##############ECHO OF PROBLEM################# ##############temp/tan_sqrt_newpostode.ode################# diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( 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=1.4; x_end=2.1; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.01; 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(tan(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 = 0.01 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.7000000000000002 estimated_steps = 70.00000000000001 step_error = 2.988071523335984e-13 est_needed_step_err = 2.988071523335984e-13 opt_iter = 1 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 3.4 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] = 1.4 y[1] (analytic) = -2.514161640922489 y[1] (numeric) = -2.514161640922489 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 3.4 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] = 1.41 y[1] (analytic) = -2.477131584442633 y[1] (numeric) = -2.476654521349345 absolute error = 0.0004770630932879882 relative error = 0.01925869002212613 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.41 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] = 1.42 y[1] (analytic) = -2.441122841917839 y[1] (numeric) = -2.440189907102738 absolute error = 0.0009329348151014827 relative error = 0.03821744645871789 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.42 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] = 1.43 y[1] (analytic) = -2.406091577540579 y[1] (numeric) = -2.404722735171035 absolute error = 0.001368842369544154 relative error = 0.05689070118201137 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.43 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] = 1.44 y[1] (analytic) = -2.371996435107576 y[1] (numeric) = -2.37021050940871 absolute error = 0.001785925698865043 relative error = 0.07529209034346829 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.44 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] = 1.45 y[1] (analytic) = -2.338798364980731 y[1] (numeric) = -2.336613120173222 absolute error = 0.002185244807508813 relative error = 0.09343451065422721 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.45 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] = 1.46 y[1] (analytic) = -2.306460465341849 y[1] (numeric) = -2.303892678961858 absolute error = 0.002567786379991333 relative error = 0.1113301709947476 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.46 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] = 1.47 y[1] (analytic) = -2.274947836382303 y[1] (numeric) = -2.272013366613008 absolute error = 0.002934469769295234 relative error = 0.1289906398012943 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.47 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] = 1.48 y[1] (analytic) = -2.244227446214388 y[1] (numeric) = -2.240941293791192 absolute error = 0.003286152423195521 relative error = 0.1464268886265817 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.48 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] = 1.49 y[1] (analytic) = -2.214268007419503 y[1] (numeric) = -2.210644372611537 absolute error = 0.003623634807965459 relative error = 0.1636493322318478 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.49 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] = 1.5 y[1] (analytic) = -2.185039863261519 y[1] (numeric) = -2.181092198379615 absolute error = 0.003947664881903901 relative error = 0.1806678655286126 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.5 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] = 1.51 y[1] (analytic) = -2.15651488269384 y[1] (numeric) = -2.152255940528763 absolute error = 0.004258942165077162 relative error = 0.1974918976565117 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.51 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] = 1.52 y[1] (analytic) = -2.128666363377312 y[1] (numeric) = -2.124108241930978 absolute error = 0.004558121446334162 relative error = 0.2141303834529668 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.52 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] = 1.53 y[1] (analytic) = -2.101468942004807 y[1] (numeric) = -2.096623125840758 absolute error = 0.004845816164048777 relative error = 0.2305918525460508 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.53 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] = 1.54 y[1] (analytic) = -2.074898511298169 y[1] (numeric) = -2.069775909805197 absolute error = 0.005122601492971501 relative error = 0.2468844362785978 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.54 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] = 1.55 y[1] (analytic) = -2.048932143105341 y[1] (numeric) = -2.043543125939371 absolute error = 0.005389017165969623 relative error = 0.2630158926494306 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.55 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] = 1.56 y[1] (analytic) = -2.02354801708094 y[1] (numeric) = -2.017902447024586 absolute error = 0.005645570056354021 relative error = 0.2789936294419152 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.56 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] = 1.57 y[1] (analytic) = -1.998725354482954 y[1] (numeric) = -1.992832617939242 absolute error = 0.005892736543712029 relative error = 0.294824725693061 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.57 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] = 1.58 y[1] (analytic) = -1.974444356662376 y[1] (numeric) = -1.968313391978697 absolute error = 0.006130964683679352 relative error = 0.3105159516393364 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.58 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] = 1.59 y[1] (analytic) = -1.9506861478622 y[1] (numeric) = -1.944325471662172 absolute error = 0.006360676200027893 relative error = 0.3260737872670444 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.59 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] = 1.6 y[1] (analytic) = -1.927432721977541 y[1] (numeric) = -1.920850453662092 absolute error = 0.00658226831544928 relative error = 0.3415044395788762 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.6 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] = 1.61 y[1] (analytic) = -1.904666892960525 y[1] (numeric) = -1.89787077752472 absolute error = 0.006796115435805605 relative error = 0.3568138586817163 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.61 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] = 1.62 y[1] (analytic) = -1.882372248582037 y[1] (numeric) = -1.875369677880989 