##############ECHO OF PROBLEM################# ##############temp/exp_sqrt_sm_hpostode.ode################# diff ( y , x , 1 ) = exp ( sqrt ( 0.1 * x + 0.2 ) ) ; ! // 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=0.0000001; glob_type_given_pole=1; array_given_rad_poles[1][1]=-2.0; 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(20.0 * exp(sqrt(0.1 * x + 0.2)) * sqrt( 0.1 * x + 0.2) - 20.0 * exp(sqrt(0.1 * x + 0.2))); } // 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 = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 1000000 step_error = 2.5e-15 est_needed_step_err = 2.5e-15 opt_iter = 1 SETTING H FOR MAX H Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 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 START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = -13.83604079041925 y[1] (numeric) = -13.83604079041925 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 14 Correct digits = 16 h = 1e-07 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 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] = 2.010000099983634 y[1] (closed_form) = -13.81721089528718 y[1] (numeric) = -13.81721089533072 absolute error = 4.354383520421834e-11 relative error = 3.151420032176713e-10 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 12 h = 1e-07 Radius of convergence (given) for eq 1 = 4.01 Order of pole (given) = 0.5 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] = 2.020000099967268 y[1] (closed_form) = -13.79836631488482 y[1] (numeric) = -13.79836631497183 absolute error = 8.701839249170007e-11 relative error = 6.30642718898034e-10 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 12 h = 1e-07 Radius of convergence (given) for eq 1 = 4.02 Order of pole (given) = 0.5 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] = 2.030000099950902 y[1] (closed_form) = -13.77950686777383 y[1] (numeric) = -13.77950686790429 absolute error = 1.304645280697514e-10 relative error = 9.468011397045648e-10 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 12 h = 1e-07 Radius of convergence (given) for eq 1 = 4.03 Order of pole (given) = 0.5 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] = 2.040000099934537 y[1] (closed_form) = -13.76063256070407 y[1] (numeric) = -13.76063256087793 absolute error = 1.738662547268177e-10 relative error = 1.263504813167701e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.04 Order of pole (given) = 0.5 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] = 2.050000099918171 y[1] (closed_form) = -13.74174340039109 y[1] (numeric) = -13.7417434006083 absolute error = 2.172093616081838e-10 relative error = 1.58065359888762e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.05 Order of pole (given) = 0.5 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] = 2.060000099901805 y[1] (closed_form) = -13.72283939351641 y[1] (numeric) = -13.72283939377689 absolute error = 2.604849669296527e-10 relative error = 1.898185641178045e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.06 Order of pole (given) = 0.5 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] = 2.070000099885439 y[1] (closed_form) = -13.70392054672767 y[1] (numeric) = -13.70392054703136 absolute error = 3.03691294334385e-10 relative error = 2.216090594650322e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.07 Order of pole (given) = 0.5 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] = 2.080000099869074 y[1] (closed_form) = -13.6849868666389 y[1] (numeric) = -13.68498686698577 absolute error = 3.468674236728475e-10 relative error = 2.53465660619987e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.08 Order of pole (given) = 0.5 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] = 2.090000099852708 y[1] (closed_form) = -13.66603835983069 y[1] (numeric) = -13.66603836022066 absolute error = 3.899689460240552e-10 relative error = 2.853562501114525e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.09 Order of pole (given) = 0.5 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] = 2.100000099836342 y[1] (closed_form) = -13.64707503285042 y[1] (numeric) = -13.64707503328343 absolute error = 4.330082958858839e-10 relative error = 3.172901847784762e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 0.5 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] = 2.110000099819976 y[1] (closed_form) = -13.62809689221244 y[1] (numeric) = -13.62809689268844 absolute error = 4.759996841130487e-10 relative error = 3.492781771936557e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.11 Order of pole (given) = 0.5 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] = 2.12000009980361 y[1] (closed_form) = -13.60910394439833 y[1] (numeric) = -13.60910394491783 absolute error = 5.195026631099608e-10 relative error = 3.817317181443046e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.12 Order of pole (given) = 0.5 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] = 2.130000099787245 y[1] (closed_form) = -13.59009619585704 y[1] (numeric) = -13.5900961964194 absolute error = 5.623643772878495e-10 relative error = 4.138045597199578e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.13 Order of pole (given) = 0.5 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] = 2.140000099770879 y[1] (closed_form) = -13.57107365300512 y[1] (numeric) = -13.5710736536103 