##############ECHO OF PROBLEM################# ##############temp/nonlinear1postode.ode################# diff ( y , x , 1 ) = y * y; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK ## problem from Boyce DePrima - ## _Elementary Differential Equations and Boundary Value Problems_ ## page 23 ## Singularity at x = 1 (which depends on init condition) ## x_start=0.0 x_end=0.5 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 $glob_max_h=0.001 ## Not Given = 0 ## No Pole = 3 ## Pole = 4 $glob_type_given_pole=4 ## Real Part $array_given_rad_poles[1][1]=1.0 ## Imag Part $array_given_rad_poles[1][2]=0.0 ## Order $array_given_ord_poles[1][1]=0.0 ## Not Used $array_given_ord_poles[1][2]=0.0 # ELIMINATED in preodein.rb # 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=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(1.0/(1.0 - x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 desired_abs_gbl_error 1.0e-10 range 0.5 estimated_steps 500000.0 step_error 2.0e-16 est_needed_step_err 2.0e-16 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0000005000002494e-156 estimated_step_error 1.0000005000002494e-156 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 6.710893110893107e-149 estimated_step_error 6.710893110893107e-149 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 4.503608634587762e-141 estimated_step_error 4.503608634587762e-141 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.022326638343124e-133 estimated_step_error 3.022326638343124e-133 best_h 1.6e-05 opt_iter 5 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.0282571864226561e-125 estimated_step_error 2.0282571864226561e-125 best_h 3.2e-05 opt_iter 6 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3611512461036852e-117 estimated_step_error 1.3611512461036852e-117 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 9.134677542999214e-110 estimated_step_error 9.134677542999214e-110 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 6.13037450743042e-102 estimated_step_error 6.13037450743042e-102 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 4.114288022161222e-94 estimated_step_error 4.114288022161222e-94 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 2.7614054584672746e-86 estimated_step_error 2.7614054584672746e-86 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 1.8536224822593133e-78 estimated_step_error 1.8536224822593133e-78 best_h 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (analytic) 1.0 y[1] (numeric) 1.0 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999996 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 1.0000000000000233 Order of pole (three term test) 651.0000000000155 Radius of convergence (six term test) for eq 1 0.8567398671708933 Order of pole (six term test) -21.1 TOP MAIN SOLVE Loop x[1] 0.010000000000000002 y[1] (analytic) 1.0101010101010102 y[1] (numeric) 1.0101010101010106 absolute error 4.440892098500626e-16 relative error 4.39648317751562e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.99 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9899999999999991 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9900000000000039 Order of pole (three term test) 651.0000000000028 Radius of convergence (six term test) for eq 1 0.2620243536482094 Order of pole (six term test) -12.285714285714285 TOP MAIN SOLVE Loop x[1] 0.02000000000000001 y[1] (analytic) 1.0204081632653061 y[1] (numeric) 1.0204081632653066 absolute error 4.440892098500626e-16 relative error 4.3520742565306136e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.98 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.979999999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9800000000000016 Order of pole (three term test) 651.0000000000016 Radius of convergence (six term test) for eq 1 0.2956033378250884 Order of pole (six term test) -12.0 TOP MAIN SOLVE Loop x[1] 0.03000000000000002 y[1] (analytic) 1.0309278350515465 y[1] (numeric) 1.0309278350515472 absolute error 6.661338147750939e-16 relative error 6.46149800331841e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.97 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9699999999999991 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9700000000000328 Order of pole (three term test) 651.0000000000229 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.04000000000000003 y[1] (analytic) 1.0416666666666667 y[1] (numeric) 1.0416666666666676 absolute error 8.881784197001252e-16 relative error 8.526512829121202e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.96 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9599999999999989 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9599999999999939 Order of pole (three term test) 650.9999999999964 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.05000000000000004 y[1] (analytic) 1.0526315789473684 y[1] (numeric) 1.0526315789473697 absolute error 1.3322676295501878e-15 relative error 1.2656542480726785e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.95 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9499999999999982 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9499999999999726 Order of pole (three term test) 650.9999999999818 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.060000000000000046 y[1] (analytic) 1.0638297872340425 y[1] (numeric) 1.0638297872340436 absolute error 1.1102230246251565e-15 relative error 1.0436096431476471e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.94 