##############ECHO OF PROBLEM################# ##############temp/tanh_sqrt_new_sm_hpostode.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=0.0000001; glob_min_h=0.000000001; 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 = 1e-09 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 999999999.9999999 step_error = 7.905694150420948e-17 est_needed_step_err = 7.905694150420948e-17 opt_iter = 1 Radius of convergence (given) for eq 1 = 2.5 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 min_size = 0.9774122355837788 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-09 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 999999999.9999999 step_error = 7.905694150420948e-17 est_needed_step_err = 7.905694150420948e-17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 2.5 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 min_size = 0.9774122355837788 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 2e-09 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 499999999.9999999 step_error = 1.118033988749895e-16 est_needed_step_err = 1.118033988749895e-16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 2.5 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 min_size = 0.9774122355837788 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 4e-09 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 250000000 step_error = 1.58113883008419e-16 est_needed_step_err = 1.58113883008419e-16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.068652859137299e-320 estimated_step_error = 2.068652859137299e-320 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 2.5 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 min_size = 0.9774122355837788 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 8e-09 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 125000000 step_error = 2.23606797749979e-16 est_needed_step_err = 2.23606797749979e-16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.421686146941337e-309 estimated_step_error = 1.421686146941337e-309 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 2.5 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 min_size = 0.9774122355837788 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1.6e-08 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 62499999.99999999 step_error = 3.162277660168379e-16 est_needed_step_err = 3.162277660168379e-16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.769752795018184e-299 estimated_step_error = 9.769752795018184e-299 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 2.5 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 min_size = 0.9774122355837788 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 3.2e-08 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 31250000 step_error = 4.47213595499958e-16 est_needed_step_err = 4.47213595499958e-16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.713722978459953e-288 estimated_step_error = 6.713722978459953e-288 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 2.5 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 min_size = 0.9774122355837788 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 6.4e-08 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 15625000 step_error = 6.324555320336759e-16 est_needed_step_err = 6.324555320336759e-16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.613635271883642e-277 estimated_step_error = 4.613635271883642e-277 Double H and LOOP opt_iter = 8 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 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] (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 = 1e-07 Radius of convergence (given) for eq 1 = 2.5 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] = 2.010000099983634 y[1] (analytic) = 0.977610918685703 y[1] (numeric) = 0.9776109186947011 absolute error = 8.998024547679506e-12 relative error = 9.204095796900899e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-07 Radius of convergence (given) for eq 1 = 2.51 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] = 2.020000099967268 y[1] (analytic) = 0.9778074815701067 y[1] (numeric) = 0.9778074815879928 absolute error = 1.788613701592112e-11 relative error = 1.829208443690838e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 2.52 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] = 2.030000099950902 y[1] (analytic) = 0.9780019533849817 y[1] (numeric) = 0.9780019534116499 absolute error = 2.666811216300857e-11 relative error = 2.726795388363699e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 2.53 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] = 2.040000099934537 y[1] (analytic) = 0.9781943608673905 y[1] (numeric) = 0.9781943609027317 absolute error = 3.53411744313803e-11 relative error = 3.612899015287959e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 2.54 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] = 2.050000099918171 y[1] (analytic) = 0.9783847303483372 y[1] (numeric) = 0.9783847303922493 absolute error = 4.39120961814865e-11 relative error = 4.488223785529886e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 2.55 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] = 2.060000099901805 y[1] (analytic) = 0.9785730877599949 y[1] (numeric) = 0.9785730878123666 absolute error = 5.237177358452527e-11 relative error = 5.35185100015442e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 2.56 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] = 2.070000099885439 y[1] (analytic) = 0.9787594586427831 y[1] (numeric) = 0.978759458703513 absolute error = 6.072986558081084e-11 relative error = 6.204779432223639e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 2.57 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] = 2.080000099869074 y[1] (analytic) = 0.9789438681523011 y[1] (numeric) = 0.9789438682212822 absolute error = 6.898115412212746e-11 relative error = 7.046487175237671e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 2.58 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] = 2.090000099852708 y[1] (analytic) = 0.9791263410661176 y[1] (numeric) = 0.9791263411432511 absolute error = 7.713352179194999e-11 relative error = 7.877790491057923e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 2.59 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] = 2.100000099836342 y[1] (analytic) = 0.9793069017904245 y[1] (numeric) = 0.97930690187561 absolute error = 8.51855253003464e-11 relative error = 8.69855253185752e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 2.6 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] = 2.110000099819976 y[1] (analytic) = 0.9794855743665523 y[1] (numeric) = 0.9794855744596959 absolute error = 9.314360394085952e-11 relative error = 9.509441116689938e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 2.61 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] = 2.12000009980361 y[1] (analytic) = 0.9796623824773566 y[1] (numeric) = 0.9796623825783523 absolute error = 1.009956562825209e-10 