##############ECHO OF PROBLEM################# ##############temp/tanh_sqrt_newpostode.ode################# diff ( y , x , 1 ) = ( 1.0 - ( tanh ( sqrt ( 2.0 * x + 1.0 ) ) * tanh ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=2.0; x_end=3.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.0001; glob_min_h=0.0001; glob_upper_ratio_limit=1.001; glob_lower_ratio_limit=0.999; glob_type_given_pole=1; array_given_rad_poles[1][1]=-0.5; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.5; array_given_ord_poles[1][2]=0.0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(tanh(sqrt(2.0*x + 1.0))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.0001 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 10000 step_error = 2.5e-14 est_needed_step_err = 2.5e-14 opt_iter = 1 SETTING H FOR MAX H Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.511 Order of pole (three term test) = 0.2394 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0.9774122355837788 y[1] (numeric) = 0.9774122355837788 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.0001 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.511 Order of pole (three term test) = 0.2394 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.010000000000021 y[1] (analytic) = 0.9776109167098525 y[1] (numeric) = 0.9776109253868541 absolute error = 8.67700167273e-09 relative error = 8.875720927843597e-07 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 9 h = 0.0001 Radius of convergence (given) for eq 1 = 2.51 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.521 Order of pole (three term test) = 0.2381 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.020000000000042 y[1] (analytic) = 0.9778074796156186 y[1] (numeric) = 0.9778074968617605 absolute error = 1.724614184794859e-08 relative error = 1.763756384306668e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 0.0001 Radius of convergence (given) for eq 1 = 2.52 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.531 Order of pole (three term test) = 0.2368 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.030000000000063 y[1] (analytic) = 0.9780019514515804 y[1] (numeric) = 0.9780019771605898 absolute error = 2.570900936582632e-08 relative error = 2.628727818760302e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 0.0001 Radius of convergence (given) for eq 1 = 2.53 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.541 Order of pole (three term test) = 0.2355 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.040000000000084 y[1] (analytic) = 0.9781943589548037 y[1] (numeric) = 0.9781943930219678 absolute error = 3.406716408971278e-08 relative error = 3.48265799918468e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 0.0001 Radius of convergence (given) for eq 1 = 2.54 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.551 Order of pole (three term test) = 0.2342 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.050000000000106 y[1] (analytic) = 0.9783847284562971 y[1] (numeric) = 0.9783847707784368 absolute error = 4.232213968169418e-08 relative error = 4.325715482954275e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 0.0001 Radius of convergence (given) for eq 1 = 2.55 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.561 Order of pole (three term test) = 0.2329 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.060000000000127 y[1] (analytic) = 0.9785730858882377 y[1] (numeric) = 0.9785731363636813 absolute error = 5.047544360259337e-08 relative error = 5.158065792988522e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 0.0001 Radius of convergence (given) for eq 1 = 2.56 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.571 Order of pole (three term test) = 0.2316 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.070000000000148 y[1] (analytic) = 0.9787594567910491 y[1] (numeric) = 0.9787595153196083 absolute error = 5.852855911037125e-08 relative error = 5.979871632838408e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 0.0001 Radius of convergence (given) for eq 1 = 2.57 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.581 Order of pole (three term test) = 0.2303 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.080000000000169 y[1] (analytic) = 0.9789438663203346 y[1] (numeric) = 0.9789439328032759 absolute error = 6.648294126332388e-08 relative error = 6.791292488835005e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 0.0001 Radius of convergence (given) for eq 1 = 2.58 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.591 Order of pole (three term test) = 0.229 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.09000000000019 y[1] (analytic) = 0.9791263392536668 y[1] (numeric) = 0.9791264135936891 absolute error = 7.434002236017534e-08 relative error = 7.592485196225094e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 0.0001 Radius of convergence (given) for eq 1 = 2.59 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.601 Order of pole (three term test) = 0.2277 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.100000000000211 y[1] (analytic) = 0.9793068999972409 y[1] (numeric) = 0.9793069820984511 absolute error = 8.210121027474315e-08 relative error = 8.383603778853643e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 0.0001 Radius of