##############ECHO OF PROBLEM################# ##############temp/divpostode.ode################# diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.0 x_end=1.5 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=10000000 $glob_display_interval=0.1 $glob_max_minutes=10 $glob_max_h=0.001 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=4 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=1.570796327 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=0.0 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=1000000000 $glob_max_minutes=10.0 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(2.0 - ln(float_abs(cos(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 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 1.5 estimated_steps 1500000.0 step_error 6.666666666666667e-17 est_needed_step_err 6.666666666666667e-17 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.122655795896327e-163 estimated_step_error 6.122655795896327e-163 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 4.108844751257343e-155 estimated_step_error 4.108844751257343e-155 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 2.757399036095542e-147 estimated_step_error 2.757399036095542e-147 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 1.850459169079025e-139 estimated_step_error 1.850459169079025e-139 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 1.2418221271752053e-131 estimated_step_error 1.2418221271752053e-131 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 8.33372722508132e-124 estimated_step_error 8.33372722508132e-124 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 5.592669671227225e-116 estimated_step_error 5.592669671227225e-116 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 3.753177087972187e-108 estimated_step_error 3.753177087972187e-108 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 2.518714519293995e-100 estimated_step_error 2.518714519293995e-100 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 1.6902807325674962e-92 estimated_step_error 1.6902807325674962e-92 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 1.1343282819665849e-84 estimated_step_error 1.1343282819665849e-84 best_h 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (analytic) 2.0 y[1] (numeric) 2.0 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.570796327 Order of pole (given) 0.0 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] 0.010000000000000002 y[1] (analytic) 2.0000500008333555 y[1] (numeric) 2.0000500008333555 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.560796327 Order of pole (given) 0.0 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] 0.02000000000000001 y[1] (analytic) 2.000200013334756 y[1] (numeric) 2.0002000133347555 absolute error 4.440892098500626e-16 relative error 2.2202240120460357e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.550796327 Order of pole (given) 0.0 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] 0.03000000000000002 y[1] (analytic) 2.0004500675162045 y[1] (numeric) 2.000450067516204 absolute error 4.440892098500626e-16 relative error 2.219946486349704e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.540796327 Order of pole (given) 0.0 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] 0.04000000000000003 y[1] (analytic) 2.0008002134244 y[1] (numeric) 2.0008002134244 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.530796327 Order of pole (given) 0.0 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] 0.05000000000000004 y[1] (analytic) 2.001250521180819 y[1] (numeric) 2.0012505211808196 absolute error 4.440892098500626e-16 relative error 2.2190585593853183e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.520796327 Order of pole (given) 0.0 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] 0.060000000000000046 y[1] (analytic) 2.0018010810379345 y[1] (numeric) 2.0018010810379345 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.510796327 Order of pole (given) 0.0 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] 0.07000000000000005 y[1] (analytic) 2.002452003451651 y[1] (numeric) 2.00245200345165 absolute error 8.881784197001252e-16 relative error 4.435454223967223e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.500796327 Order of pole (given) 0.0 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] 0.08000000000000006 y[1] (analytic) 2.003203419170097 y[1] (numeric) 2.0032034191700965 absolute error 4.440892098500626e-16 relative error 2.2168952269163132e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.490796327 Order of pole (given) 0.0 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] 0.09000000000000007 y[1] (analytic) 2.004055479338916 y[1] (numeric) 2.004055479338915 absolute error 8.881784197001252e-16 relative error 4.4319053482147684e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.480796327 Order of pole (given) 0.0 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] 0.10000000000000007 y[1] (analytic) 2.0050083556232354 y[1] (numeric) 2.0050083556232345 absolute error 8.881784197001252e-16 relative error 4.429799093899758e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.470796327 Order of pole (given) 0.0 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] 0.11000000000000008 y[1] (analytic) 2.0060622403465325 y[1] (numeric) 2.006062240346531 absolute error 1.3322676295501878e-15 relative error 6.641207848665994e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.460796327 Order of pole (given) 0.0 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] 0.12000000000000009 y[1] (analytic) 2.0072173466466277 y[1] (numeric) 2.0072173466466263 absolute error 1.3322676295501878e-15 relative error 6.637385989992317e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.450796327 Order of pole (given) 0.0 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] 0.1300000000000001 y[1] (analytic) 2.008473908649082 y[1] (numeric) 2.008473908649081 absolute error 1.3322676295501878e-15 relative error 6.633233440638933e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.440796327 Order of pole (given) 0.0 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] 0.1400000000000001 y[1] (analytic) 2.009832181658296 y[1] (numeric) 2.009832181658294 absolute error 1.7763568394002505e-15 relative error 8.838334143573088e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.430796327 Order of pole (given) 0.0 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] 0.1500000000000001 y[1] (analytic) 2.0112924423666416 y[1] (numeric) 2.0112924423666403 absolute error 1.3322676295501878e-15 relative error 6.62393792909866e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.420796327 Order of pole (given) 0.0 