##############ECHO OF PROBLEM################# ##############temp/h5h3postode.ode################# diff ( y , x , 5 ) = m1 * diff ( y , x , 3) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=64; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=1.5 ## ## Trouble about Pi/2 ## $array_y_init[0 + 1] = exact_soln_y(x_start) $array_y_init[1 + 1] = exact_soln_yp(x_start) $array_y_init[2 + 1] = exact_soln_ypp(x_start) $array_y_init[3 + 1] = exact_soln_yppp(x_start) $array_y_init[4 + 1] = exact_soln_ypppp(x_start) $glob_look_poles=true $glob_display_interval=0.1 $glob_max_minutes=2 $glob_desired_digits_correct=10 #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(cos(x)) end def exact_soln_yp (x) return(-sin(x)) end def exact_soln_ypp (x) return(-cos(x)) end def exact_soln_yppp (x) return(sin(x)) end def exact_soln_ypppp (x) return(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 desired_abs_gbl_error 1.0e-10 range 1.4 estimated_steps 1400000.0 step_error 7.142857142857143e-17 est_needed_step_err 7.142857142857143e-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 2.4672086055323005e-183 estimated_step_error 2.4672086055323005e-183 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.655715664606565e-175 estimated_step_error 1.655715664606565e-175 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 1.111131969458435e-167 estimated_step_error 1.111131969458435e-167 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 7.456680367024182e-160 estimated_step_error 7.456680367024182e-160 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 5.004093412037814e-152 estimated_step_error 5.004093412037814e-152 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 3.3581901424816223e-144 estimated_step_error 3.3581901424816223e-144 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 2.2536431215809188e-136 estimated_step_error 2.2536431215809188e-136 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 1.512394117654306e-128 estimated_step_error 1.512394117654306e-128 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 1.014950270158055e-120 estimated_step_error 1.014950270158055e-120 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 6.811212724408104e-113 estimated_step_error 6.811212724408104e-113 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 4.5709231343600224e-105 estimated_step_error 4.5709231343600224e-105 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 3.06748875023402e-97 estimated_step_error 3.06748875023402e-97 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 2.0585490116180894e-89 estimated_step_error 2.0585490116180894e-89 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 1.3814583197402437e-81 estimated_step_error 1.3814583197402437e-81 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 9.2706681184281e-74 estimated_step_error 9.2706681184281e-74 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 6.221249002016112e-66 estimated_step_error 6.221249002016112e-66 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 4.174750875079239e-58 estimated_step_error 4.174750875079239e-58 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 2.801274754399601e-50 estimated_step_error 2.801274754399601e-50 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (analytic) 0.9950041652780258 y[1] (numeric) 0.9950041652780258 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11 y[1] (analytic) 0.9939560979566968 y[1] (numeric) 0.9939560979566969 absolute error 1.1102230246251565e-16 relative error 1.1169739054948934e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12 y[1] (analytic) 0.9928086358538663 y[1] (numeric) 0.9928086358538664 absolute error 1.1102230246251565e-16 relative error 1.1182648745498752e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.13 y[1] (analytic) 0.9915618937147881 y[1] (numeric) 0.9915618937147882 absolute error 1.1102230246251565e-16 relative error 1.1196709269108925e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.14 y[1] (analytic) 0.9902159962126371 y[1] (numeric) 0.9902159962126373 absolute error 2.220446049250313e-16 relative error 2.242385558042933e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15000000000000002 y[1] (analytic) 0.9887710779360422 y[1] (numeric) 0.9887710779360425 absolute error 2.220446049250313e-16 relative error 2.2456624175185883e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16000000000000003 y[1] (analytic) 0.9872272833756269 y[1] (numeric) 0.9872272833756272 absolute error 2.220446049250313e-16 relative error 2.249174112832397e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17000000000000004 y[1] (analytic) 0.9855847669095607 y[1] (numeric) 0.9855847669095609 absolute error 2.220446049250313e-16 relative error 2.2529224515237114e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000005 y[1] (analytic) 0.9838436927881214 y[1] (numeric) 0.9838436927881216 