convergence (given) for eq 1 = 2.6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.612 Order of pole (three term test) = 0.2264 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.110000000000232 y[1] (analytic) = 0.9794855725923918 y[1] (numeric) = 0.9794856623602809 absolute error = 8.976788912207212e-08 relative error = 9.164799526805138e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 0.0001 Radius of convergence (given) for eq 1 = 2.61 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.622 Order of pole (three term test) = 0.2251 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.120000000000253 y[1] (analytic) = 0.9796623807219783 y[1] (numeric) = 0.9796624780633975 absolute error = 9.734141914741201e-08 relative error = 9.936220994387337e-06 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 8 h = 0.0001 Radius of convergence (given) for eq 1 = 2.62 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.632 Order of pole (three term test) = 0.2238 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.130000000000274 y[1] (analytic) = 0.9798373477166399 y[1] (numeric) = 0.9798374525397781 absolute error = 1.048231381695075e-07 relative error = 1.069801415651094e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.63 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.642 Order of pole (three term test) = 0.2225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.140000000000295 y[1] (analytic) = 0.980010496560926 y[1] (numeric) = 0.9800106087752878 absolute error = 1.122143618026428e-07 relative error = 1.145032244005833e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.64 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.652 Order of pole (three term test) = 0.2212 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.150000000000317 y[1] (analytic) = 0.9801818498993026 y[1] (numeric) = 0.980181969415686 absolute error = 1.195163834566415e-07 relative error = 1.219328673234664e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.65 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.662 Order of pole (three term test) = 0.2199 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.160000000000338 y[1] (analytic) = 0.9803514300420387 y[1] (numeric) = 0.9803515567725125 absolute error = 1.267304737817554e-07 relative error = 1.292704533274573e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.66 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.672 Order of pole (three term test) = 0.2186 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.170000000000359 y[1] (analytic) = 0.980519258970975 y[1] (numeric) = 0.9805193928288595 absolute error = 1.338578844434224e-07 relative error = 1.365173434572842e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.67 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.682 Order of pole (three term test) = 0.2173 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.18000000000038 y[1] (analytic) = 0.9806853583451771 y[1] (numeric) = 0.9806854992450219 absolute error = 1.408998447915977e-07 relative error = 1.436748734878169e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.68 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.692 Order of pole (three term test) = 0.2161 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.190000000000401 y[1] (analytic) = 0.9808497495064775 y[1] (numeric) = 0.9808498973640426 absolute error = 1.478575650804004e-07 relative error = 1.50744357282852e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.69 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.702 Order of pole (three term test) = 0.2148 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.200000000000422 y[1] (analytic) = 0.9810124534849067 y[1] (numeric) = 0.9810126082171413 absolute error = 1.547322345807345e-07 relative error = 1.577270849427755e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.7 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.712 Order of pole (three term test) = 0.2135 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.210000000000443 y[1] (analytic) = 0.9811734910040177 y[1] (numeric) = 0.9811736525290405 absolute error = 1.615250228015341e-07 relative error = 1.646243241205471e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.71 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.723 Order of pole (three term test) = 0.2122 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.220000000000464 y[1] (analytic) = 0.9813328824861055 y[1] (numeric) = 0.9813330507231867 absolute error = 1.682370811550982e-07 relative error = 1.714373217871665e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.72 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.733 Order of pole (three term test) = 0.2109 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.230000000000485 y[1] (analytic) = 0.9814906480573237 y[1] (numeric) = 0.9814908229268655 absolute error = 1.748695418468671e-07 relative error = 1.781673031658411e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.73 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.743 Order of pole (three term test) = 0.2096 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.240000000000506 y[1] (analytic) = 0.981646807552701 y[1] (numeric) = 0.9816469889762196 absolute error = 1.814235186525792e-07 relative