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] 0.16000000000000011 y[1] (analytic) 2.0128549890820095 y[1] (numeric) 2.012854989082008 absolute error 1.3322676295501878e-15 relative error 6.618795873406594e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.410796327 Order of pole (given) 0.0 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] 0.17000000000000012 y[1] (analytic) 2.014520141974147 y[1] (numeric) 2.0145201419741463 absolute error 8.881784197001252e-16 relative error 4.4088832928210225e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.400796327 Order of pole (given) 0.0 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] 0.18000000000000013 y[1] (analytic) 2.016288243340249 y[1] (numeric) 2.0162882433402483 absolute error 8.881784197001252e-16 relative error 4.405017103252756e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3907963269999999 Order of pole (given) 0.0 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] 0.19000000000000014 y[1] (analytic) 2.01815965789026 y[1] (numeric) 2.01815965789026 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3807963269999999 Order of pole (given) 0.0 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] 0.20000000000000015 y[1] (analytic) 2.0201347730524084 y[1] (numeric) 2.0201347730524084 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3707963269999999 Order of pole (given) 0.0 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] 0.21000000000000016 y[1] (analytic) 2.022213999299519 y[1] (numeric) 2.0222139992995185 absolute error 4.440892098500626e-16 relative error 2.1960544729879828e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3607963269999999 Order of pole (given) 0.0 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] 0.22000000000000017 y[1] (analytic) 2.0243977704967033 y[1] (numeric) 2.0243977704967024 absolute error 8.881784197001252e-16 relative error 4.38737106236885e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3507963269999999 Order of pole (given) 0.0 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] 0.23000000000000018 y[1] (analytic) 2.026686544271061 y[1] (numeric) 2.02668654427106 absolute error 8.881784197001252e-16 relative error 4.382416324866738e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3407963269999998 Order of pole (given) 0.0 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] 0.24000000000000019 y[1] (analytic) 2.029080802404081 y[1] (numeric) 2.0290808024040805 absolute error 4.440892098500626e-16 relative error 2.1886225985870056e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3307963269999998 Order of pole (given) 0.0 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] 0.25000000000000017 y[1] (analytic) 2.0315810512474695 y[1] (numeric) 2.031581051247469 absolute error 4.440892098500626e-16 relative error 2.1859290800993377e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3207963269999998 Order of pole (given) 0.0 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] 0.2600000000000002 y[1] (analytic) 2.0341878221631884 y[1] (numeric) 2.0341878221631884 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3107963269999998 Order of pole (given) 0.0 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] 0.2700000000000002 y[1] (analytic) 2.036901671988538 y[1] (numeric) 2.0369016719885384 absolute error 4.440892098500626e-16 relative error 2.180219182679141e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3007963269999998 Order of pole (given) 0.0 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] 0.2800000000000002 y[1] (analytic) 2.039723183527177 y[1] (numeric) 2.0397231835271765 absolute error 4.440892098500626e-16 relative error 2.177203325610706e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2907963269999998 Order of pole (given) 0.0 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] 0.2900000000000002 y[1] (analytic) 2.042652966067024 y[1] (numeric) 2.042652966067024 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2807963269999998 Order of pole (given) 0.0 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] 0.3000000000000002 y[1] (analytic) 2.045691655926058 y[1] (numeric) 2.0456916559260576 absolute error 4.440892098500626e-16 relative error 2.1708511571800355e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2707963269999998 Order of pole (given) 0.0 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] 0.3100000000000002 y[1] (analytic) 2.048839917027086 y[1] (numeric) 2.048839917027085 absolute error 8.881784197001252e-16 relative error 4.3350308255849125e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2607963269999998 Order of pole (given) 0.0 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] 0.32000000000000023 y[1] (analytic) 2.0520984415026304 y[1] (numeric) 2.05209844150263 absolute error 4.440892098500626e-16 relative error 2.1640736178566674e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2507963269999998 Order of pole (given) 0.0 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] 0.33000000000000024 y[1] (analytic) 2.0554679503311526 y[1] (numeric) 2.055467950331152 absolute error 4.440892098500626e-16 relative error 2.160526072802625e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2407963269999998 Order of pole (given) 0.0 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] 0.34000000000000025 y[1] (analytic) 2.058949194005907 y[1] (numeric) 2.0589491940059066 absolute error 4.440892098500626e-16 relative error 2.1568730843039372e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2307963269999997 Order of pole (given) 0.0 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] 0.35000000000000026 y[1] (analytic) 2.062542953237805 y[1] (numeric) 2.062542953237805 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2207963269999997 Order of pole (given) 0.0 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] 0.36000000000000026 y[1] (analytic) 2.066250039693758 y[1] (numeric) 2.066250039693758 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2107963269999997 Order of pole (given) 0.0 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] 0.3700000000000003 y[1] (analytic) 2.0700712967720554 y[1] (numeric) 2.0700712967720554 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2007963269999997 Order of pole (given) 0.0 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] 0.3800000000000003 y[1] (analytic) 2.07400760041643 y[1] (numeric) 2.0740076004164307 absolute error 8.881784197001252e-16 relative error 4.2824260601638695e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1907963269999997 Order of pole (given) 0.0 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] 0.3900000000000003 y[1] (analytic) 2.078059859970587 y[1] (numeric) 2.0780598599705877 