relative error = 1.030923082165557e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.62 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] = 2.130000099787245 y[1] (analytic) = 0.9798373494534731 y[1] (numeric) = 0.9798373495622372 absolute error = 1.087641088304281e-10 relative error = 1.110022075511755e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.63 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] = 2.140000099770879 y[1] (analytic) = 0.9800104982794478 y[1] (numeric) = 0.9800104983958822 absolute error = 1.164344176629584e-10 relative error = 1.188093575195124e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.64 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] = 2.150000099754513 y[1] (analytic) = 0.9801818515997429 y[1] (numeric) = 0.9801818517237629 absolute error = 1.240200164787097e-10 relative error = 1.265275584079609e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.65 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] = 2.160000099738147 y[1] (analytic) = 0.9803514317246245 y[1] (numeric) = 0.9803514318561394 absolute error = 1.315149100733493e-10 relative error = 1.341507808500769e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.66 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] = 2.170000099721781 y[1] (analytic) = 0.9805192606359294 y[1] (numeric) = 0.9805192607748437 absolute error = 1.38914324487871e-10 relative error = 1.416742435000983e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.67 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] = 2.180000099705416 y[1] (analytic) = 0.9806853599927203 y[1] (numeric) = 0.9806853601389454 absolute error = 1.462250320827252e-10 relative error = 1.491049403284766e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.68 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] = 2.19000009968905 y[1] (analytic) = 0.9808497511368264 y[1] (numeric) = 0.9808497512902786 absolute error = 1.534522509061276e-10 relative error = 1.564482742930536e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.69 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] = 2.200000099672684 y[1] (analytic) = 0.9810124550982748 y[1] (numeric) = 0.9810124552588685 absolute error = 1.605936494897264e-10 relative error = 1.637019475697061e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.7 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] = 2.210000099656318 y[1] (analytic) = 0.9811734926006157 y[1] (numeric) = 0.9811734927682468 absolute error = 1.676311311982204e-10 relative error = 1.708475947040838e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.71 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] = 2.220000099639952 y[1] (analytic) = 0.9813328840661406 y[1] (numeric) = 0.9813328842407432 absolute error = 1.746025546367491e-10 relative error = 1.779238803384287e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.72 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] = 2.230000099623587 y[1] (analytic) = 0.9814906496210003 y[1] (numeric) = 0.9814906498024937 absolute error = 1.814933758836901e-10 relative error = 1.849160518786126e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.73 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] = 2.240000099607221 y[1] (analytic) = 0.9816468091002206 y[1] (numeric) = 0.9816468092885222 absolute error = 1.883015965375989e-10 relative error = 1.918221449832822e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.74 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] = 2.250000099590855 y[1] (analytic) = 0.9818013820526217 y[1] (numeric) = 0.9818013822476548 absolute error = 1.950331007805062e-10 relative error = 1.98648223913432e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.75 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] = 2.260000099574489 y[1] (analytic) = 0.9819543877456401 y[1] (numeric) = 0.9819543879473339 absolute error = 2.016937727944423e-10 relative error = 2.054003478282618e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.76 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] = 2.270000099558124 y[1] (analytic) = 0.9821058451700588 y[1] (numeric) = 0.9821058453783237 absolute error = 2.082648498102913e-10 relative error = 2.120594748870766e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.77 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] = 2.280000099541758 y[1] (analytic) = 0.982255773044644 y[1] (numeric) = 0.9822557732594046 absolute error = 2.147606537050706e-10 relative error = 2.186402560296376e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.78 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] = 2.290000099525392 y[1] (analytic) = 0.9824041898206932 y[1] (numeric) = 0.9824041900418735 absolute error = 2.211802963003606e-10 relative error = 2.251418495484329e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.79 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] = 2.300000099509026 y[1] (analytic) = 0.9825511136864957 y[1] (numeric) = 0.9825511139140207 absolute error = 2.275249988414885e-10 relative error = 2.315655599715551e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.8 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] = 2.31000009949266 y[1] (analytic) = 0.9826965625717069 y[1] (numeric) = 0.982696562805501 absolute error = 2.337940951946393e-10 relative error = 2.379107693048224e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.81 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] = 2.320000099476295 y[1] (analytic) = 0.9828405541516392 y[1] (numeric) = 0.9828405543916332 absolute error = 2.399940246533561e-10 relative error = 2.44184088293459e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.82 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] = 2.330000099459929 y[1] (analytic) = 0.9829831058514706 y[1] (numeric) = 0.9829831060975925 absolute error = 2.461219006377746e-10 relative error = 2.503826354417161e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.83 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] = 2.340000099443563 y[1] (analytic) = 0.9831242348503736 y[1] (numeric) = 0.9831242351025539 absolute error = 2.521802766608516e-10 relative error = 2.565090633730865e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.84 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] = 2.350000099427197 y[1] (analytic) = 0.9832639580855647 y[1] (numeric) = 0.9832639583437327 absolute error = 2.581680424995625e-10 relative error = 2.625622960921104e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 2.85 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 Finished! Maximum Time Reached before Solution Completed! 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 = 3545055 Total Elapsed Time = 10 Minutes 0.0 Seconds Elapsed Time(since restart) = 10 Minutes 0.0 Seconds Expected Time Remaining = 18 Minutes 12.5 Seconds Optimized Time Remaining = 18 Minutes 12.5 Seconds Expected Total Time = 28 Minutes 12.5 Seconds Time to Timeout = 0.0 Seconds Percent Done = 35.45 %