absolute error 1.1102230246251565e-16 relative error 1.1284546851938319e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000006 y[1] (analytic) 0.9820042351172703 y[1] (numeric) 0.9820042351172704 absolute error 1.1102230246251565e-16 relative error 1.1305684689766887e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20000000000000007 y[1] (analytic) 0.9800665778412416 y[1] (numeric) 0.9800665778412417 absolute error 1.1102230246251565e-16 relative error 1.1328036785731495e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.21000000000000008 y[1] (analytic) 0.9780309147241483 y[1] (numeric) 0.9780309147241484 absolute error 1.1102230246251565e-16 relative error 1.1351614840705652e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.22000000000000008 y[1] (analytic) 0.9758974493306055 y[1] (numeric) 0.9758974493306056 absolute error 1.1102230246251565e-16 relative error 1.137643125706178e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2300000000000001 y[1] (analytic) 0.9736663950053748 y[1] (numeric) 0.973666395005375 absolute error 2.220446049250313e-16 relative error 2.280499830989911e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2400000000000001 y[1] (analytic) 0.9713379748520296 y[1] (numeric) 0.9713379748520298 absolute error 2.220446049250313e-16 relative error 2.2859664779281058e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y[1] (analytic) 0.9689124217106447 y[1] (numeric) 0.968912421710645 absolute error 2.220446049250313e-16 relative error 2.2916891139965438e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y[1] (analytic) 0.9663899781345132 y[1] (numeric) 0.9663899781345134 absolute error 2.220446049250313e-16 relative error 2.2976708156024005e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (analytic) 0.9637708963658905 y[1] (numeric) 0.9637708963658908 absolute error 2.220446049250313e-16 relative error 2.3039148179541338e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (analytic) 0.9610554383107709 y[1] (numeric) 0.9610554383107712 absolute error 3.3306690738754696e-16 relative error 3.4656367792161125e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y[1] (analytic) 0.9582438755126971 y[1] (numeric) 0.9582438755126974 absolute error 3.3306690738754696e-16 relative error 3.4758052297422036e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y[1] (analytic) 0.955336489125606 y[1] (numeric) 0.9553364891256062 absolute error 2.220446049250313e-16 relative error 2.3242554581816802e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y[1] (analytic) 0.9523335698857134 y[1] (numeric) 0.9523335698857136 absolute error 2.220446049250313e-16 relative error 2.3315843518115003e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y[1] (analytic) 0.9492354180824408 y[1] (numeric) 0.949235418082441 absolute error 2.220446049250313e-16 relative error 2.3391942683047546e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y[1] (analytic) 0.9460423435283869 y[1] (numeric) 0.9460423435283871 absolute error 2.220446049250313e-16 relative error 2.347089498096748e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y[1] (analytic) 0.9427546655283462 y[1] (numeric) 0.9427546655283464 absolute error 2.220446049250313e-16 relative error 2.3552745273404854e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y[1] (analytic) 0.9393727128473789 y[1] (numeric) 0.9393727128473791 absolute error 2.220446049250313e-16 relative error 2.3637540444620856e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y[1] (analytic) 0.9358968236779348 y[1] (numeric) 0.935896823677935 absolute error 2.220446049250313e-16 relative error 2.3725329470873632e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y[1] (analytic) 0.9323273456060344 y[1] (numeric) 0.9323273456060346 absolute error 2.220446049250313e-16 relative error 2.3816163493595392e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y[1] (analytic) 0.9286646355765101 y[1] (numeric) 0.9286646355765104 absolute error 2.220446049250313e-16 relative error 2.3910095896694418e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y[1] (analytic) 0.924909059857313 y[1] (numeric) 0.9249090598573132 absolute error 2.220446049250313e-16 relative error 2.4007182388210842e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y[1] (analytic) 0.921060994002885 y[1] (numeric) 0.9210609940028852 absolute error 2.220446049250313e-16 relative error 2.4107481086571322e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y[1] (analytic) 0.917120822816605 y[1] (numeric) 0.9171208228166052 absolute error 2.220446049250313e-16 relative error 2.421105261170514e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y[1] (analytic) 0.9130889403123081 y[1] (numeric) 0.9130889403123084 absolute error 2.220446049250313e-16 relative error 2.4317960181303295e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y[1] (analytic) 0.908965749674885 