absolute error 8.881784197001252e-16 relative error 4.2740752410890445e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1807963269999997 Order of pole (given) 0.0 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] 0.4000000000000003 y[1] (analytic) 2.0822290190750556 y[1] (numeric) 2.082229019075056 absolute error 4.440892098500626e-16 relative error 2.132758720495265e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1707963269999997 Order of pole (given) 0.0 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] 0.4100000000000003 y[1] (analytic) 2.086516056608366 y[1] (numeric) 2.0865160566083665 absolute error 4.440892098500626e-16 relative error 2.1283766709753008e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1607963269999997 Order of pole (given) 0.0 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] 0.4200000000000003 y[1] (analytic) 2.0909219876746725 y[1] (numeric) 2.0909219876746725 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1507963269999997 Order of pole (given) 0.0 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] 0.4300000000000003 y[1] (analytic) 2.0954478646400734 y[1] (numeric) 2.0954478646400734 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1407963269999997 Order of pole (given) 0.0 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] 0.44000000000000034 y[1] (analytic) 2.1000947782200377 y[1] (numeric) 2.1000947782200377 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1307963269999997 Order of pole (given) 0.0 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] 0.45000000000000034 y[1] (analytic) 2.10486385862049 y[1] (numeric) 2.1048638586204897 absolute error 4.440892098500626e-16 relative error 2.109823911087128e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1207963269999996 Order of pole (given) 0.0 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] 0.46000000000000035 y[1] (analytic) 2.109756276735282 y[1] (numeric) 2.109756276735282 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1107963269999996 Order of pole (given) 0.0 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] 0.47000000000000036 y[1] (analytic) 2.1147732454029446 y[1] (numeric) 2.1147732454029446 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1007963269999996 Order of pole (given) 0.0 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] 0.48000000000000037 y[1] (analytic) 2.1199160207258236 y[1] (numeric) 2.1199160207258227 absolute error 8.881784197001252e-16 relative error 4.1896868131409654e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.0907963269999996 Order of pole (given) 0.0 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] 0.4900000000000004 y[1] (analytic) 2.1251859034548866 y[1] (numeric) 2.1251859034548852 absolute error 1.3322676295501878e-15 relative error 6.268946294930425e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.0807963269999996 Order of pole (given) 0.0 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] 0.5000000000000003 y[1] (analytic) 2.130584240443723 y[1] (numeric) 2.130584240443721 absolute error 1.7763568394002505e-15 relative error 8.337416590626335e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.0707963269999996 Order of pole (given) 0.0 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] 0.5100000000000003 y[1] (analytic) 2.1361124261754862 y[1] (numeric) 2.1361124261754845 absolute error 1.7763568394002505e-15 relative error 8.315839642301294e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.0607963269999998 Order of pole (given) 0.0 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] 0.5200000000000004 y[1] (analytic) 2.1417719043667884 y[1] (numeric) 2.141771904366786 absolute error 2.220446049250313e-15 relative error 1.036733204279652e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.0507963269999996 Order of pole (given) 0.0 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] 0.5300000000000004 y[1] (analytic) 2.1475641696528216 y[1] (numeric) 2.1475641696528194 absolute error 2.220446049250313e-15 relative error 1.033936997379349e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.0407963269999998 Order of pole (given) 0.0 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] 0.5400000000000004 y[1] (analytic) 2.1534907693582817 y[1] (numeric) 2.153490769358279 absolute error 2.6645352591003757e-15 relative error 1.2373098120566266e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.0307963269999996 Order of pole (given) 0.0 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] 0.5500000000000004 y[1] (analytic) 2.159553305358981 y[1] (numeric) 2.1595533053589784 absolute error 2.6645352591003757e-15 relative error 1.2338362996126422e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.0207963269999998 Order of pole (given) 0.0 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] 0.5600000000000004 y[1] (analytic) 2.1657534360393846 y[1] (numeric) 2.1657534360393824 absolute error 2.220446049250313e-15 relative error 1.0252533886364034e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.0107963269999996 Order of pole (given) 0.0 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] 0.5700000000000004 y[1] (analytic) 2.172092878351663 y[1] (numeric) 2.1720928783516618 absolute error 1.3322676295501878e-15 relative error 6.133566583769688e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.0007963269999998 Order of pole (given) 0.0 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] 0.5800000000000004 y[1] (analytic) 2.17857340998226 y[1] (numeric) 2.178573409982259 absolute error 8.881784197001252e-16 relative error 4.0768808415198534e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9907963269999996 Order of pole (given) 0.0 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] 0.5900000000000004 y[1] (analytic) 2.1851968716324017 y[1] (numeric) 2.185196871632401 absolute error 8.881784197001252e-16 relative error 4.064523573277092e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9807963269999996 Order of pole (given) 0.0 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] 0.6000000000000004 y[1] (analytic) 2.1919651694194378 y[1] (numeric) 2.1919651694194373 absolute error 4.440892098500626e-16 relative error 2.0259866171490478e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9707963269999996 Order of pole (given) 0.0 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] 0.6100000000000004 y[1] (analytic) 2.198880277406405 y[1] (numeric) 2.198880277406404 absolute error 8.881784197001252e-16 relative error 4.039230461186082e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9607963269999996 Order of pole (given) 0.0 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] 0.6200000000000004 y[1] (analytic) 