##############ECHO OF PROBLEM################# ##############temp/arcsin_sqrtpostode.ode################# diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.0; x_end=0.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; 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(10.0 * (0.1 * x + 0.2) * arcsin(sqrt ( 0.1 * x + 0.2)) + 5.0 * sqrt( 0.1 * x + 0.2) * sqrt( 0.8 - 0.1 * x) - 5.0 * arcsin(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 = 0.5 estimated_steps = 500000 step_error = 4.714045207910317e-15 est_needed_step_err = 4.714045207910317e-15 opt_iter = 1 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.609057172997582 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 500000 step_error = 4.714045207910317e-15 est_needed_step_err = 4.714045207910317e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.25875997052594e-168 estimated_step_error = 1.25875997052594e-168 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.609057172997582 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 250000 step_error = 6.666666666666667e-15 est_needed_step_err = 6.666666666666667e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.44739325058823e-161 estimated_step_error = 8.44739325058823e-161 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.609057172997582 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 125000 step_error = 9.428090415820634e-15 est_needed_step_err = 9.428090415820634e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.668947075830024e-153 estimated_step_error = 5.668947075830024e-153 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.609057172997582 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 62500 step_error = 1.333333333333333e-14 est_needed_step_err = 1.333333333333333e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.804362530936719e-145 estimated_step_error = 3.804362530936719e-145 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.609057172997582 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 31250 step_error = 1.885618083164127e-14 est_needed_step_err = 1.885618083164127e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.553059843214273e-137 estimated_step_error = 2.553059843214273e-137 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.609057172997582 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 15625 step_error = 2.666666666666667e-14 est_needed_step_err = 2.666666666666667e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.713323238756048e-129 estimated_step_error = 1.713323238756048e-129 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.609057172997582 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 7812.5 step_error = 3.771236166328254e-14 est_needed_step_err = 3.771236166328254e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.14978341491193e-121 estimated_step_error = 1.14978341491193e-121 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.609057172997582 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 3906.25 step_error = 5.333333333333334e-14 est_needed_step_err = 5.333333333333334e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.71595384942909e-114 estimated_step_error = 7.71595384942909e-114 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.609057172997582 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 1953.125 step_error = 7.542472332656507e-14 est_needed_step_err = 7.542472332656507e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.177938614013485e-106 estimated_step_error = 5.177938614013485e-106 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.609057172997582 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 976.5625 step_error = 1.066666666666667e-13 est_needed_step_err = 1.066666666666667e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.474653988869495e-98 estimated_step_error = 3.474653988869495e-98 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.609057172997582 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 488.28125 step_error = 1.508494466531301e-13 est_needed_step_err = 1.508494466531301e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.331530024410956e-90 estimated_step_error = 2.331530024410956e-90 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.609057172997582 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 244.140625 step_error = 2.133333333333333e-13 est_needed_step_err = 2.133333333333333e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.564299984757036e-82 estimated_step_error = 1.564299984757036e-82 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.609057172997582 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 122.0703125 step_error = 3.016988933062603e-13 est_needed_step_err = 3.016988933062603e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.049296638925e-74 estimated_step_error = 1.049296638925e-74 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.609057172997582 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 61.03515625 step_error = 4.266666666666667e-13 est_needed_step_err = 4.266666666666667e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.03517910716513e-67 estimated_step_error = 7.03517910716513e-67 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.221 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 0.609057172997582 y[1] (numeric) = 0.609057172997582 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = 0.6136998951900665 y[1] (numeric) = 0.6136998938889993 absolute error = 1.301067253933752e-09 relative error = 2.120038253437869e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 h = 0.01 Radius of convergence (given) for eq 1 = 2.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.01 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (analytic) = 0.6183550940668945 y[1] (numeric) = 0.6183550914655535 absolute error = 2.601341031471804e-09 relative error = 4.206872485456371e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 h = 0.01 Radius of convergence (given) for eq 1 = 2.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.02 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = 0.6230227465023472 y[1] (numeric) = 0.6230227426015073 absolute error = 3.900839984360971e-09 relative error = 6.26115178981876e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 h = 0.01 Radius of convergence (given) for eq 1 = 2.