y[1] (numeric) 0.9089657496748852 absolute error 2.220446049250313e-16 relative error 2.4428269712522314e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y[1] (analytic) 0.9047516632199633 y[1] (numeric) 0.9047516632199635 absolute error 2.220446049250313e-16 relative error 2.454204992945648e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y[1] (analytic) 0.9004471023526768 y[1] (numeric) 0.900447102352677 absolute error 2.220446049250313e-16 relative error 2.4659372476725838e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y[1] (analytic) 0.8960524975255251 y[1] (numeric) 0.8960524975255253 absolute error 2.220446049250313e-16 relative error 2.4780312039552808e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y[1] (analytic) 0.8915682881953289 y[1] (numeric) 0.891568288195329 absolute error 1.1102230246251565e-16 relative error 1.2452473235363927e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y[1] (analytic) 0.886994922779284 y[1] (numeric) 0.8869949227792843 absolute error 2.220446049250313e-16 relative error 2.5033356924894588e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y[1] (analytic) 0.8823328586101213 y[1] (numeric) 0.8823328586101216 absolute error 2.220446049250313e-16 relative error 2.5165628000616798e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5000000000000003 y[1] (analytic) 0.8775825618903725 y[1] (numeric) 0.8775825618903728 absolute error 2.220446049250313e-16 relative error 2.530184789072519e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5100000000000003 y[1] (analytic) 0.8727445076457511 y[1] (numeric) 0.8727445076457513 absolute error 2.220446049250313e-16 relative error 2.5442108541479325e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5200000000000004 y[1] (analytic) 0.8678191796776498 y[1] (numeric) 0.8678191796776499 absolute error 1.1102230246251565e-16 relative error 1.2793252910560785e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y[1] (analytic) 0.8628070705147608 y[1] (numeric) 0.862807070514761 absolute error 2.220446049250313e-16 relative error 2.5735139698444625e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5400000000000004 y[1] (analytic) 0.8577086813638239 y[1] (numeric) 0.8577086813638242 absolute error 2.220446049250313e-16 relative error 2.588811443204271e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y[1] (analytic) 0.8525245220595056 y[1] (numeric) 0.8525245220595058 absolute error 2.220446049250313e-16 relative error 2.6045538770969542e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5600000000000004 y[1] (analytic) 0.8472551110134159 y[1] (numeric) 0.8472551110134162 absolute error 3.3306690738754696e-16 relative error 3.931128925137555e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y[1] (analytic) 0.8419009751622685 y[1] (numeric) 0.8419009751622688 absolute error 3.3306690738754696e-16 relative error 3.956129250513713e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5800000000000004 y[1] (analytic) 0.8364626499151867 y[1] (numeric) 0.836462649915187 absolute error 3.3306690738754696e-16 relative error 3.9818503243548093e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y[1] (analytic) 0.8309406791001632 y[1] (numeric) 0.8309406791001636 absolute error 3.3306690738754696e-16 relative error 4.00831149280391e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6000000000000004 y[1] (analytic) 0.8253356149096781 y[1] (numeric) 0.8253356149096783 absolute error 2.220446049250313e-16 relative error 2.69035530411869e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6100000000000004 y[1] (analytic) 0.8196480178454792 y[1] (numeric) 0.8196480178454796 absolute error 3.3306690738754696e-16 relative error 4.063535812153175e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6200000000000004 y[1] (analytic) 0.8138784566625337 y[1] (numeric) 0.813878456662534 absolute error 3.3306690738754696e-16 relative error 4.0923421017107686e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y[1] (analytic) 0.8080275083121516 y[1] (numeric) 0.808027508312152 absolute error 3.3306690738754696e-16 relative error 4.1219748580499915e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 11.665835667855504 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y[1] (analytic) 0.8020957578842923 y[1] (numeric) 0.8020957578842928 absolute error 4.440892098500626e-16 relative error 5.5366108782503427e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 11.912701155535418 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y[1] (analytic) 0.7960837985490555 y[1] (numeric) 0.796083798549056 absolute error 4.440892098500626e-16 relative error 5.5784229079835664e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.163270386138818 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y[1] (analytic) 0.7899922314973647 y[1] (numeric) 0.7899922314973652 absolute error 4.440892098500626e-16 