2.2059442402677547 y[1] (numeric) 2.205944240267754 absolute error 8.881784197001252e-16 relative error 4.0262958758754446e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9507963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9507958652431612 Order of pole (three term test) 1.1013541288958215e-05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y[1] (analytic) 2.2131591760997757 y[1] (numeric) 2.2131591760997757 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9407963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9407960023978882 Order of pole (three term test) 7.824152468602778e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y[1] (analytic) 2.220527279384879 y[1] (numeric) 2.2205272793848785 absolute error 4.440892098500626e-16 relative error 1.9999268370757522e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9307963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9307960992747653 Order of pole (three term test) 5.5473203694958394e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y[1] (analytic) 2.2280508241196166 y[1] (numeric) 2.2280508241196157 absolute error 8.881784197001252e-16 relative error 3.986347214727818e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9207963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.920796167565574 Order of pole (three term test) 3.924999155252422e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y[1] (analytic) 2.235732167117059 y[1] (numeric) 2.235732167117058 absolute error 8.881784197001252e-16 relative error 3.9726512538638166e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9107963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9107962156064824 Order of pole (three term test) 2.7712796391041795e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y[1] (analytic) 2.2435737514949814 y[1] (numeric) 2.2435737514949814 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9007963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9007962493306698 Order of pole (three term test) 1.9524444224241117e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y[1] (analytic) 2.251578110362207 y[1] (numeric) 2.251578110362207 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8907963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8907962729531081 Order of pole (three term test) 1.3724838394658572e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y[1] (analytic) 2.259747870716431 y[1] (numeric) 2.259747870716432 absolute error 8.881784197001252e-16 relative error 3.930431492866224e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8807963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8807962894626267 Order of pole (three term test) 9.625805671704156e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y[1] (analytic) 2.2680857575679316 y[1] (numeric) 2.268085757567932 absolute error 4.440892098500626e-16 relative error 1.957991263638371e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8707963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8707963009743299 Order of pole (three term test) 6.735028451615204e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y[1] (analytic) 2.2765945983047113 y[1] (numeric) 2.2765945983047122 absolute error 8.881784197001252e-16 relative error 3.901346424881778e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8607963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8607963089821093 Order of pole (three term test) 4.700932124052051e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7200000000000005 y[1] (analytic) 2.285277327315926 y[1] (numeric) 2.285277327315927 absolute error 8.881784197001252e-16 relative error 3.886523570175603e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8507963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.850796314538858 Order of pole (three term test) 3.272947044311004e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7300000000000005 y[1] (analytic) 2.294136990891822 y[1] (numeric) 2.2941369908918223 absolute error 4.440892098500626e-16 relative error 1.935757156670176e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8407963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8407963183850485 Order of pole (three term test) 2.2728667325434543e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7400000000000005 y[1] (analytic) 2.303176752419951 y[1] (numeric) 2.3031767524199513 absolute error 4.440892098500626e-16 relative error 1.9281594839972984e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8307963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8307963210403914 Order of pole (three term test) 1.5741704688856797e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7500000000000006 y[1] (analytic) 2.312399897899106 y[1] (numeric) 2.312399897899106 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8207963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8207963228686569 Order of pole (three term test) 1.0872811644602448e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7600000000000006 y[1] (analytic) 2.32180984179426 y[1] (numeric) 2.3218098417942596 absolute error 4.440892098500626e-16 relative error 1.9126855346038034e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8107963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8107963241240044 Order of pole (three term test) 7.488708965502951e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7700000000000006 y[1] (analytic) 2.3314101332578185 y[1] (numeric) 2.3314101332578177 absolute error 8.881784197001252e-16 relative error 3.809618938470601e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8007963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8007963249835183 Order of pole (three term test) 5.1429508541353335e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7800000000000006 y[1] (analytic) 2.341204462744726 y[1] (numeric) 2.341204462744725 absolute error 8.881784197001252e-16 relative error 3.7936815593579707e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7907963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7907963255703048 Order of pole (three term test) 3.5213825629408174e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7900000000000006 y[1] (analytic) 2.351196669051421 y[1] (numeric) 2.35119666905142 absolute error 1.3322676295501878e-15 relative error 5.6663385376761557e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7807963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7807963259696714 Order of pole (three term test) 2.4037059242205803e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y[1] (analytic) 2.3613907468113444 y[1] (numeric) 2.3613907468113426 absolute error 1.7763568394002505e-15 relative error 