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9399999999999987 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9400000000000139 Order of pole (three term test) 651.0000000000105 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.07000000000000005 y[1] (analytic) 1.0752688172043012 y[1] (numeric) 1.075268817204302 absolute error 6.661338147750939e-16 relative error 6.195044477408372e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9299999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.929999999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9299999999999996 Order of pole (three term test) 651.0000000000005 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.08000000000000006 y[1] (analytic) 1.0869565217391306 y[1] (numeric) 1.086956521739131 absolute error 4.440892098500626e-16 relative error 4.0856207306205754e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9199999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9199999999999988 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9199999999999642 Order of pole (three term test) 650.9999999999746 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09000000000000007 y[1] (analytic) 1.098901098901099 y[1] (numeric) 1.0989010989010994 absolute error 4.440892098500626e-16 relative error 4.041211809635569e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9099999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9099999999999994 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.909999999999986 Order of pole (three term test) 650.9999999999902 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10000000000000007 y[1] (analytic) 1.1111111111111112 y[1] (numeric) 1.1111111111111116 absolute error 4.440892098500626e-16 relative error 3.9968028886505635e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8999999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.8999999999999995 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9000000000000139 Order of pole (three term test) 651.0000000000103 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11000000000000008 y[1] (analytic) 1.1235955056179776 y[1] (numeric) 1.1235955056179783 absolute error 6.661338147750939e-16 relative error 5.928590951498336e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8899999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.889999999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8900000000000259 Order of pole (three term test) 651.00000000002 Radius of convergence (six term test) for eq 1 0.1752252094184739 Order of pole (six term test) -12.507874015748031 TOP MAIN SOLVE Loop x[1] 0.12000000000000009 y[1] (analytic) 1.1363636363636365 y[1] (numeric) 1.136363636363637 absolute error 4.440892098500626e-16 relative error 3.9079850466805504e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8799999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.8799999999999992 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8800000000000265 Order of pole (three term test) 651.0000000000205 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1300000000000001 y[1] (analytic) 1.149425287356322 y[1] (numeric) 1.1494252873563229 absolute error 8.881784197001252e-16 relative error 7.727152251391088e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8699999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.8699999999999988 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8700000000000158 Order of pole (three term test) 651.0000000000128 Radius of convergence (six term test) for eq 1 0.09329523031752482 Order of pole (six term test) -11.8203125 TOP MAIN SOLVE Loop x[1] 0.1400000000000001 y[1] (analytic) 1.1627906976744187 y[1] (numeric) 1.1627906976744196 absolute error 8.881784197001252e-16 relative error 7.638334409421077e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8599999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.859999999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8600000000000078 Order of pole (three term test) 651.0000000000068 Radius of convergence (six term test) for eq 1 0.5916926656012527 Order of pole (six term test) -16.263157894736842 TOP MAIN SOLVE Loop x[1] 0.1500000000000001 y[1] (analytic) 1.1764705882352944 y[1] (numeric) 1.1764705882352953 absolute error 8.881784197001252e-16 relative error 7.549516567451063e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8499999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.8499999999999989 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8500000000000211 Order of pole (three term test) 651.0000000000172 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16000000000000011 y[1] (analytic) 1.1904761904761907 y[1] (numeric) 1.1904761904761911 absolute error 4.440892098500626e-16 relative error 3.7303493627405253e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8399999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.8399999999999994 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8400000000000226 Order of pole (three term test) 651.0000000000183 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17000000000000012 y[1] (analytic) 1.204819277108434 y[1] (numeric) 1.2048192771084343 absolute error 2.220446049250313e-16 relative error 1.8429702208777592e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8299999999999998 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.8299999999999993 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8300000000000031 Order