absolute error = 0.007002570701047706 relative error = 0.3720077527876135 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.62 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] = 1.63 y[1] (analytic) = -1.860533107288227 y[1] (numeric) = -1.853331139873482 absolute error = 0.007201967414745436 relative error = 0.3870916022151566 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.63 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] = 1.64 y[1] (analytic) = -1.839134477912738 y[1] (numeric) = -1.831739857549794 absolute error = 0.007394620362944027 relative error = 0.4020706724685132 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.64 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] = 1.65 y[1] (analytic) = -1.818162022026492 y[1] (numeric) = -1.810581194994487 absolute error = 0.007580827032004356 relative error = 0.4169500264643575 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.65 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] = 1.66 y[1] (analytic) = -1.797602018725757 y[1] (numeric) = -1.789841149991561 absolute error = 0.007760868734196347 relative error = 0.431734535973524 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.66 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] = 1.67 y[1] (analytic) = -1.777441331676191 y[1] (numeric) = -1.769506320027294 absolute error = 0.007935011648896761 relative error = 0.4464288923344526 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.67 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] = 1.68 y[1] (analytic) = -1.757667378246002 y[1] (numeric) = -1.749563870459433 absolute error = 0.008103507786569208 relative error = 0.4610376164946406 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.68 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] = 1.69 y[1] (analytic) = -1.738268100575331 y[1] (numeric) = -1.73000150469335 absolute error = 0.008266595881981198 relative error = 0.4755650684290372 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.69 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] = 1.7 y[1] (analytic) = -1.719231938441568 y[1] (numeric) = -1.710807436219045 absolute error = 0.008424502222523556 relative error = 0.4900154559808906 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.7 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] = 1.71 y[1] (analytic) = -1.700547803791882 y[1] (numeric) = -1.691970362374923 absolute error = 0.008577441416959264 relative error = 0.5043928431669654 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.71 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] = 1.72 y[1] (analytic) = -1.682205056824624 y[1] (numeric) = -1.673479439715175 absolute error = 0.008725617109448747 relative error = 0.5187011579860222 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.72 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] = 1.73 y[1] (analytic) = -1.664193483510801 y[1] (numeric) = -1.655324260867552 absolute error = 0.008869222643249186 relative error = 0.5329441997656773 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.73 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] = 1.74 y[1] (analytic) = -1.646503274455459 y[1] (numeric) = -1.637494832777362 absolute error = 0.009008441678097112 relative error = 0.5471256460802628 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.74 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] = 1.75 y[1] (analytic) = -1.629125005006667 y[1] (numeric) = -1.619981556241752 absolute error = 0.009143448764915352 relative error = 0.5612490592689621 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.75 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] = 1.76 y[1] (analytic) = -1.612049616527053 y[1] (numeric) = -1.602775206645858 absolute error = 0.009274409881195655 relative error = 0.5753178925829926 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.76 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] = 1.77 y[1] (analytic) = -1.595268398749357 y[1] (numeric) = -1.585866915819255 absolute error = 0.009401482930101679 relative error = 0.5893354959875193 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.77 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] = 1.78 y[1] (analytic) = -1.578772973143466 y[1] (numeric) = -1.569248154937427 absolute error = 0.009524818206038344 relative error = 0.6033051216397285 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.78 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] = 1.79 y[1] (analytic) = -1.56255527722794 y[1] (numeric) = -1.552910718398667 absolute error = 0.009644558829272842 relative error = 0.6172299290673943 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.79 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] = 1.8 y[1] (analytic) = -1.546607549764017 y[1] (numeric) = -1.536846708612102 absolute error = 0.009760841151914779 relative error = 0.6311129900668142 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.8 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] = 1.81 y[1] (analytic) = -1.530922316774701 y[1] (numeric) = -1.52104852163731 absolute error = 0.009873795137391506 relative error = 0.6449572933389137 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.81 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] = 1.82 y[1] (analytic) = -1.515492378335793 y[1] (numeric) = -1.50550883362042 absolute error = 0.009983544715373327 relative error = 0.6587657488806741 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.82 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] = 1.83 y[1] (analytic) = -1.50031079608956 y[1] (numeric) = -1.490220587975608 absolute error = 0.01009020811395178 relative error = 0.6725411921483936 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.83 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] = 1.84 y[1] (analytic) = -1.485370881435338 y[1] (numeric) = -1.475176983264629 absolute error = 0.01019389817070948 relative error = 0.6862863880069435 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.84 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] = 1.85 y[1] (analytic) = -1.470666184354625 y[1] (numeric) = -1.460371461730414 absolute error = 0.01029472262421138 relative error = 0.7000040344797235 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.85 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] = 1.86 y[1] (analytic) = -1.456190482831233 y[1] (numeric) = -1.44579769844393 absolute error = 0.01039278438730307 relative error = 0.7136967663115508 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.86 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] = 1.87 