7.522502753087e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7707963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7707963262406597 Order of pole (three term test) 1.6355558752504304e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y[1] (analytic) 2.371790854482695 y[1] (numeric) 2.3717908544826933 absolute error 1.7763568394002505e-15 relative error 7.48951719770286e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7607963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7607963264239463 Order of pole (three term test) 1.109218738671669e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y[1] (analytic) 2.3824013228674414 y[1] (numeric) 2.382401322867439 absolute error 2.220446049250313e-15 relative error 9.320201545967075e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7507963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7507963265474851 Order of pole (three term test) 7.497766308329694e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8300000000000006 y[1] (analytic) 2.393226664204251 y[1] (numeric) 2.3932266642042483 absolute error 2.6645352591003757e-15 relative error 1.1133651897474303e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7407963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7407963266304927 Order of pole (three term test) 5.050202263125101e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y[1] (analytic) 2.4042715818820777 y[1] (numeric) 2.404271581882075 absolute error 2.6645352591003757e-15 relative error 1.1082505317533896e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7307963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7307963266860479 Order of pole (three term test) 3.3898153970056583e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y[1] (analytic) 2.4155409808256354 y[1] (numeric) 2.4155409808256323 absolute error 3.1086244689504383e-15 relative error 1.286926818309622e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7207963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7207963267231191 Order of pole (three term test) 2.2667137538906852e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y[1] (analytic) 2.427039978609021 y[1] (numeric) 2.4270399786090184 absolute error 2.6645352591003757e-15 relative error 1.097853880687811e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7107963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7107963267477574 Order of pole (three term test) 1.5097524938561957e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y[1] (analytic) 2.4387739173593155 y[1] (numeric) 2.4387739173593133 absolute error 2.220446049250313e-15 relative error 9.104763805472358e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7007963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.700796326764066 Order of pole (three term test) 1.0016606218122232e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y[1] (analytic) 2.4507483765182263 y[1] (numeric) 2.450748376518225 absolute error 1.3322676295501878e-15 relative error 5.436166529029545e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.6907963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6907963267748116 Order of pole (three term test) 6.621217912643122e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y[1] (analytic) 2.462969186536775 y[1] (numeric) 2.4629691865367724 absolute error 2.6645352591003757e-15 relative error 1.0818386497343989e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6807963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6807963267818851 Order of pole (three term test) 4.353293522027423e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y[1] (analytic) 2.4754424435858153 y[1] (numeric) 2.475442443585812 absolute error 3.552713678800501e-15 relative error 1.435183309555846e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6707963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6707963267864948 Order of pole (three term test) 2.854155232670969e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y[1] (analytic) 2.488174525373867 y[1] (numeric) 2.488174525373864 absolute error 3.1086244689504383e-15 relative error 1.2493594951838613e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6607963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6607963267894958 Order of pole (three term test) 1.8613280048577267e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y[1] (analytic) 2.501172108173523 y[1] (numeric) 2.50117210817352 absolute error 3.1086244689504383e-15 relative error 1.242867077716018e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6507963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6507963267914519 Order of pole (three term test) 1.206549705571506e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y[1] (analytic) 2.5144421851686616 y[1] (numeric) 2.514442185168658 absolute error 3.552713678800501e-15 relative error 1.4129231921720225e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6407963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6407963267926974 Order of pole (three term test) 7.814559304745372e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y[1] (analytic) 2.5279920862470626 y[1] (numeric) 2.5279920862470586 absolute error 3.9968028886505635e-15 relative error 1.581018750174977e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6307963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6307963267935018 Order of pole (three term test) 5.033651029699896e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y[1] (analytic) 2.5418294993769632 y[1] (numeric) 2.5418294993769592 absolute error 3.9968028886505635e-15 relative error 1.5724118748445691e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6207963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6207963267940191 Order of pole (three term test) 3.22765569994697e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y[1] (analytic) 2.555962493721842 y[1] (numeric) 2.555962493721838 absolute error 3.9968028886505635e-15 relative error 1.5637173465838515e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6107963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6107963267943408 Order of pole (three term test) 2.0756598930177894e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y[1] (analytic) 2.570399544665549 y[1] (numeric) 2.570399544665546 absolute error 3.1086244689504383e-15 relative error 1.209393487250606e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6007963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.60079632679455 Order of pole (three term test) 1.315189641037449e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y[1] (analytic) 2.5851495609401414 y[1] (numeric) 2.5851495609401383 absolute error 3.1086244689504383e-15 relative error 