error = 1.848154725882295e-05 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.74 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.753 Order of pole (three term test) = 0.2084 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.250000000000528 y[1] (analytic) = 0.9818013805210604 y[1] (numeric) = 0.9818015684211663 absolute error = 1.879001059190699e-07 relative error = 1.913830125390003e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.75 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.763 Order of pole (three term test) = 0.2071 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.260000000000549 y[1] (analytic) = 0.9819543862298417 y[1] (numeric) = 0.9819545805302239 absolute error = 1.943003822280076e-07 relative error = 1.978710874483823e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.76 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.773 Order of pole (three term test) = 0.2058 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.27000000000057 y[1] (analytic) = 0.9821058436698304 y[1] (numeric) = 0.9821060442952373 absolute error = 2.006254068431801e-07 relative error = 2.042808401317561e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.77 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.783 Order of pole (three term test) = 0.2045 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.280000000000591 y[1] (analytic) = 0.9822557715597956 y[1] (numeric) = 0.9822559784360185 absolute error = 2.068762229301413e-07 relative error = 2.106133951258209e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.78 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.793 Order of pole (three term test) = 0.2033 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.290000000000612 y[1] (analytic) = 0.9824041883510375 y[1] (numeric) = 0.9824044014048945 absolute error = 2.130538570010998e-07 relative error = 2.16869858177936e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.79 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.803 Order of pole (three term test) = 0.202 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.300000000000633 y[1] (analytic) = 0.982551112231848 y[1] (numeric) = 0.9825513313911663 absolute error = 2.191593183598073e-07 relative error = 2.23051315734599e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.813 Order of pole (three term test) = 0.2007 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.310000000000654 y[1] (analytic) = 0.9826965611318853 y[1] (numeric) = 0.9826967863254854 absolute error = 2.251936001007593e-07 relative error = 2.291588360107598e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.81 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.824 Order of pole (three term test) = 0.1995 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.320000000000675 y[1] (analytic) = 0.9828405527264642 y[1] (numeric) = 0.9828407838841443 absolute error = 2.311576801083959e-07 relative error = 2.351934700569175e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.82 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.834 Order of pole (three term test) = 0.1982 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.330000000000696 y[1] (analytic) = 0.9829831044407655 y[1] (numeric) = 0.9829833414932853 absolute error = 2.370525197248341e-07 relative error = 2.411562504522364e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.83 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.844 Order of pole (three term test) = 0.1969 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.340000000000718 y[1] (analytic) = 0.9831242334539642 y[1] (numeric) = 0.9831244763330301 absolute error = 2.428790659703139e-07 relative error = 2.470481936113184e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.84 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.854 Order of pole (three term test) = 0.1957 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.350000000000739 y[1] (analytic) = 0.9832639567032789 y[1] (numeric) = 0.9832642053415295 absolute error = 2.486382505439977e-07 relative error = 2.528702988133934e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.85 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.864 Order of pole (three term test) = 0.1944 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.36000000000076 y[1] (analytic) = 0.9834022908879467 y[1] (numeric) = 0.9834025452189362 absolute error = 2.543309894909029e-07 relative error = 2.586235479086173e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.86 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.874 Order of pole (three term test) = 0.1932 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.370000000000781 y[1] (analytic) = 0.9835392524731199 y[1] (numeric) = 0.9835395124313053 absolute error = 2.599581854223487e-07 relative error = 2.643089076197834e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.87 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.884 Order of pole (three term test) = 0.1919 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.380000000000802 y[1] (analytic) = 0.983674857693691 y[1] (numeric) = 0.983675123214418 absolute error = 2.655207269608439e-07 relative error = 2.699273290194483e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.88 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.894 