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.03 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = 0.627702829575655 y[1] (numeric) = 0.6277028243760722 absolute error = 5.199582875370368e-09 relative error = 8.283510333839715e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 h = 0.01 Radius of convergence (given) for eq 1 = 2.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.04 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.05 y[1] (analytic) = 0.6323953205685546 y[1] (numeric) = 0.6323953140709647 absolute error = 6.497589910559043e-09 relative error = 1.027456987619293e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.05 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (analytic) = 0.6371001969628827 y[1] (numeric) = 0.637100189168004 absolute error = 7.794878631450786e-09 relative error = 1.223493363933917e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.06 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.07000000000000001 y[1] (analytic) = 0.6418174364382216 y[1] (numeric) = 0.6418174273467517 absolute error = 9.091469910238459e-09 relative error = 1.41651961976785e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.07 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = 0.6465470168695724 y[1] (numeric) = 0.646547006482192 absolute error = 1.038738040026743e-08 relative error = 1.606593198830407e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.08 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = 0.6512889163250812 y[1] (numeric) = 0.6512889046424514 absolute error = 1.168262986350754e-08 relative error = 1.793770716908121e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.09 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09999999999999999 y[1] (analytic) = 0.6560431130637943 y[1] (numeric) = 0.6560431000865576 absolute error = 1.29772366186387e-08 relative error = 1.978107285972954e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.1 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0.660809585533455 y[1] (numeric) = 0.6608095712622362 absolute error = 1.42712188733185e-08 relative error = 2.159656758277455e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.11 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0.665588312368337 y[1] (numeric) = 0.6655882968037442 absolute error = 1.556459283680312e-08 relative error = 2.338471476673055e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.12 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0.6703792723871183 y[1] (numeric) = 0.6703792555297406 absolute error = 1.685737760492856e-08 relative error = 2.51460304625798e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.13 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 0.675182444590785 y[1] (numeric) = 0.6751824264411925 absolute error = 1.814959249557546e-08 relative error = 2.688101955401933e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.14 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0.6799978081605684 y[1] (numeric) = 0.6799977887193155 absolute error = 1.944125294084387e-08 relative error = 2.859017000868507e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.15 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0.6848253424559259 y[1] (numeric) = 0.6848253217235487 absolute error = 2.073237714839138e-08 relative error = 3.027396310136651e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.16 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0.6896650270125453 y[1] (numeric) = 0.6896650049895635 absolute error = 2.202298177156337e-08 relative error = 3.193286727465558e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.17 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0.6945168415403891 y[1] (numeric) = 0.6945168182273043 absolute error = 2.331308479597283e-08 relative error = 3.356734264969883e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.18 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 0.6993807659217648 y[1] (numeric) = 0.6993807413190617 absolute error = 2.460270309700974e-08 relative error = 3.51778377327607e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.19 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0.7042567802094295 y[1] (numeric) = 0.7042567543175777 absolute error = 2.589185177370723e-08 relative error = 3.676478878344288e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 0.7091448646247316 y[1] (numeric) = 0.7091448374441804 absolute error = 2.718055114314666e-08 relative error = 3.832863001487035e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.21 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.21 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (analytic) = 0.7140449995557643 y[1] (numeric) = 0.7140449710869501 absolute error = 2.846881419493741e-08 relative error = 3.98697760122247e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.22 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.22 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (analytic) = 0.7189571655555724 y[1] (numeric) = 0.7189571357989138 absolute error = 2.975665858162557e-08 relative error = 4.138863899997601e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.23 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.23 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (analytic) = 0.7238813433403708 y[1] (numeric) = 0.7238813122962698 absolute error = 3.104410095655652e-08 relative error = 4.288562102360954e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.24 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.24 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (analytic) = 0.7288175137877979 y[1] (numeric) = 0.7288174814566396 absolute error = 3.233115830614253e-08 relative error = 4.436111604688474e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.25 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (analytic) = 0.7337656579351934 y[1] (numeric) = 0.7337656243173482 absolute error = 3.361784528532752e-08 relative error = 4.581550652006211e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.26 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.26 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (analytic) = 0.7387257569779107 y[1] (numeric) = 0.7387257220737315 absolute error = 3.490417910256838e-08 relative error = 4.724917030828815e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.27 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.27 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (analytic) = 0.7436977922676444 y[1] (numeric) = 0.7436977560774707 absolute error = 3.619017374667521e-08 