absolute error = 6.051799061879137e-10 relative error = 4.45933698144734e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.14 Order of pole (given) = 0.5 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] = 2.150000099754513 y[1] (closed_form) = -13.55203632222692 y[1] (numeric) = -13.55203632287487 absolute error = 6.479439207396354e-10 relative error = 4.781155431799808e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.15 Order of pole (given) = 0.5 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] = 2.160000099738147 y[1] (closed_form) = -13.5329842098748 y[1] (numeric) = -13.53298421056544 absolute error = 6.906386573746204e-10 relative error = 5.103372963892711e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.16 Order of pole (given) = 0.5 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] = 2.170000099721781 y[1] (closed_form) = -13.51391732226931 y[1] (numeric) = -13.51391732300259 absolute error = 7.332836560181022e-10 relative error = 5.426136911535925e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.17 Order of pole (given) = 0.5 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] = 2.180000099705416 y[1] (closed_form) = -13.49483566569936 y[1] (numeric) = -13.49483566647524 absolute error = 7.75884245740599e-10 relative error = 5.749490138014138e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.18 Order of pole (given) = 0.5 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] = 2.19000009968905 y[1] (closed_form) = -13.47573924642246 y[1] (numeric) = -13.4757392472409 absolute error = 8.184350974715926e-10 relative error = 6.073396661254562e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.19 Order of pole (given) = 0.5 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] = 2.200000099672684 y[1] (closed_form) = -13.45662807066491 y[1] (numeric) = -13.45662807152583 absolute error = 8.609166712858496e-10 relative error = 6.397714693197361e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 0.5 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] = 2.210000099656318 y[1] (closed_form) = -13.43750214462194 y[1] (numeric) = -13.43750214552527 absolute error = 9.033236381128518e-10 relative error = 6.722407396782344e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.21 Order of pole (given) = 0.5 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] = 2.220000099639952 y[1] (closed_form) = -13.41836147445795 y[1] (numeric) = -13.41836147540362 absolute error = 9.456719851641537e-10 relative error = 7.047596585948697e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.22 Order of pole (given) = 0.5 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] = 2.230000099623587 y[1] (closed_form) = -13.39920606630666 y[1] (numeric) = -13.39920606729466 absolute error = 9.880043450039011e-10 relative error = 7.373603630802534e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.23 Order of pole (given) = 0.5 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] = 2.240000099607221 y[1] (closed_form) = -13.38003592627131 y[1] (numeric) = -13.38003592730159 absolute error = 1.030283414138466e-09 relative error = 7.700154318087706e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.24 Order of pole (given) = 0.5 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] = 2.250000099590855 y[1] (closed_form) = -13.36085106042486 y[1] (numeric) = -13.36085106149734 absolute error = 1.072477218144741e-09 relative error = 8.027012750119206e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.25 Order of pole (given) = 0.5 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] = 2.260000099574489 y[1] (closed_form) = -13.34165147481015 y[1] (numeric) = -13.34165147592477 absolute error = 1.114612402375315e-09 relative error = 8.354381048551377e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.26 Order of pole (given) = 0.5 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] = 2.270000099558124 y[1] (closed_form) = -13.32243717544009 y[1] (numeric) = -13.32243717659679 absolute error = 1.156703177684903e-09 relative error = 8.682369167537047e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.27 Order of pole (given) = 0.5 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] = 2.280000099541758 y[1] (closed_form) = -13.30320816829781 y[1] (numeric) = -13.30320816949657 absolute error = 1.198758425857704e-09 relative error = 9.011047641232916e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.28 Order of pole (given) = 0.5 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] = 2.290000099525392 y[1] (closed_form) = -13.2839644593369 y[1] (numeric) = -13.28396446057761 absolute error = 1.240707092620141e-09 relative error = 9.339885667550738e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.29 Order of pole (given) = 0.5 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] = 2.300000099509026 y[1] (closed_form) = -13.26470605448153 y[1] (numeric) = -13.26470605576417 absolute error = 1.282643324884702e-09 relative error = 9.669594784962134e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 0.5 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] = 2.31000009949266 y[1] (closed_form) = -13.24543295962663 y[1] (numeric) = -13.24543296095114 absolute error = 1.324508502875688e-09 relative error = 9.999737320123232e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.31 