1.2024930843149845e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.5907963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5907963267946756 Order of pole (three term test) 8.578957455721484e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9900000000000008 y[1] (analytic) 2.6002219140717493 y[1] (numeric) 2.6002219140717466 absolute error 2.6645352591003757e-15 relative error 1.0247337908663021e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.5807963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5807963267947645 Order of pole (three term test) 5.215941123734067e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0000000000000007 y[1] (analytic) 2.6156264703860153 y[1] (numeric) 2.6156264703860135 absolute error 1.7763568394002505e-15 relative error 6.791324600481256e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5707963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5707963267948153 Order of pole (three term test) 3.1282943779388086e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0109999999999995 y[1] (analytic) 2.6329676013074854 y[1] (numeric) 2.632967601307485 absolute error 4.440892098500626e-16 relative error 1.6866489721694097e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5597963270000006 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5597963267948489 Order of pole (three term test) 2.0236164844020844e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0209999999999984 y[1] (analytic) 2.6491043018182907 y[1] (numeric) 2.6491043018182916 absolute error 8.881784197001252e-16 relative error 3.3527499052811845e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5497963270000017 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5497963267948637 Order of pole (three term test) 1.3944346996491517e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0309999999999973 y[1] (analytic) 2.665607330148701 y[1] (numeric) 2.665607330148703 absolute error 2.220446049250313e-15 relative error 8.329981779898713e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5397963270000028 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5397963267948807 Order of pole (three term test) 7.192363222487755e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0409999999999962 y[1] (analytic) 2.6824889814152275 y[1] (numeric) 2.682488981415231 absolute error 3.552713678800501e-15 relative error 1.3244094210318657e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.5297963270000039 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.529796326794892 Order of pole (three term test) 2.7049168253096264e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.050999999999995 y[1] (analytic) 2.6997622599819158 y[1] (numeric) 2.699762259981921 absolute error 5.329070518200751e-15 relative error 1.9739036274388279e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.519796327000005 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5197963267948943 Order of pole (three term test) 3.377468293951243e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.060999999999994 y[1] (analytic) 2.717440934425537 y[1] (numeric) 2.717440934425545 absolute error 7.993605777301127e-15 relative error 2.941593201175121e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.5097963270000061 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5097963267948947 Order of pole (three term test) 3.6853676421252904e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0709999999999928 y[1] (analytic) 2.735539597948169 y[1] (numeric) 2.7355395979481787 absolute error 9.769962616701378e-15 relative error 3.5714937645316776e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4997963270000072 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4997963267948971 Order of pole (three term test) 1.4815396831962834e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0809999999999917 y[1] (analytic) 2.7540737348978195 y[1] (numeric) 2.754073734897831 absolute error 1.1546319456101628e-14 relative error 4.1924510988192607e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4897963270000083 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4897963267948961 Order of pole (three term test) 3.5083093046895456e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0909999999999906 y[1] (analytic) 2.7730597941531556 y[1] (numeric) 2.7730597941531694 absolute error 1.3766765505351941e-14 relative error 4.96446760159244e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4797963270000094 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4797963267948984 Order of pole (three term test) 3.6221862344844596e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1009999999999895 y[1] (analytic) 2.792515270239914 y[1] (numeric) 2.792515270239929 absolute error 1.509903313490213e-14 relative error 5.406965288897032e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4697963270000105 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.46979632679490346 Order of pole (three term test) 1.3746587016766762e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1109999999999884 y[1] (analytic) 2.8124587931772473 y[1] (numeric) 2.8124587931772647 absolute error 1.7319479184152442e-14 relative error 6.158127267915115e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4597963270000116 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.45979632679489907 Order of pole (three term test) 5.109346957161507e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1209999999999873 y[1] (analytic) 2.8329102282059897 y[1] (numeric) 2.832910228206009 absolute error 1.9095836023552692e-14 relative error 6.740713430811961e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4497963270000127 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4497963267949112 Order of pole (three term test) 7.43265731307243e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1309999999999862 y[1] (analytic) 2.8538907867321233 y[1] (numeric) 2.853890786732145 absolute error 2.1760371282653068e-14 relative error 7.624808694088117e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4397963270000138 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.43979632679490827 Order of pole (three term test) 1.0569294332353908e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1409999999999851 y[1] (analytic) 2.8754231500335132 y[1] (numeric) 2.875423150033538 absolute error 2.4868995751603507e-14 relative error 8.648812523928402e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4297963270000149 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.42979632679491087 Order of pole (three term test) 7.338151399401004e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.150999999999984 y[1] (analytic) 2.897531607533112 y[1] (numeric) 2.897531607533139 absolute error 2.708944180085382e-14 relative error 