relative error 5.621437681840597e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.417678605498601 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y[1] (analytic) 0.783821665880849 y[1] (numeric) 0.7838216658808493 absolute error 3.3306690738754696e-16 relative error 4.2492689585615184e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.6760667956521 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y[1] (analytic) 0.7775727187509276 y[1] (numeric) 0.777572718750928 absolute error 4.440892098500626e-16 relative error 5.711224161303343e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.938582002281041 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y[1] (analytic) 0.7712460149971063 y[1] (numeric) 0.7712460149971067 absolute error 3.3306690738754696e-16 relative error 4.3185559589412806e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.205377684304404 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y[1] (analytic) 0.764842187284488 y[1] (numeric) 0.7648421872844885 absolute error 4.440892098500626e-16 relative error 5.806285495662398e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.476614087409258 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y[1] (analytic) 0.7583618759905079 y[1] (numeric) 0.7583618759905082 absolute error 3.3306690738754696e-16 relative error 4.391925780189349e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.75245864347105 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7200000000000005 y[1] (analytic) 0.7518057291408946 y[1] (numeric) 0.751805729140895 absolute error 4.440892098500626e-16 relative error 5.90696761991337e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.033086397997346 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7300000000000005 y[1] (analytic) 0.74517440234487 y[1] (numeric) 0.7451744023448704 absolute error 4.440892098500626e-16 relative error 5.95953388163401e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.318680467933017 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7400000000000005 y[1] (analytic) 0.7384685587295875 y[1] (numeric) 0.7384685587295879 absolute error 4.440892098500626e-16 relative error 6.013650880601394e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.609432532388803 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7500000000000006 y[1] (analytic) 0.7316888688738205 y[1] (numeric) 0.7316888688738209 absolute error 4.440892098500626e-16 relative error 6.069372225568812e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.905543359105149 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7600000000000006 y[1] (analytic) 0.7248360107409048 y[1] (numeric) 0.7248360107409052 absolute error 4.440892098500626e-16 relative error 6.126754235018325e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.207223369740847 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7700000000000006 y[1] (analytic) 0.717910669610943 y[1] (numeric) 0.7179106696109434 absolute error 4.440892098500626e-16 relative error 6.185856105060086e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.469206910711575 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7800000000000006 y[1] (analytic) 0.710913538012277 y[1] (numeric) 0.7109135380122774 absolute error 4.440892098500626e-16 relative error 6.246740090106338e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.162825441853833 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7900000000000006 y[1] (analytic) 0.7038453156522356 y[1] (numeric) 0.7038453156522362 absolute error 5.551115123125783e-16 relative error 7.886839621830409e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.862576333113338 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y[1] (analytic) 0.6967067093471649 y[1] (numeric) 0.6967067093471655 absolute error 5.551115123125783e-16 relative error 7.967649871388987e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.568219009757115 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y[1] (analytic) 0.6894984329517466 y[1] (numeric) 0.6894984329517471 absolute error 4.440892098500626e-16 relative error 6.44075734804667e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.279524559122938 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y[1] (analytic) 0.6822212072876132 y[1] (numeric) 0.6822212072876136 absolute error 4.440892098500626e-16 relative error 6.50946064276835e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.996275015528227 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8300000000000006 y[1] (analytic) 0.6748757600712666 y[1] (numeric) 0.6748757600712672 absolute error 5.551115123125783e-16 relative error 8.22538821447608e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.71826269676305 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y[1] (analytic) 0.6674628258413077 y[1] (numeric) 0.6674628258413081 absolute error 4.440892098500626e-16 