Order of pole (given) = 0.5 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] = 2.320000099476295 y[1] (closed_form) = -13.22614518063811 y[1] (numeric) = -13.22614518200446 absolute error = 1.36635058822776e-09 relative error = 1.033067889068673e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.32 Order of pole (given) = 0.5 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] = 2.330000099459929 y[1] (closed_form) = -13.20684272335296 y[1] (numeric) = -13.20684272476109 absolute error = 1.408126948376776e-09 relative error = 1.06621012900143e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.33 Order of pole (given) = 0.5 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] = 2.340000099443563 y[1] (closed_form) = -13.18752559357948 y[1] (numeric) = -13.18752559502936 absolute error = 1.44987488681636e-09 relative error = 1.099429060082545e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.34 Order of pole (given) = 0.5 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] = 2.350000099427197 y[1] (closed_form) = -13.16819379709743 y[1] (numeric) = -13.16819379858901 absolute error = 1.49157841633496e-09 relative error = 1.132712989585358e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.35 Order of pole (given) = 0.5 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] = 2.360000099410831 y[1] (closed_form) = -13.14884733965818 y[1] (numeric) = -13.14884734119138 absolute error = 1.533198457082108e-09 relative error = 1.166032593942919e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.36 Order of pole (given) = 0.5 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] = 2.370000099394466 y[1] (closed_form) = -13.12948622698491 y[1] (numeric) = -13.12948622855963 absolute error = 1.574724350916767e-09 relative error = 1.199380024239069e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.37 Order of pole (given) = 0.5 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] = 2.3800000993781 y[1] (closed_form) = -13.11011046477272 y[1] (numeric) = -13.11011046638896 absolute error = 1.616246692037748e-09 relative error = 1.232824617596209e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.38 Order of pole (given) = 0.5 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] = 2.390000099361734 y[1] (closed_form) = -13.09072005868886 y[1] (numeric) = -13.09072006034662 absolute error = 1.657760151374532e-09 relative error = 1.266362846308219e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.39 Order of pole (given) = 0.5 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] = 2.400000099345368 y[1] (closed_form) = -13.07131501437287 y[1] (numeric) = -13.07131501607205 absolute error = 1.699181240155667e-09 relative error = 1.299931367492324e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 0.5 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] = 2.410000099329002 y[1] (closed_form) = -13.05189533743669 y[1] (numeric) = -13.05189533917745 absolute error = 1.740762201052348e-09 relative error = 1.333723689968099e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.41 Order of pole (given) = 0.5 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] = 2.420000099312637 y[1] (closed_form) = -13.03246103346489 y[1] (numeric) = -13.03246103524696 absolute error = 1.78207315570944e-09 relative error = 1.367411075416542e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.42 Order of pole (given) = 0.5 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] = 2.430000099296271 y[1] (closed_form) = -13.0130121080148 y[1] (numeric) = -13.01301210983815 absolute error = 1.823348583229745e-09 relative error = 1.401173354865883e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.43 Order of pole (given) = 0.5 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] = 2.440000099279905 y[1] (closed_form) = -12.99354856661665 y[1] (numeric) = -12.99354856848118 absolute error = 1.864529863837561e-09 relative error = 1.434965863465472e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.44 Order of pole (given) = 0.5 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] = 2.450000099263539 y[1] (closed_form) = -12.97407041477376 y[1] (numeric) = -12.97407041667943 absolute error = 1.90567206459491e-09 relative error = 1.468831294783859e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.45 Order of pole (given) = 0.5 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] = 2.460000099247174 y[1] (closed_form) = -12.95457765796266 y[1] (numeric) = -12.95457765990948 absolute error = 1.946816041709098e-09 relative error = 1.502801629748592e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.46 Order of pole (given) = 0.5 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] = 2.470000099230808 y[1] (closed_form) = -12.93507030163327 y[1] (numeric) = -12.93507030362113 absolute error = 1.987856990126602e-09 relative error = 1.53679643308595e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.47 Order of pole (given) = 0.5 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] = 2.480000099214442 y[1] (closed_form) = -12.91554835120904 y[1] (numeric) = -12.9155483532379 absolute error = 2.02885352962312e-09 relative error = 1.570861317268962e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.48 Order of pole (given) = 0.5 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] = 