9.349144537517957e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.419796327000016 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.41979632679491025 Order of pole (three term test) 1.9877861023527151e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.160999999999983 y[1] (analytic) 2.9202422117462765 y[1] (numeric) 2.9202422117463063 absolute error 2.9753977059954195e-14 relative error 1.0188873012064847e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.4097963270000171 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4097963267949107 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1709999999999818 y[1] (analytic) 2.9435829523744457 y[1] (numeric) 2.943582952374477 absolute error 3.1530333899354446e-14 relative error 1.0711549295364838e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3997963270000182 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.39979632679491034 Order of pole (three term test) 3.3674196566539095e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1809999999999807 y[1] (analytic) 2.9675839524559287 y[1] (numeric) 2.967583952455963 absolute error 3.419486915845482e-14 relative error 1.1522797570783348e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3897963270000193 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.38979632679491405 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1909999999999796 y[1] (analytic) 2.992277690014306 y[1] (numeric) 2.9922776900143435 absolute error 3.730349362740526e-14 relative error 1.2466588161885106e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3797963270000204 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3797963267949104 Order of pole (three term test) 3.8126652112612337e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2009999999999785 y[1] (analytic) 3.0176992492877788 y[1] (numeric) 3.0176992492878187 absolute error 3.9968028886505635e-14 relative error 1.3244536842410215e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3697963270000215 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.36979632679491914 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2109999999999774 y[1] (analytic) 3.043886606406725 y[1] (numeric) 3.043886606406768 absolute error 4.3076653355456074e-14 relative error 1.4151858766614042e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3597963270000226 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.35979632679492 Order of pole (three term test) 8.442514203249971e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2209999999999763 y[1] (analytic) 3.0708809553474636 y[1] (numeric) 3.07088095534751 absolute error 4.618527782440651e-14 relative error 1.503974868969831e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3497963270000237 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.349796326794919 Order of pole (three term test) 9.234718954125141e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2309999999999752 y[1] (analytic) 3.0987270811740393 y[1] (numeric) 3.0987270811740877 absolute error 4.8405723873656825e-14 relative error 1.5621163983023947e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3397963270000248 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.33979632679492233 Order of pole (three term test) 9.728406122063428e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2409999999999741 y[1] (analytic) 3.12747378904666 y[1] (numeric) 3.127473789046711 absolute error 5.062616992290714e-14 relative error 1.6187560100492284e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3297963270000259 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.32979632679492327 Order of pole (three term test) 9.848041435693367e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.250999999999973 y[1] (analytic) 3.157174399303809 y[1] (numeric) 3.157174399303863 absolute error 5.3734794391857577e-14 relative error 1.7019900580628892e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.319796327000027 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3197963267949238 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.260999999999972 y[1] (analytic) 3.1878873212183434 y[1] (numeric) 3.1878873212184016 absolute error 5.81756864903582e-14 relative error 1.8248978281994195e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3097963270000281 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3097963267949212 Order of pole (three term test) 2.659449802630272e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2709999999999708 y[1] (analytic) 3.2196767209236077 y[1] (numeric) 3.219676720923669 absolute error 6.128431095930864e-14 relative error 1.9034305699402146e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.29979632700002923 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2997963267949254 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2809999999999697 y[1] (analytic) 3.252613302687653 y[1] (numeric) 3.2526133026877173 absolute error 6.439293542825908e-14 relative error 1.979729203439303e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.28979632700003033 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.28979632679492595 Order of pole (three term test) 1.3169967054702847e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2909999999999686 y[1] (analytic) 3.286775227430942 y[1] (numeric) 3.286775227431011 absolute error 6.88338275267597e-14 relative error 2.0942663481300064e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.27979632700003143 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.27979632679492494 Order of pole (three term test) 3.142143532104182e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3009999999999675 y[1] (analytic) 3.3222491984746414 y[1] (numeric) 3.3222491984747142 absolute error 7.283063041541027e-14 relative error 2.1922085329676447e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.26979632700003253 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2697963267949301 Order of pole (three term test) 1.570796226542241e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3109999999999664 y[1] (analytic) 3.359131752440537 y[1] (numeric) 3.359131752440614 absolute error 7.682743330406083e-14 relative error 2.287121761396908e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.25979632700003363 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2597963267949296 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3209999999999653 y[1] (analytic) 3.3975308036510983 y[1] (numeric) 3.39753080365118 absolute error 8.171241461241152e-14 relative error 2.4050529438791452e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.24979632700003473 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24979632679492922 Order of pole (three term test) 