of pole (three term test) 651.0000000000027 Radius of convergence (six term test) for eq 1 0.7353040187568677 Order of pole (six term test) -14.75 TOP MAIN SOLVE Loop x[1] 0.18000000000000013 y[1] (analytic) 1.2195121951219514 y[1] (numeric) 1.2195121951219519 absolute error 4.440892098500626e-16 relative error 3.641531520770513e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8199999999999998 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.819999999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8200000000000086 Order of pole (three term test) 651.0000000000074 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000014 y[1] (analytic) 1.234567901234568 y[1] (numeric) 1.2345679012345685 absolute error 4.440892098500626e-16 relative error 3.5971225997855066e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8099999999999998 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.8099999999999993 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8100000000000247 Order of pole (three term test) 651.0000000000205 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20000000000000015 y[1] (analytic) 1.2500000000000002 y[1] (numeric) 1.2500000000000004 absolute error 2.220446049250313e-16 relative error 1.77635683940025e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7999999999999998 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.7999999999999995 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.800000000000017 Order of pole (three term test) 651.0000000000148 Radius of convergence (six term test) for eq 1 0.1910835269867978 Order of pole (six term test) -12.514285714285714 TOP MAIN SOLVE Loop x[1] 0.21000000000000016 y[1] (analytic) 1.2658227848101269 y[1] (numeric) 1.2658227848101269 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7899999999999998 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.7899999999999995 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7900000000000175 Order of pole (three term test) 651.000000000015 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.22000000000000017 y[1] (analytic) 1.2820512820512824 y[1] (numeric) 1.2820512820512822 absolute error 2.220446049250313e-16 relative error 1.731947918415244e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7799999999999998 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.7799999999999997 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7800000000000112 Order of pole (three term test) 651.0000000000098 Radius of convergence (six term test) for eq 1 0.44340500673763256 Order of pole (six term test) -16.333333333333332 TOP MAIN SOLVE Loop x[1] 0.23000000000000018 y[1] (analytic) 1.2987012987012991 y[1] (numeric) 1.2987012987012987 absolute error 4.440892098500626e-16 relative error 3.419486915845481e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7699999999999998 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.7699999999999997 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7700000000000121 Order of pole (three term test) 651.0000000000103 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.24000000000000019 y[1] (analytic) 1.3157894736842108 y[1] (numeric) 1.3157894736842104 absolute error 4.440892098500626e-16 relative error 3.375077994860475e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7599999999999998 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.7599999999999996 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7599999999999736 Order of pole (three term test) 650.9999999999767 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.25000000000000017 y[1] (analytic) 1.3333333333333337 y[1] (numeric) 1.333333333333333 absolute error 6.661338147750939e-16 relative error 4.996003610813203e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7499999999999998 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.7499999999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7499999999999734 Order of pole (three term test) 650.9999999999761 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2600000000000002 y[1] (analytic) 1.3513513513513518 y[1] (numeric) 1.3513513513513513 absolute error 4.440892098500626e-16 relative error 3.286260152890462e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7399999999999998 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.7399999999999994 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7399999999999923 Order of pole (three term test) 650.9999999999931 Radius of convergence (six term test) for eq 1 0.06473990897393576 Order of pole (six term test) -12.395348837209303 TOP MAIN SOLVE Loop x[1] 0.2700000000000002 y[1] (analytic) 1.3698630136986305 y[1] (numeric) 1.3698630136986298 absolute error 6.661338147750939e-16 relative error 4.8627768478581844e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7299999999999998 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.7299999999999996 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7300000000000068 Order of pole (three term test) 651.0000000000061 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2800000000000002 y[1] (analytic) 1.3888888888888893 y[1] (numeric) 1.3888888888888882 absolute error 1.1102230246251565e-15 relative error 7.993605777301125e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7199999999999998 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.7200000000000002 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7199999999999845 Order of pole (three term test) 