2.490000099198076 y[1] (closed_form) = -12.8960118120871 y[1] (numeric) = -12.89601181415691 absolute error = 2.069810989269172e-09 relative error = 1.605000847881661e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.49 Order of pole (given) = 0.5 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] = 2.50000009918171 y[1] (closed_form) = -12.87646068963842 y[1] (numeric) = -12.87646069174912 absolute error = 2.110706276425844e-09 relative error = 1.639197546049523e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 0.5 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] = 2.510000099165345 y[1] (closed_form) = -12.85689498920793 y[1] (numeric) = -12.85689499135945 absolute error = 2.151523403881583e-09 relative error = 1.673439353504537e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.51 Order of pole (given) = 0.5 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] = 2.520000099148979 y[1] (closed_form) = -12.8373147161147 y[1] (numeric) = -12.83731471830704 absolute error = 2.192336978623644e-09 relative error = 1.707784709734972e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.52 Order of pole (given) = 0.5 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] = 2.530000099132613 y[1] (closed_form) = -12.81771987565209 y[1] (numeric) = -12.81771987788518 absolute error = 2.233088380876325e-09 relative error = 1.742188472318067e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.53 Order of pole (given) = 0.5 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] = 2.540000099116247 y[1] (closed_form) = -12.79811047308785 y[1] (numeric) = -12.79811047536165 absolute error = 2.2737989269217e-09 relative error = 1.776667682079393e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.54 Order of pole (given) = 0.5 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] = 2.550000099099881 y[1] (closed_form) = -12.77848651366432 y[1] (numeric) = -12.77848651597874 absolute error = 2.314424207838783e-09 relative error = 1.811188050606712e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.55 Order of pole (given) = 0.5 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] = 2.560000099083516 y[1] (closed_form) = -12.75884800259852 y[1] (numeric) = -12.75884800495355 absolute error = 2.355031725187473e-09 relative error = 1.845802790900745e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.56 Order of pole (given) = 0.5 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] = 2.57000009906715 y[1] (closed_form) = -12.73919494508232 y[1] (numeric) = -12.73919494747792 absolute error = 2.395601939042535e-09 relative error = 1.880497118828771e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.57 Order of pole (given) = 0.5 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] = 2.580000099050784 y[1] (closed_form) = -12.71952734628261 y[1] (numeric) = -12.7195273487187 absolute error = 2.436092216839825e-09 relative error = 1.915238004147845e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.58 Order of pole (given) = 0.5 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] = 2.590000099034418 y[1] (closed_form) = -12.69984521134137 y[1] (numeric) = -12.6998452138177 absolute error = 2.476333804679598e-09 relative error = 1.94989290300023e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.59 Order of pole (given) = 0.5 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] = 2.600000099018053 y[1] (closed_form) = -12.68014854537585 y[1] (numeric) = -12.68014854789258 absolute error = 2.516729935564399e-09 relative error = 1.984779536736729e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 0.5 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] = 2.610000099001687 y[1] (closed_form) = -12.66043735347873 y[1] (numeric) = -12.66043735603581 absolute error = 2.557078104814536e-09 relative error = 2.019739155466003e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.61 Order of pole (given) = 0.5 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] = 2.620000098985321 y[1] (closed_form) = -12.64071164071819 y[1] (numeric) = -12.64071164331561 absolute error = 2.597417392280477e-09 relative error = 2.05480313617288e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.62 Order of pole (given) = 0.5 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] = 2.630000098968955 y[1] (closed_form) = -12.62097141213812 y[1] (numeric) = -12.62097141477579 absolute error = 2.637674967331805e-09 relative error = 2.089914382339098e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.63 Order of pole (given) = 0.5 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] = 2.640000098952589 y[1] (closed_form) = -12.60121667275819 y[1] (numeric) = -12.60121667543607 absolute error = 2.677882804391629e-09 relative error = 2.125098610660971e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.64 Order of pole (given) = 0.5 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] = 2.650000098936224 y[1] (closed_form) = -12.58144742757403 y[1] (numeric) = -12.58144743029204 absolute error = 2.718010705393681e-09 relative error = 2.1603322837377e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.65 Order of pole (given) = 0.5 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] = 2.660000098919858 y[1] (closed_form) = -12.56166368155733 y[1] (numeric) = -12.56166368431546 