Order of pole (three term test) = 0.1906 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.390000000000823 y[1] (analytic) = 0.9838091225580459 y[1] (numeric) = 0.9838093935775327 absolute error = 2.710194868527083e-07 relative error = 2.754797456523054e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.89 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.904 Order of pole (three term test) = 0.1894 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.400000000000844 y[1] (analytic) = 0.9839420628517457 y[1] (numeric) = 0.9839423393070716 absolute error = 2.76455325964875e-07 relative error = 2.809670776383198e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.914 Order of pole (three term test) = 0.1881 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.410000000000865 y[1] (analytic) = 0.9840736941411402 y[1] (numeric) = 0.9840739759702319 absolute error = 2.818290917305788e-07 relative error = 2.863902301306284e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.91 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.925 Order of pole (three term test) = 0.1869 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.420000000000886 y[1] (analytic) = 0.9842040317769145 y[1] (numeric) = 0.9842043189185312 absolute error = 2.871416167060659e-07 relative error = 2.917500918865887e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.92 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.935 Order of pole (three term test) = 0.1856 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.430000000000907 y[1] (analytic) = 0.9843330908975683 y[1] (numeric) = 0.9843333832912896 absolute error = 2.923937213461514e-07 relative error = 2.970475381250578e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.93 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.945 Order of pole (three term test) = 0.1844 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.440000000000929 y[1] (analytic) = 0.9844608864328314 y[1] (numeric) = 0.9844611840190448 absolute error = 2.975862134491081e-07 relative error = 3.022834299973095e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.94 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.955 Order of pole (three term test) = 0.1831 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45000000000095 y[1] (analytic) = 0.9845874331070166 y[1] (numeric) = 0.9845877358269055 absolute error = 3.027198889338223e-07 relative error = 3.074586154106632e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.95 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.965 Order of pole (three term test) = 0.1819 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.460000000000971 y[1] (analytic) = 0.984712745442309 y[1] (numeric) = 0.9847130532378398 absolute error = 3.07795530729571e-07 relative error = 3.125739279339953e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.96 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.975 Order of pole (three term test) = 0.1806 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.470000000000992 y[1] (analytic) = 0.9848368377619967 y[1] (numeric) = 0.9848371505759058 absolute error = 3.128139091090887e-07 relative error = 3.176301871688168e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.97 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.985 Order of pole (three term test) = 0.1794 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.480000000001013 y[1] (analytic) = 0.9849597241936403 y[1] (numeric) = 0.9849600419694234 absolute error = 3.177757831318573e-07 relative error = 3.226282002464737e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.98 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.995 Order of pole (three term test) = 0.1782 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.490000000001034 y[1] (analytic) = 0.9850814186721856 y[1] (numeric) = 0.9850817413540853 absolute error = 3.226818997559278e-07 relative error = 3.275687609567118e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 2.99 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.005 Order of pole (three term test) = 0.1769 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.500000000001055 y[1] (analytic) = 0.9852019349430188 y[1] (numeric) = 0.9852022624760144 absolute error = 3.27532995614277e-07 relative error = 3.324526515807346e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.015 Order of pole (three term test) = 0.1757 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.510000000001076 y[1] (analytic) = 0.9853212865649666 y[1] (numeric) = 0.985321618894761 absolute error = 3.323297943502723e-07 relative error = 3.372806402151755e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.026 Order of pole (three term test) = 0.1744 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.520000000001097 y[1] (analytic) = 0.9854394869132407 y[1] (numeric) = 0.9854398239862507 absolute error = 3.370730100593633e-07 relative error = 3.420534842937947e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.036 Order of pole (three term test) = 0.1732 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.530000000001118 y[1] (analytic) = 0.9855565491823299 y[1] (numeric) = 0.9855568909456747 absolute error = 3.417633447355684e-07 relative error = 