650.9999999999856 Radius of convergence (six term test) for eq 1 0.3620386719675124 Order of pole (six term test) -17.5 TOP MAIN SOLVE Loop x[1] 0.2900000000000002 y[1] (analytic) 1.4084507042253527 y[1] (numeric) 1.4084507042253511 absolute error 1.5543122344752192e-15 relative error 1.1035616864774051e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7099999999999997 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.7100000000000004 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.710000000000001 Order of pole (three term test) 651.0000000000006 Radius of convergence (six term test) for eq 1 0.33049457887636624 Order of pole (six term test) -13.333333333333334 TOP MAIN SOLVE Loop x[1] 0.3000000000000002 y[1] (analytic) 1.428571428571429 y[1] (numeric) 1.4285714285714273 absolute error 1.7763568394002505e-15 relative error 1.2434497875801748e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6999999999999997 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.7000000000000003 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.6999999999999984 Order of pole (three term test) 650.999999999998 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3100000000000002 y[1] (analytic) 1.4492753623188412 y[1] (numeric) 1.4492753623188397 absolute error 1.5543122344752192e-15 relative error 1.0724754417879007e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6899999999999997 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.6900000000000003 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.6899999999999864 Order of pole (three term test) 650.9999999999865 Radius of convergence (six term test) for eq 1 0.10159050113696577 Order of pole (six term test) -11.637795275590552 TOP MAIN SOLVE Loop x[1] 0.32000000000000023 y[1] (analytic) 1.4705882352941182 y[1] (numeric) 1.4705882352941169 absolute error 1.3322676295501878e-15 relative error 9.059419880941274e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.6799999999999997 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.6800000000000002 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.6800000000000056 Order of pole (three term test) 651.0000000000051 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.33000000000000024 y[1] (analytic) 1.4925373134328366 y[1] (numeric) 1.4925373134328348 absolute error 1.7763568394002505e-15 relative error 1.1901590823981673e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6699999999999997 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.6700000000000003 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.669999999999993 Order of pole (three term test) 650.9999999999927 Radius of convergence (six term test) for eq 1 0.2956033378250884 Order of pole (six term test) -15.833333333333332 TOP MAIN SOLVE Loop x[1] 0.34000000000000025 y[1] (analytic) 1.5151515151515158 y[1] (numeric) 1.5151515151515145 absolute error 1.3322676295501878e-15 relative error 8.792966355031236e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.6599999999999997 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.6600000000000003 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.6600000000000139 Order of pole (three term test) 651.0000000000136 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.35000000000000026 y[1] (analytic) 1.5384615384615392 y[1] (numeric) 1.5384615384615379 absolute error 1.3322676295501878e-15 relative error 8.659739592076217e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.6499999999999997 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.6499999999999976 Order of pole (three term test) 650.9999999999973 Radius of convergence (six term test) for eq 1 0.1478016689125442 Order of pole (six term test) -11.333333333333334 TOP MAIN SOLVE Loop x[1] 0.36000000000000026 y[1] (analytic) 1.5625000000000009 y[1] (numeric) 1.5624999999999991 absolute error 1.7763568394002505e-15 relative error 1.1368683772161597e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6399999999999997 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.6399999999999938 Order of pole (three term test) 650.9999999999932 Radius of convergence (six term test) for eq 1 0.128 Order of pole (six term test) -12.0 TOP MAIN SOLVE Loop x[1] 0.3700000000000003 y[1] (analytic) 1.587301587301588 y[1] (numeric) 1.5873015873015868 absolute error 1.3322676295501878e-15 relative error 8.39328606616618e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.6299999999999997 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.6299999999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.6299999999999719 Order of pole (three term test) 650.9999999999702 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3800000000000003 y[1] (analytic) 1.6129032258064524 y[1] (numeric) 1.612903225806451 absolute error 1.3322676295501878e-15 relative error 8.260059303211161e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.6199999999999997 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.6199999999999825 Order of pole (three term test) 650.9999999999811 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3900000000000003 y[1] (analytic) 1.639344262295083 y[1] (numeric) 1.6393442622950818 absolute error 1.1102230246251565e-15 relative error 6.772360450213451e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.6099999999999997 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.6099999999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.6100000000000024 Order of pole (three term test) 651.0000000000026 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4000000000000003 y[1] (analytic) 1.6666666666666676 y[1] (numeric) 1.6666666666666663 absolute error 1.3322676295501878e-15 relative error 7.993605777301122e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5999999999999996 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.5999999999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.6000000000000112 Order of pole (three term test) 651.0000000000122 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4100000000000003 y[1] (analytic) 1.6949152542372892 y[1] (numeric) 1.6949152542372878 absolute error 1.3322676295501878e-15 relative error 7.860379014346103e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5899999999999996 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.5900000000000001 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.5899999999999924 Order of pole (three term test) 650.9999999999914 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4200000000000003 y[1] (analytic) 1.7241379310344838 y[1] (numeric) 1.7241379310344827 absolute error 1.1102230246251565e-15 relative error 6.439293542825904e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5799999999999996 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.5799999999999996 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.5799999999999919 Order of pole (three term test) 650.9999999999908 Radius of convergence (six term test) for eq 1 0.0905096679918781 Order of pole (six term test) -11.875 TOP MAIN SOLVE Loop x[1] 0.4300000000000003 y[1] (analytic) 1.754385964912282 y[1] (numeric) 1.7543859649122808 absolute error 1.1102230246251565e-15 relative error 6.328271240363387e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5699999999999996 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.5699999999999997 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.5699999999999892 Order of pole (three term test) 650.9999999999875 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.44000000000000034 y[1] (analytic) 1.785714285714287 y[1] (numeric) 1.7857142857142856 absolute error 1.3322676295501878e-15 relative error 7.460698725481047e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5599999999999996 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.5599999999999996 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.5600000000000085 Order of pole (three term test) 651.0000000000098 Radius of convergence (six term test) for eq 1 0.059252486385443295 Order of pole (six term test) -11.818181818181818 TOP MAIN SOLVE Loop x[1] 0.45000000000000034 y[1] (analytic) 1.8181818181818195 y[1] (numeric) 1.8181818181818183 absolute error 1.1102230246251565e-15 relative error 6.106226635438357e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5499999999999996 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.5499999999999997 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.5499999999999944 Order of pole (three term test) 650.9999999999933 Radius of convergence (six term test) for eq 1 0.06841887792958065 Order of pole (six term test) -12.0 TOP MAIN SOLVE Loop x[1] 0.46000000000000035 y[1] (analytic) 1.8518518518518532 y[1] (numeric) 1.8518518518518519 absolute error 1.3322676295501878e-15 relative error 7.194245199571009e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5399999999999996 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.5399999999999998 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.5399999999999993 Order of pole (three term test) 650.9999999999989 Radius of convergence (six term test) for eq 1 0.14310835055998655 Order of pole (six term test) -12.3125 TOP MAIN SOLVE Loop x[1] 0.47000000000000036 y[1] (analytic) 1.8867924528301903 y[1] (numeric) 1.8867924528301885 absolute error 1.7763568394002505e-15 relative error 9.41469124882132e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5299999999999996 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.5299999999999997 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.5299999999999981 Order of pole (three term test) 650.9999999999976 Radius of convergence (six term test) for eq 1 0.08305736761895043 Order of pole (six term test) -11.736842105263158 TOP MAIN SOLVE Loop x[1] 0.48000000000000037 y[1] (analytic) 1.9230769230769247 y[1] (numeric) 1.9230769230769234 absolute error 1.3322676295501878e-15 relative error 6.92779167366097e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5199999999999996 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.5199999999999997 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.5200000000000019 Order of pole (three term test) 651.0000000000024 Radius of convergence (six term test) for eq 1 0.10041146119075023 Order of pole (six term test) -11.846153846153847 TOP MAIN SOLVE Loop x[1] 0.4900000000000004 y[1] (analytic) 1.960784313725492 y[1] (numeric) 1.9607843137254901 absolute error 1.7763568394002505e-15 relative error 9.05941988094127e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5099999999999996 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.5099999999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.5099999999999838 Order of pole (three term test) 650.9999999999787 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = y * y; Iterations 500 Total Elapsed Time 1.0 Seconds Elapsed Time(since restart) 1.0 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.20000000000007%