absolute error = 2.758124395541017e-09 relative error = 2.195668078258149e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.66 Order of pole (given) = 0.5 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] = 2.670000098903492 y[1] (closed_form) = -12.541865439656 y[1] (numeric) = -12.54186544245421 absolute error = 2.798209663978923e-09 relative error = 2.231095268436936e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.67 Order of pole (given) = 0.5 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] = 2.680000098887126 y[1] (closed_form) = -12.52205270679427 y[1] (numeric) = -12.5220527096325 absolute error = 2.838236312641129e-09 relative error = 2.266590294018765e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.68 Order of pole (given) = 0.5 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] = 2.69000009887076 y[1] (closed_form) = -12.50222548787283 y[1] (numeric) = -12.50222549075103 absolute error = 2.878199012457117e-09 relative error = 2.302149337531123e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.69 Order of pole (given) = 0.5 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] = 2.700000098854395 y[1] (closed_form) = -12.48238378776899 y[1] (numeric) = -12.48238379068713 absolute error = 2.918140395991031e-09 relative error = 2.337806981107572e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.7 Order of pole (given) = 0.5 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] = 2.710000098838029 y[1] (closed_form) = -12.46252761133674 y[1] (numeric) = -12.46252761429474 absolute error = 2.957998290753494e-09 relative error = 2.373513931525979e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.71 Order of pole (given) = 0.5 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] = 2.720000098821663 y[1] (closed_form) = -12.44265696340695 y[1] (numeric) = -12.44265696640477 absolute error = 2.997815329308651e-09 relative error = 2.409304811765712e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.72 Order of pole (given) = 0.5 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] = 2.730000098805297 y[1] (closed_form) = -12.42277184878744 y[1] (numeric) = -12.42277185182508 absolute error = 3.037637696934326e-09 relative error = 2.445217326623304e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.73 Order of pole (given) = 0.5 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] = 2.740000098788931 y[1] (closed_form) = -12.40287227226312 y[1] (numeric) = -12.40287227534053 absolute error = 3.0774014447843e-09 relative error = 2.481200626137524e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.74 Order of pole (given) = 0.5 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] = 2.750000098772566 y[1] (closed_form) = -12.38295823859615 y[1] (numeric) = -12.38295824171322 absolute error = 3.117063940294429e-09 relative error = 2.51722074825297e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.75 Order of pole (given) = 0.5 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] = 2.7600000987562 y[1] (closed_form) = -12.363029752526 y[1] (numeric) = -12.36302975568268 absolute error = 3.156680250526733e-09 relative error = 2.553322538014409e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.76 Order of pole (given) = 0.5 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] = 2.770000098739834 y[1] (closed_form) = -12.3430868187696 y[1] (numeric) = -12.34308682196587 absolute error = 3.196275244476965e-09 relative error = 2.589526664931602e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.77 Order of pole (given) = 0.5 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] = 2.780000098723468 y[1] (closed_form) = -12.32312944202148 y[1] (numeric) = -12.32312944525731 absolute error = 3.23583115857673e-09 relative error = 2.62581933736949e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.78 Order of pole (given) = 0.5 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] = 2.790000098707103 y[1] (closed_form) = -12.30315762695388 y[1] (numeric) = -12.30315763022919 absolute error = 3.275317794759758e-09 relative error = 2.662176568057748e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.79 Order of pole (given) = 0.5 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] = 2.800000098690737 y[1] (closed_form) = -12.28317137821682 y[1] (numeric) = -12.28317138153183 absolute error = 3.315003382908799e-09 relative error = 2.698817170936554e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.8 Order of pole (given) = 0.5 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] = 2.810000098674371 y[1] (closed_form) = -12.26317070043832 y[1] (numeric) = -12.26317070379272 absolute error = 3.354399424893018e-09 relative error = 2.735344314152882e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.81 Order of pole (given) = 0.5 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] = 2.820000098658005 y[1] (closed_form) = -12.24315559822441 y[1] (numeric) = -12.24315560161816 absolute error = 3.393749281599412e-09 relative error = 2.771956342768034e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.82 Order of pole (given) = 0.5 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] = 2.830000098641639 y[1] (closed_form) = -12.22312607615931 y[1] (numeric) = -12.22312607959238 absolute error = 3.433072492953215e-09 relative error = 