3.46771928022916e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.046 Order of pole (three term test) = 0.172 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.54000000000114 y[1] (analytic) = 0.9856724863888392 y[1] (numeric) = 0.9856728327903296 absolute error = 3.464014903808987e-07 relative error = 3.514367045487829e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.056 Order of pole (three term test) = 0.1707 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.550000000001161 y[1] (analytic) = 0.9857873113742784 y[1] (numeric) = 0.9857876623624064 absolute error = 3.509881280061578e-07 relative error = 3.560485349693211e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.066 Order of pole (three term test) = 0.1695 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.560000000001182 y[1] (analytic) = 0.9859010368077995 y[1] (numeric) = 0.9859013923317282 absolute error = 3.555239287411638e-07 relative error = 3.606081294855894e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.076 Order of pole (three term test) = 0.1683 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.570000000001203 y[1] (analytic) = 0.9860136751888857 y[1] (numeric) = 0.9860140351984396 absolute error = 3.600095538347503e-07 relative error = 3.651161874258844e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.086 Order of pole (three term test) = 0.167 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.580000000001224 y[1] (analytic) = 0.986125238849992 y[1] (numeric) = 0.9861256032956464 absolute error = 3.64445654321699e-07 relative error = 3.695733969315209e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.096 Order of pole (three term test) = 0.1658 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.590000000001245 y[1] (analytic) = 0.9862357399591387 y[1] (numeric) = 0.9862361087920104 absolute error = 3.688328716888734e-07 relative error = 3.739804356554293e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.106 Order of pole (three term test) = 0.1646 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.600000000001266 y[1] (analytic) = 0.9863451905224584 y[1] (numeric) = 0.9863455636942953 absolute error = 3.731718368760184e-07 relative error = 3.783379697713663e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.117 Order of pole (three term test) = 0.1634 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.610000000001287 y[1] (analytic) = 0.9864536023866978 y[1] (numeric) = 0.9864539798498702 absolute error = 3.77463172385184e-07 relative error = 3.826466561345836e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.127 Order of pole (three term test) = 0.1621 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.620000000001308 y[1] (analytic) = 0.9865609872416755 y[1] (numeric) = 0.9865613689491668 absolute error = 3.817074912815244e-07 relative error = 3.869071412896022e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.137 Order of pole (three term test) = 0.1609 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.630000000001329 y[1] (analytic) = 0.9866673566226957 y[1] (numeric) = 0.9866677425280913 absolute error = 3.859053956389857e-07 relative error = 3.911200599155496e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.147 Order of pole (three term test) = 0.1597 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.640000000001351 y[1] (analytic) = 0.9867727219129198 y[1] (numeric) = 0.9867731119704017 absolute error = 3.900574819803992e-07 relative error = 3.952860403601842e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.157 Order of pole (three term test) = 0.1585 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.650000000001372 y[1] (analytic) = 0.986877094345696 y[1] (numeric) = 0.9868774885100304 absolute error = 3.941643343940981e-07 relative error = 3.994056976825781e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.167 Order of pole (three term test) = 0.1573 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.660000000001393 y[1] (analytic) = 0.986980485006848 y[1] (numeric) = 0.9869808832333801 absolute error = 3.982265320834344e-07 relative error = 4.034796413230717e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.177 Order of pole (three term test) = 0.156 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.670000000001414 y[1] (analytic) = 0.9870829048369233 y[1] (numeric) = 0.9870833070815659 absolute error = 4.022446425944182e-07 relative error = 4.075084682586751e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.187 Order of pole (three term test) = 0.1548 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.680000000001435 y[1] (analytic) = 0.987184364633403 y[1] (numeric) = 0.987184770852629 absolute error = 4.062192260345654e-07 relative error = 4.114927672962258e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.197 Order of pole (three term test) = 0.1536 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.690000000001456 y[1] (analytic) = 0.9872848750528721 y[1] (numeric) = 0.9872852852037062 absolute error = 4.10150834073697e-07 relative error = 4.154331180772239e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.208 Order of pole (three term test) = 0.1524 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700000000001477 y[1] (analytic) = 0.9873844466131529 y[1] (numeric) = 