1.454020505928397e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3309999999999642 y[1] (analytic) 3.437567504217098 y[1] (numeric) 3.437567504217184 absolute error 8.615330671091215e-14 relative error 2.5062287971137156e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.23979632700003584 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23979632679493235 Order of pole (three term test) 8.880318238351848e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.340999999999963 y[1] (analytic) 3.4793785005598505 y[1] (numeric) 3.479378500559941 absolute error 9.059419880941277e-14 relative error 2.6037465827542384e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.22979632700003694 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.22979632679493306 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.350999999999962 y[1] (analytic) 3.523118692288129 y[1] (numeric) 3.5231186922882243 absolute error 9.547918011776346e-14 relative error 2.7100756022430072e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.21979632700003804 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.21979632679493127 Order of pole (three term test) 4.138586900925603e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.360999999999961 y[1] (analytic) 3.5689646339113597 y[1] (numeric) 3.5689646339114613 absolute error 1.0169642905566434e-13 relative error 2.8494658671977784e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.20979632700003914 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.20979632679493748 Order of pole (three term test) 1.9439037708794291e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3709999999999598 y[1] (analytic) 3.61711876795355 y[1] (numeric) 3.6171187679536567 absolute error 1.0658141036401503e-13 relative error 2.946583101121542e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.19979632700004024 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.19979632679493756 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3809999999999587 y[1] (analytic) 3.6678147458948995 y[1] (numeric) 3.6678147458950114 absolute error 1.1191048088221578e-13 relative error 3.0511486712208816e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.18979632700004134 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.18979632679493832 Order of pole (three term test) 1.2399129435442947e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3909999999999576 y[1] (analytic) 3.7213241906626253 y[1] (numeric) 3.721324190662744 absolute error 1.1857181902996672e-13 relative error 3.1862802850523384e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.17979632700004244 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.17979632679493657 Order of pole (three term test) 2.467635331902391e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4009999999999565 y[1] (analytic) 3.7779653963066835 y[1] (numeric) 3.7779653963068087 absolute error 1.2523315717771766e-13 relative error 3.3148307102056796e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.16979632700004355 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.16979632679493986 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4109999999999554 y[1] (analytic) 3.8381146714576984 y[1] (numeric) 3.8381146714578303 absolute error 1.318944953254686e-13 relative error 3.4364396745701105e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.15979632700004465 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1597963267949411 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4209999999999543 y[1] (analytic) 3.902221353428768 y[1] (numeric) 3.9022213534289065 absolute error 1.3855583347321954e-13 relative error 3.5506912838625767e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.14979632700004575 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.14979632679494204 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4309999999999532 y[1] (analytic) 3.970828017539234 y[1] (numeric) 3.9708280175393798 absolute error 1.4566126083082054e-13 relative error 3.6682843021010115e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.13979632700004685 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.13979632679494133 Order of pole (three term test) 3.038633999457949e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.440999999999952 y[1] (analytic) 4.044598200305071 y[1] (numeric) 4.0445982003052245 absolute error 1.5365486660812167e-13 relative error 3.799014364307732e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.12979632700004795 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1297963267949429 Order of pole (three term test) 2.133057880005887e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.450999999999951 y[1] (analytic) 4.124355260143009 y[1] (numeric) 4.124355260143171 absolute error 1.6253665080512292e-13 relative error 3.940898408433591e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.11979632700004905 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11979632679494479 Order of pole (three term test) 2.5619724927679074e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.46099999999995 y[1] (analytic) 4.2111382176271075 y[1] (numeric) 4.211138217627281 absolute error 1.7319479184152442e-13 relative error 4.112778609748797e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.10979632700005015 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10979632679494716 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4709999999999488 y[1] (analytic) 4.306284337869535 y[1] (numeric) 4.3062843378697195 absolute error 1.8474111129762605e-13 relative error 4.290035139412641e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.09979632700005125 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09979632679494801 Order of pole (three term test) 7.846602783903249e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4809999999999477 y[1] (analytic) 4.411555466912819 y[1] (numeric) 4.411555466913015 absolute error 1.9539925233402755e-13 relative error 4.429259788288841e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.08979632700005236 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.08979632679494796 Order of pole (three term test) 2.34227345291987e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4909999999999466 y[1] (analytic) 4.529339273357407 y[1] (numeric) 4.529339273357615 absolute error 2.078337502098293e-13 relative error 4.5886107810990044e-12% Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.07979632700005346 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.07979632679495043 Order of pole (three term test) 8.751357305822811e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; Iterations 1501 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 9 Minutes 59.0 Seconds Percent Done 100.13333333332969%