y[1] (analytic) = -1.441937772829835 y[1] (numeric) = -1.431449591026342 absolute error = 0.01048818180349387 relative error = 0.7273671583559791 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.87 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] = 1.88 y[1] (analytic) = -1.427902258798844 y[1] (numeric) = -1.417321249911217 absolute error = 0.01058100888762703 relative error = 0.7410177287994356 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.88 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] = 1.89 y[1] (analytic) = -1.414078344665849 y[1] (numeric) = -1.403406989113936 absolute error = 0.01067135555191334 relative error = 0.7546509422315645 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.89 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] = 1.9 y[1] (analytic) = -1.400460625296089 y[1] (numeric) = -1.389701317477751 absolute error = 0.01075930781833878 relative error = 0.7682692125716863 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.9 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] = 1.91 y[1] (analytic) = -1.387043878386374 y[1] (numeric) = -1.376198930368001 absolute error = 0.01084494801837277 relative error = 0.7818749058601739 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.91 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] = 1.92 y[1] (analytic) = -1.373823056768795 y[1] (numeric) = -1.362894701787956 absolute error = 0.01092835498083899 relative error = 0.7954703429233656 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.92 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] = 1.93 y[1] (analytic) = -1.360793281100244 y[1] (numeric) = -1.349783676891491 absolute error = 0.01100960420875241 relative error = 0.8090578019205682 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.93 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] = 1.94 y[1] (analytic) = -1.347949832915341 y[1] (numeric) = -1.33686106486951 absolute error = 0.01108876804583092 relative error = 0.8226395207786165 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.94 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] = 1.95 y[1] (analytic) = -1.33528814802188 y[1] (numeric) = -1.324122232188488 absolute error = 0.01116591583339122 relative error = 0.8362176995229538 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.95 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] = 1.96 y[1] (analytic) = -1.322803810219232 y[1] (numeric) = -1.311562696160992 absolute error = 0.01124111405824002 relative error = 0.8497945025103155 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.96 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] = 1.97 y[1] (analytic) = -1.310492545321434 y[1] (numeric) = -1.299178118829279 absolute error = 0.01131442649215542 relative error = 0.86337206056981 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.97 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] = 1.98 y[1] (analytic) = -1.298350215467837 y[1] (numeric) = -1.286964301144349 absolute error = 0.01138591432348757 relative error = 0.8769524730571143 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.98 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] = 1.99 y[1] (analytic) = -1.286372813705315 y[1] (numeric) = -1.274917177423916 absolute error = 0.01145563628139956 relative error = 0.8905378098284219 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.99 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 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = -1.274556458827018 y[1] (numeric) = -1.263032810073816 absolute error = 0.01152364875320289 relative error = 0.9041301131381945 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 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] = 2.01 y[1] (analytic) = -1.262897390453587 y[1] (numeric) = -1.251307384558368 absolute error = 0.01159000589521852 relative error = 0.9177313994651469 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 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] = 2.02 y[1] (analytic) = -1.251391964343671 y[1] (numeric) = -1.239737204606084 absolute error = 0.01165475973758734 relative error = 0.9313436612724307 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 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] = 2.03 y[1] (analytic) = -1.240036647921336 y[1] (numeric) = -1.22831868763796 absolute error = 0.01171796028337591 relative error = 0.9449688687038913 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 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] = 2.04 y[1] (analytic) = -1.228828016008764 y[1] (numeric) = -1.217048360406409 absolute error = 0.01177965560235572 relative error = 0.9586089712225201 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 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] = 2.049999999999999 y[1] (analytic) = -1.217762746753328 y[1] (numeric) = -1.205922854833563 absolute error = 0.01183989191976531 relative error = 0.9722658991935493 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 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] = 2.059999999999999 y[1] (analytic) = -1.206837617738771 y[1] (numeric) = -1.194938904038412 absolute error = 0.01189871370035966 relative error = 0.98594156541574 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 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] = 2.069999999999999 y[1] (analytic) = -1.196049502270869 y[1] (numeric) = -1.184093338542833 absolute error = 0.01195616372803565 relative error = 0.9996378666046171 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 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] = 2.079999999999999 y[1] (analytic) = -1.185395365828491 y[1] (numeric) = -1.173383082647195 absolute error = 0.01201228318129588 relative error = 1.013356684830661 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 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] = 2.089999999999999 y[1] (analytic) = -1.174872262671539 y[1] (numeric) = -1.162805150966744 absolute error = 0.0120671117047948 relative error = 1.027099888915193 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 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] = 2.099999999999998 y[1] (analytic) = -1.164477332597708 y[1] (numeric) = -1.152356645120511 absolute error = 0.01212068747719708 relative error = 1.040869335786754 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 3 h = 0.01 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 Finished! diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; Iterations = 71 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 102.9 %