0.9873848606531644 absolute error = 4.140400114982512e-07 relative error = 4.193300926690288e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.218 Order of pole (three term test) = 0.1512 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.710000000001498 y[1] (analytic) = 0.9874830896954004 y[1] (numeric) = 0.9874835075826941 absolute error = 4.178872936577704e-07 relative error = 4.231842529948257e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.21 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.228 Order of pole (three term test) = 0.15 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.720000000001519 y[1] (analytic) = 0.9875808145461626 y[1] (numeric) = 0.9875812362393723 absolute error = 4.216932096845483e-07 relative error = 4.269961541105222e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.22 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.238 Order of pole (three term test) = 0.1488 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.730000000001541 y[1] (analytic) = 0.9876776312794039 y[1] (numeric) = 0.9876780567376823 absolute error = 4.254582783858041e-07 relative error = 4.307663400604506e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.23 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.248 Order of pole (three term test) = 0.1476 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.740000000001562 y[1] (analytic) = 0.9877735498784946 y[1] (numeric) = 0.9877739790615088 absolute error = 4.291830141278652e-07 relative error = 4.344953498508425e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.24 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.258 Order of pole (three term test) = 0.1464 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.750000000001583 y[1] (analytic) = 0.9878685801981661 y[1] (numeric) = 0.9878690130660874 absolute error = 4.328679212850517e-07 relative error = 4.38183711843754e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.268 Order of pole (three term test) = 0.1452 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.760000000001604 y[1] (analytic) = 0.987962731966432 y[1] (numeric) = 0.9879631684799303 absolute error = 4.365134982364793e-07 relative error = 4.4183194781816e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.26 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.278 Order of pole (three term test) = 0.144 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.770000000001625 y[1] (analytic) = 0.9880560147864766 y[1] (numeric) = 0.9880564549067117 absolute error = 4.401202350345912e-07 relative error = 4.454405706236231e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.27 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.288 Order of pole (three term test) = 0.1428 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.780000000001646 y[1] (analytic) = 0.9881484381385115 y[1] (numeric) = 0.9881488818271278 absolute error = 4.436886162917375e-07 relative error = 4.490100871156206e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.28 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.299 Order of pole (three term test) = 0.1416 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.790000000001667 y[1] (analytic) = 0.9882400113815999 y[1] (numeric) = 0.9882404586007189 absolute error = 4.472191189597297e-07 relative error = 4.525409959211215e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.29 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.309 Order of pole (three term test) = 0.1404 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.800000000001688 y[1] (analytic) = 0.9883307437554506 y[1] (numeric) = 0.9883311944676633 absolute error = 4.507122126629071e-07 relative error = 4.560337877887869e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.319 Order of pole (three term test) = 0.1392 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.810000000001709 y[1] (analytic) = 0.9884206443821811 y[1] (numeric) = 0.9884210985505416 absolute error = 4.541683604752933e-07 relative error = 4.594889463879766e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.31 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.329 Order of pole (three term test) = 0.138 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.82000000000173 y[1] (analytic) = 0.988509722268051 y[1] (numeric) = 0.9885101798560706 absolute error = 4.575880195867299e-07 relative error = 4.629069489947285e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.32 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.339 Order of pole (three term test) = 0.1368 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.830000000001752 y[1] (analytic) = 0.988597986305166 y[1] (numeric) = 0.9885984472768052 absolute error = 4.609716391934526e-07 relative error = 4.662882643695344e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.33 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.349 Order of pole (three term test) = 0.1356 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.840000000001773 y[1] (analytic) = 0.9886854452731535 y[1] (numeric) = 0.9886859095928174 absolute error = 4.643196639397829e-07 relative error = 4.696333562506332e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.34 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.359 Order of pole (three term test) = 