relative error 6.653392408638004e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.445289587865162 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y[1] (analytic) 0.6599831458849816 y[1] (numeric) 0.6599831458849822 absolute error 5.551115123125783e-16 relative error 8.41099527728425e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.17716676828019 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y[1] (analytic) 0.6524374681640513 y[1] (numeric) 0.6524374681640519 absolute error 5.551115123125783e-16 relative error 8.50827151105612e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.913713878872148 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y[1] (analytic) 0.6448265472400007 y[1] (numeric) 0.6448265472400012 absolute error 5.551115123125783e-16 relative error 8.608695077592223e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.654758625574924 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y[1] (analytic) 0.6371511441985797 y[1] (numeric) 0.6371511441985802 absolute error 5.551115123125783e-16 relative error 8.712399206483537e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.400136316766108 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y[1] (analytic) 0.6294120265736963 y[1] (numeric) 0.6294120265736969 absolute error 5.551115123125783e-16 relative error 8.819525030915208e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.149689431707928 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y[1] (analytic) 0.621609968270664 y[1] (numeric) 0.6216099682706645 absolute error 5.551115123125783e-16 relative error 8.930222175440877e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 11.903267217634768 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y[1] (analytic) 0.613745749488811 y[1] (numeric) 0.6137457494888116 absolute error 5.551115123125783e-16 relative error 9.04464939716374e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 11.66072531328044 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y[1] (analytic) 0.6058201566434622 y[1] (numeric) 0.6058201566434629 absolute error 6.661338147750939e-16 relative error 1.099557034328139e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 11.421925396829359 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y[1] (analytic) 0.5978339822872977 y[1] (numeric) 0.5978339822872983 absolute error 6.661338147750939e-16 relative error 1.1142454837151993e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 11.186734856449434 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y[1] (analytic) 0.5897880250310976 y[1] (numeric) 0.5897880250310983 absolute error 6.661338147750939e-16 relative error 1.1294461509963191e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 10.955026481721179 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y[1] (analytic) 0.5816830894638829 y[1] (numeric) 0.5816830894638836 absolute error 6.661338147750939e-16 relative error 1.145183394258627e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y[1] (analytic) 0.573519986072456 y[1] (numeric) 0.5735199860724568 absolute error 7.771561172376096e-16 relative error 1.3550637050326385e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y[1] (analytic) 0.5652995311603537 y[1] (numeric) 0.5652995311603545 absolute error 7.771561172376096e-16 relative error 1.3747687277263288e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y[1] (analytic) 0.5570225467662167 y[1] (numeric) 0.5570225467662174 absolute error 7.771561172376096e-16 relative error 1.3951968762294703e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9900000000000008 y[1] (analytic) 0.548689860581587 y[1] (numeric) 0.5486898605815878 absolute error 7.771561172376096e-16 relative error 1.416385052958439e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0000000000000007 y[1] (analytic) 0.5403023058681392 y[1] (numeric) 0.5403023058681399 absolute error 6.661338147750939e-16 relative error 1.2328909344644994e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0100000000000007 y[1] (analytic) 0.5318607213743549 y[1] (numeric) 0.5318607213743556 absolute error 6.661338147750939e-16 relative error 1.2524591269943202e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0200000000000007 y[1] (analytic) 0.523365951251649 y[1] (numeric) 0.5233659512516496 absolute error 6.661338147750939e-16 relative error 1.27278783264752e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0300000000000007 y[1] (analytic) 0.5148188449699548 y[1] (numeric) 0.5148188449699554 absolute error 6.661338147750939e-16 relative error 1.2939188634673425e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0400000000000007 y[1] (analytic) 0.5062202572327777 y[1] (numeric) 0.5062202572327785 absolute error 7.771561172376096e-16 relative error 1.5352133900881134e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0500000000000007 y[1] (analytic) 0.49757104789172635 