLVE Loop x[1] -1.6399999999999997 y[1] (analytic) -1.023234090854899 y[1] (numeric) -1.0232340908548996 absolute error 6.661338147750939e-16 relative error 6.510082304026323e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.920833152566875 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.003930343875034228 Order of pole (three term test) -1.4208003587089966 Radius of convergence (six term test) for eq 1 1.9208331525669338 Order of pole (six term test) 1.3749001936957939e-12 TOP MAIN SOLVE Loop x[1] -1.6299999999999997 y[1] (analytic) -1.0205116757141932 y[1] (numeric) -1.0205116757141939 absolute error 6.661338147750939e-16 relative error 6.52744922598664e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9123022773609821 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.009678198182838481 Order of pole (three term test) -6.026873484815323 Radius of convergence (six term test) for eq 1 1.9123022773610652 Order of pole (six term test) 1.936228954946273e-12 TOP MAIN SOLVE Loop x[1] -1.6199999999999997 y[1] (analytic) -1.017764882644256 y[1] (numeric) -1.0177648826442567 absolute error 6.661338147750939e-16 relative error 6.545065821532483e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9037857022259619 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.010889803440270403 Order of pole (three term test) -15.292865626736788 Radius of convergence (six term test) for eq 1 1.903785702225983 Order of pole (six term test) 4.831690603168681e-13 TOP MAIN SOLVE Loop x[1] -1.6099999999999997 y[1] (analytic) -1.0149934247437171 y[1] (numeric) -1.014993424743718 absolute error 8.881784197001252e-16 relative error 8.750582989484761e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.8952836199366043 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.007497061273029342 Order of pole (three term test) -28.740852862367515 Radius of convergence (six term test) for eq 1 1.8952836199367555 Order of pole (six term test) 3.5278446830488974e-12 TOP MAIN SOLVE Loop x[1] -1.5999999999999996 y[1] (analytic) -1.0121970114513341 y[1] (numeric) -1.0121970114513348 absolute error 6.661338147750939e-16 relative error 6.581068776521687e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.8867962264113205 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8867962264132934 Order of pole (six term test) 4.5993431285751285e-11 TOP MAIN SOLVE Loop x[1] -1.5899999999999996 y[1] (analytic) -1.0093753485109522 y[1] (numeric) -1.009375348510953 absolute error 6.661338147750939e-16 relative error 6.59946585537071e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.8783237207680679 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8783237207681407 Order of pole (six term test) 1.694644424787839e-12 TOP MAIN SOLVE Loop x[1] -1.5799999999999996 y[1] (analytic) -1.0065281379369648 y[1] (numeric) -1.0065281379369655 absolute error 6.661338147750939e-16 relative error 6.618134055749681e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.869866305381216 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.869866305381072 Order of pole (six term test) -3.346656285430072e-12 TOP MAIN SOLVE Loop x[1] -1.5699999999999996 y[1] (analytic) -1.003655077980327 y[1] (numeric) -1.0036550779803277 absolute error 6.661338147750939e-16 relative error 6.637079106056703e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.8614241859393572 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.861424185939571 Order of pole (six term test) 4.973799150320701e-12 TOP MAIN SOLVE Loop x[1] -1.5599999999999996 y[1] (analytic) -1.0007558630951863 y[1] (numeric) -1.000755863095187 absolute error 6.661338147750939e-16 relative error 6.656306891021781e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.8529975715040747 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8529975715038116 Order of pole (six term test) -6.117772954894463e-12 TOP MAIN SOLVE Loop x[1] -1.5499999999999996 y[1] (analytic) -0.9978301839061904 y[1] (numeric) -0.997830183906191 absolute error 6.661338147750939e-16 relative error 6.675823456927212e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.8445866745696715 Order of pole (given) 1.0 Radius of convergence (ratio test) for eq 1 0.8208363651377616 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 1.8445866745699189 Order of pole (six term test) 5.7482907322992105e-12 TOP MAIN SOLVE Loop x[1] -1.5399999999999996 y[1] (analytic) -0.9948777271765434 y[1] (numeric) -0.9948777271765442 absolute error 7.771561172376096e-16 relative error 7.811574186540225e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.8361917111238681 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8361917111238568 Order of pole (six term test) -2.6290081223123707e-13 TOP MAIN SOLVE Loop x[1] -1.5299999999999996 y[1] (analytic) -0.991898175776877 y[1] (numeric) -0.9918981757768777 absolute error 6.661338147750939e-16 relative error 6.715747957227192e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.8278129007094788 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8278129007096053 Order of pole (six term test) 2.9523050670832163e-12 TOP MAIN SOLVE Loop x[1] -1.5199999999999996 y[1] (analytic) -0.9888912086550109 y[1] (numeric) -0.9888912086550117 absolute error 7.771561172376096e-16 relative error 7.858863648860001e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.819450466487065 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8194504664871352 Order of pole (six term test) 1.6271428648906294e-12 TOP MAIN SOLVE Loop x[1] -1.5099999999999996 y[1] (analytic) -0.9858565008066834 y[1] (numeric) -0.9858565008066842 absolute error 7.771561172376096e-16 relative error 7.883055156624687e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.811104635298579 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8111046352986406 Order of pole (six term test) 1.4210854715202004e-12 Finished! diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ; Iterations 50 Total Elapsed Time 0.0 Seconds Elapsed Time(since restart) 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 102.00000000000009%