relative error = 4.866247301383809e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.28 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.28 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (analytic) = 0.7486817453107992 y[1] (numeric) = 0.7486817078349518 absolute error = 3.747584742530563e-08 relative error = 5.005577825294556e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.29 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.29 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000001 y[1] (analytic) = 0.7536775977668664 y[1] (numeric) = 0.7536775590056521 absolute error = 3.876121423829204e-08 relative error = 5.142943660942139e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.3 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3100000000000001 y[1] (analytic) = 0.7586853314468405 y[1] (numeric) = 0.7586852914005512 absolute error = 4.004628928466758e-08 relative error = 5.278379273301337e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.31 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.31 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3200000000000001 y[1] (analytic) = 0.7637049283116548 y[1] (numeric) = 0.7637048869805663 absolute error = 4.13310885516438e-08 relative error = 5.411918532857405e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.32 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.32 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3300000000000001 y[1] (analytic) = 0.7687363704706405 y[1] (numeric) = 0.7687363278550124 absolute error = 4.261562802643226e-08 relative error = 5.543594613630921e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.33 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.33 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3400000000000001 y[1] (analytic) = 0.7737796401800079 y[1] (numeric) = 0.7737795962800863 absolute error = 4.389992158682077e-08 relative error = 5.673439737521153e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.34 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.34 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500000000000001 y[1] (analytic) = 0.7788347198413588 y[1] (numeric) = 0.7788346746573727 absolute error = 4.518398610819929e-08 relative error = 5.801485855356171e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.35 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (analytic) = 0.783901592000209 y[1] (numeric) = 0.7839015455323743 absolute error = 4.646783469119953e-08 relative error = 5.927763786348725e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.36 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.36 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (analytic) = 0.7889802393445478 y[1] (numeric) = 0.7889801915930642 absolute error = 4.775148354507763e-08 relative error = 6.052304121678332e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.37 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.37 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (analytic) = 0.7940706447034058 y[1] (numeric) = 0.7940705956684592 absolute error = 4.903494665864372e-08 relative error = 6.175136555634645e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.38 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.38 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (analytic) = 0.7991727910454558 y[1] (numeric) = 0.799172740727216 absolute error = 5.031823979706473e-08 relative error = 6.296290409391917e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.39 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.39 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (analytic) = 0.8042866614776245 y[1] (numeric) = 0.8042866098762478 absolute error = 5.160137672710619e-08 relative error = 6.415794168748844e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.4 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4100000000000002 y[1] (analytic) = 0.8094122392437333 y[1] (numeric) = 0.8094121863593616 absolute error = 5.288437165962279e-08 relative error = 6.533675807649611e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.41 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4200000000000002 y[1] (analytic) = 0.8145495077231564 y[1] (numeric) = 0.8145494535559163 absolute error = 5.416724002671458e-08 relative error = 6.649962895211101e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.42 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4300000000000002 y[1] (analytic) = 0.8196984504294957 y[1] (numeric) = 0.8196983949795003 absolute error = 5.544999548412477e-08 relative error = 6.76468223833664e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.43 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4400000000000002 y[1] (analytic) = 0.8248590510092804 y[1] (numeric) = 0.8248589942766288 absolute error = 5.673265157657426e-08 relative error = 6.877860103148213e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.44 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4500000000000002 y[1] (analytic) = 0.8300312932406859 y[1] (numeric) = 0.8300312352254611 absolute error = 5.80152248463861e-08 relative error = 6.989522602199446e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.45 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4600000000000002 y[1] (analytic) = 0.8352151610322625 y[1] (numeric) = 0.8352151017345355 absolute error = 5.929772695090207e-08 relative error = 7.099694751423644e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.46 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (analytic) = 0.8404106384216976 y[1] (numeric) = 0.8404105778415238 absolute error = 6.058017376631142e-08 relative error = 7.208401583311915e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.47 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (analytic) = 0.8456177095745812 y[1] (numeric) = 0.8456176477120035 absolute error = 6.186257761608971e-08 relative error = 7.315667223574579e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.48 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (analytic) = 0.850836358783202 y[1] (numeric) = 0.8508362956382483 absolute error = 6.314495371029238e-08 relative error = 7.421515672014445e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 Radius of convergence (given) for eq 1 = 2.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.49 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 50 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 102 %