0.1344 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.850000000001794 y[1] (analytic) = 0.9887721078408099 y[1] (numeric) = 0.9887725754733402 absolute error = 4.676325302543916e-07 relative error = 4.729426796590821e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.369 Order of pole (three term test) = 0.1332 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.860000000001815 y[1] (analytic) = 0.9888579825677203 y[1] (numeric) = 0.9888584534783899 absolute error = 4.709106695699461e-07 relative error = 4.762166841664714e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.36 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.379 Order of pole (three term test) = 0.132 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.870000000001836 y[1] (analytic) = 0.9889430779058508 y[1] (numeric) = 0.9889435520603572 absolute error = 4.741545064357311e-07 relative error = 4.794558119965642e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.37 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.39 Order of pole (three term test) = 0.1308 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.880000000001857 y[1] (analytic) = 0.9890274022011147 y[1] (numeric) = 0.9890278795655753 absolute error = 4.773644605160499e-07 relative error = 4.826605000565795e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.38 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.4 Order of pole (three term test) = 0.1297 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.890000000001878 y[1] (analytic) = 0.9891109636949128 y[1] (numeric) = 0.989111444235857 absolute error = 4.805409441477337e-07 relative error = 4.858311774774287e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.39 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.41 Order of pole (three term test) = 0.1285 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.900000000001899 y[1] (analytic) = 0.9891937705256466 y[1] (numeric) = 0.9891942542100122 absolute error = 4.836843655597889e-07 relative error = 4.889682688789724e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.42 Order of pole (three term test) = 0.1273 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.91000000000192 y[1] (analytic) = 0.9892758307302089 y[1] (numeric) = 0.9892763175253353 absolute error = 4.867951264309056e-07 relative error = 4.920721919099046e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.43 Order of pole (three term test) = 0.1261 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.920000000001941 y[1] (analytic) = 0.9893571522454473 y[1] (numeric) = 0.9893576421190688 absolute error = 4.898736215563915e-07 relative error = 4.951433569207775e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.44 Order of pole (three term test) = 0.1249 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.930000000001963 y[1] (analytic) = 0.9894377429096053 y[1] (numeric) = 0.989438235829847 absolute error = 4.929202417347511e-07 relative error = 4.981821698909905e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.45 Order of pole (three term test) = 0.1238 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.940000000001984 y[1] (analytic) = 0.9895176104637385 y[1] (numeric) = 0.9895181063991106 absolute error = 4.959353721023518e-07 relative error = 5.011890307540167e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.46 Order of pole (three term test) = 0.1226 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.950000000002005 y[1] (analytic) = 0.9895967625531085 y[1] (numeric) = 0.9895972614725 absolute error = 4.989193915783119e-07 relative error = 5.041643328451537e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.47 Order of pole (three term test) = 0.1214 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.960000000002026 y[1] (analytic) = 0.9896752067285529 y[1] (numeric) = 0.9896757086012286 absolute error = 5.018726756400582e-07 relative error = 5.071084657147639e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.481 Order of pole (three term test) = 0.1202 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.970000000002047 y[1] (analytic) = 0.989752950447834 y[1] (numeric) = 0.9897534552434263 absolute error = 5.047955923265235e-07 relative error = 5.100218110975253e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.491 Order of pole (three term test) = 0.1191 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.980000000002068 y[1] (analytic) = 0.9898300010769645 y[1] (numeric) = 0.9898305087654705 absolute error = 5.076885060129044e-07 relative error = 5.129047467348173e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.501 Order of pole (three term test) = 0.1179 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.990000000002089 y[1] (analytic) = 0.9899063658915122 y[1] (numeric) = 0.9899068764432882 absolute error = 5.10551776078394e-07 relative error = 5.157576450360432e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.511 Order of pole (three term test) = 0.1167 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = ( 1.0 - ( tanh ( sqrt ( 2.0 * x + 1.0 ) ) * tanh ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; Iterations = 10000 Total Elapsed Time = 2.0 Seconds Elapsed Time(since restart) = 2.0 Seconds Time to Timeout = 9 Minutes 58.0 Seconds Percent Done = 100 %