y[1] (numeric) 0.4975710478917271 absolute error 7.771561172376096e-16 relative error 1.5618997940706593e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0600000000000007 y[1] (analytic) 0.48887208186052694 y[1] (numeric) 0.4888720818605277 absolute error 7.771561172376096e-16 relative error 1.5896921629886175e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0700000000000007 y[1] (analytic) 0.48012422902853347 y[1] (numeric) 0.4801242290285343 absolute error 8.326672684688674e-16 relative error 1.734274627534747e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0800000000000007 y[1] (analytic) 0.47132836417373936 y[1] (numeric) 0.4713283641737402 absolute error 8.326672684688674e-16 relative error 1.766639421178422e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0900000000000007 y[1] (analytic) 0.46248536687530023 y[1] (numeric) 0.46248536687530106 absolute error 8.326672684688674e-16 relative error 1.800418625338646e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1000000000000008 y[1] (analytic) 0.4535961214255767 y[1] (numeric) 0.4535961214255776 absolute error 8.881784197001252e-16 relative error 1.9580820420349476e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1100000000000008 y[1] (analytic) 0.4446615167417062 y[1] (numeric) 0.44466151674170706 absolute error 8.881784197001252e-16 relative error 1.997425876222268e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1200000000000008 y[1] (analytic) 0.4356824462767115 y[1] (numeric) 0.4356824462767124 absolute error 8.881784197001252e-16 relative error 2.0385912429807273e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1300000000000008 y[1] (analytic) 0.4266598079301566 y[1] (numeric) 0.4266598079301575 absolute error 8.881784197001252e-16 relative error 2.081701634866714e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1400000000000008 y[1] (analytic) 0.4175945039583574 y[1] (numeric) 0.4175945039583583 absolute error 8.881784197001252e-16 relative error 2.1268920239158478e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1500000000000008 y[1] (analytic) 0.40848744088415656 y[1] (numeric) 0.4084874408841575 absolute error 9.43689570931383e-16 relative error 2.310204614586927e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1600000000000008 y[1] (analytic) 0.39933952940627243 y[1] (numeric) 0.3993395294062734 absolute error 9.43689570931383e-16 relative error 2.3631258651865396e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1700000000000008 y[1] (analytic) 0.39015168430822944 y[1] (numeric) 0.39015168430823044 absolute error 9.992007221626409e-16 relative error 2.561057051270469e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1800000000000008 y[1] (analytic) 0.380924824366881 y[1] (numeric) 0.380924824366882 absolute error 9.992007221626409e-16 relative error 2.623091639730674e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1900000000000008 y[1] (analytic) 0.37165987226053215 y[1] (numeric) 0.3716598722605332 absolute error 1.0547118733938987e-15 relative error 2.8378416722226866e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2000000000000008 y[1] (analytic) 0.3623577544766728 y[1] (numeric) 0.36235775447667384 absolute error 1.0547118733938987e-15 relative error 2.9106921553731976e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2100000000000009 y[1] (analytic) 0.35301940121932956 y[1] (numeric) 0.3530194012193306 absolute error 1.0547118733938987e-15 relative error 2.98768812634921e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2200000000000009 y[1] (analytic) 0.3436457463160462 y[1] (numeric) 0.3436457463160473 absolute error 1.0547118733938987e-15 relative error 3.0691835551600133e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2300000000000009 y[1] (analytic) 0.3342377271245018 y[1] (numeric) 0.33423772712450284 absolute error 1.0547118733938987e-15 relative error 3.155573975648249e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2400000000000009 y[1] (analytic) 0.3247962844387754 y[1] (numeric) 0.32479628443877645 absolute error 1.0547118733938987e-15 relative error 3.247302767691339e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2500000000000009 y[1] (analytic) 0.31532236239526784 y[1] (numeric) 0.3153223623952689 absolute error 1.0547118733938987e-15 relative error 3.3448686143984287e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.260000000000001 y[1] (analytic) 0.30581690837828845 y[1] (numeric) 0.30581690837828956 absolute error 1.1102230246251565e-15 relative error 3.630351998888944e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.270000000000001 y[1] (analytic) 0.29628087292531785 y[1] (numeric) 0.29628087292531896 absolute error 1.1102230246251565e-15 relative error 3.7471977642816157e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.280000000000001 y[1] (analytic) 0.2867152096319546 y[1] (numeric) 0.28671520963195574 