2.808669788368852e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.83 Order of pole (given) = 0.5 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] = 2.840000098625274 y[1] (closed_form) = -12.20308213880552 y[1] (numeric) = -12.20308214227784 absolute error = 3.472319320962924e-09 relative error = 2.845444520873157e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.84 Order of pole (given) = 0.5 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] = 2.850000098608908 y[1] (closed_form) = -12.18302379070395 y[1] (numeric) = -12.18302379421546 absolute error = 3.511514634624291e-09 relative error = 2.882301385066402e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.85 Order of pole (given) = 0.5 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] = 2.860000098592542 y[1] (closed_form) = -12.16295103637402 y[1] (numeric) = -12.16295103992471 absolute error = 3.550688632003585e-09 relative error = 2.919265745118139e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.86 Order of pole (given) = 0.5 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] = 2.870000098576176 y[1] (closed_form) = -12.1428638803138 y[1] (numeric) = -12.14286388390362 absolute error = 3.589821773175572e-09 relative error = 2.956322172889913e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.87 Order of pole (given) = 0.5 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] = 2.88000009855981 y[1] (closed_form) = -12.12276232700008 y[1] (numeric) = -12.12276233062894 absolute error = 3.628862543791911e-09 relative error = 2.993428763104288e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.88 Order of pole (given) = 0.5 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] = 2.890000098543445 y[1] (closed_form) = -12.1026463808885 y[1] (numeric) = -12.10264638455638 absolute error = 3.667878445412498e-09 relative error = 3.030641671233581e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.89 Order of pole (given) = 0.5 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] = 2.900000098527079 y[1] (closed_form) = -12.08251604641368 y[1] (numeric) = -12.08251605012053 absolute error = 3.706846385398421e-09 relative error = 3.067942447714508e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.9 Order of pole (given) = 0.5 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] = 2.910000098510713 y[1] (closed_form) = -12.06237132798931 y[1] (numeric) = -12.06237133173504 absolute error = 3.745721954828696e-09 relative error = 3.105294848731101e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.91 Order of pole (given) = 0.5 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] = 2.920000098494347 y[1] (closed_form) = -12.04221223000826 y[1] (numeric) = -12.04221223379287 absolute error = 3.784615287827364e-09 relative error = 3.142790722784637e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.92 Order of pole (given) = 0.5 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] = 2.930000098477981 y[1] (closed_form) = -12.02203875684267 y[1] (numeric) = -12.02203876066612 absolute error = 3.823453553764011e-09 relative error = 3.180370344079776e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.93 Order of pole (given) = 0.5 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] = 2.940000098461616 y[1] (closed_form) = -12.0018509128441 y[1] (numeric) = -12.00185091670637 absolute error = 3.862266950704907e-09 relative error = 3.218059429959756e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.94 Order of pole (given) = 0.5 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] = 2.95000009844525 y[1] (closed_form) = -11.98164870234362 y[1] (numeric) = -11.98164870624465 absolute error = 3.901030609654299e-09 relative error = 3.255837912265992e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.95 Order of pole (given) = 0.5 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] = 2.960000098428884 y[1] (closed_form) = -11.96143212965188 y[1] (numeric) = -11.96143213359164 absolute error = 3.939755188753225e-09 relative error = 3.293715289314512e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.96 Order of pole (given) = 0.5 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] = 2.970000098412518 y[1] (closed_form) = -11.94120119905928 y[1] (numeric) = -11.94120120303769 absolute error = 3.978415819005932e-09 relative error = 3.331671372658347e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.97 Order of pole (given) = 0.5 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] = 2.980000098396153 y[1] (closed_form) = -11.920955914836 y[1] (numeric) = -11.92095591885304 absolute error = 4.01704269847869e-09 relative error = 3.36973203086789e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.98 Order of pole (given) = 0.5 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] = 2.990000098379787 y[1] (closed_form) = -11.90069628123218 y[1] (numeric) = -11.90069628528794 absolute error = 4.055767277577615e-09 relative error = 3.40800839020966e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.99 Order of pole (given) = 0.5 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 , 1 ) = exp ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 10000001 Total Elapsed Time = 2 Minutes 5.0 Seconds Elapsed Time(since restart) = 2 Minutes 5.0 Seconds Time to Timeout = 7 Minutes 55.0 Seconds Percent Done = 100 %