absolute error 1.1102230246251565e-15 relative error 3.8722153109711463e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.290000000000001 y[1] (analytic) 0.27712087505655675 y[1] (numeric) 0.27712087505655786 absolute error 1.1102230246251565e-15 relative error 4.0062771323112146e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.300000000000001 y[1] (analytic) 0.2674988286245865 y[1] (numeric) 0.2674988286245876 absolute error 1.1102230246251565e-15 relative error 4.1503846216211544e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.310000000000001 y[1] (analytic) 0.25785003253266875 y[1] (numeric) 0.25785003253266986 absolute error 1.1102230246251565e-15 relative error 4.3056927847565616e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.320000000000001 y[1] (analytic) 0.24817545165237204 y[1] (numeric) 0.24817545165237315 absolute error 1.1102230246251565e-15 relative error 4.473540864872826e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.330000000000001 y[1] (analytic) 0.23847605343372227 y[1] (numeric) 0.23847605343372338 absolute error 1.1102230246251565e-15 relative error 4.655490598068421e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.340000000000001 y[1] (analytic) 0.22875280780845852 y[1] (numeric) 0.22875280780845964 absolute error 1.1102230246251565e-15 relative error 4.853374414336278e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.350000000000001 y[1] (analytic) 0.21900668709304064 y[1] (numeric) 0.21900668709304175 absolute error 1.1102230246251565e-15 relative error 5.069356736826489e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.360000000000001 y[1] (analytic) 0.2092386658914184 y[1] (numeric) 0.2092386658914195 absolute error 1.1102230246251565e-15 relative error 5.306012729030168e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.370000000000001 y[1] (analytic) 0.199449720997572 y[1] (numeric) 0.19944972099757313 absolute error 1.1379786002407855e-15 relative error 5.705591336749169e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.380000000000001 y[1] (analytic) 0.18964083129783338 y[1] (numeric) 0.18964083129783452 absolute error 1.1379786002407855e-15 relative error 6.000704555305262e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.390000000000001 y[1] (analytic) 0.17981297767299848 y[1] (numeric) 0.17981297767299964 absolute error 1.1657341758564144e-15 relative error 6.483036936168074e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.400000000000001 y[1] (analytic) 0.16996714290023993 y[1] (numeric) 0.1699671429002411 absolute error 1.1657341758564144e-15 relative error 6.858585465195631e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.410000000000001 y[1] (analytic) 0.16010431155483018 y[1] (numeric) 0.16010431155483135 absolute error 1.1657341758564144e-15 relative error 7.281091711619464e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.420000000000001 y[1] (analytic) 0.15022546991168476 y[1] (numeric) 0.15022546991168592 absolute error 1.1657341758564144e-15 relative error 7.759897017075277e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.430000000000001 y[1] (analytic) 0.14033160584673562 y[1] (numeric) 0.14033160584673682 absolute error 1.1934897514720433e-15 relative error 8.504782256789132e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.440000000000001 y[1] (analytic) 0.13042370873814443 y[1] (numeric) 0.13042370873814566 absolute error 1.2212453270876722e-15 relative error 9.363675814031655e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.450000000000001 y[1] (analytic) 0.12050276936736551 y[1] (numeric) 0.12050276936736673 absolute error 1.2212453270876722e-15 relative error 1.0134583076382054e-12% Correct digits 14 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.460000000000001 y[1] (analytic) 0.11056977982006848 y[1] (numeric) 0.11056977982006971 absolute error 1.2351231148954867e-15 relative error 1.1170530654084843e-12% Correct digits 14 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.470000000000001 y[1] (analytic) 0.10062573338693062 y[1] (numeric) 0.10062573338693186 absolute error 1.2351231148954867e-15 relative error 1.2274425967621378e-12% Correct digits 14 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.480000000000001 y[1] (analytic) 0.09067162446430857 y[1] (numeric) 0.0906716244643098 absolute error 1.2351231148954867e-15 relative error 1.3621936545116969e-12% Correct digits 14 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.490000000000001 y[1] (analytic) 0.08070844845479952 y[1] (numeric) 0.08070844845480077 absolute error 1.2490009027033011e-15 relative error 1.5475466653318204e-12% Correct digits 14 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 5 ) = m1 * diff ( y , x , 3) ; Iterations 140 Total Elapsed Time 0.0 Seconds Elapsed Time(since restart) 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.71428571428581%