##############ECHO OF PROBLEM################# ##############temp/arccos_sqrtpostode.ode################# diff ( y , x , 1 ) = arccos ( 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) * arccos(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 = 2.532535480592211 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-10 range = 0.5 estimated_steps = 500000 step_error = 1.193848674614856e-14 est_needed_step_err = 1.193848674614856e-14 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 = 2.532535480592211 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-10 range = 0.5 estimated_steps = 250000 step_error = 1.688356987061474e-14 est_needed_step_err = 1.688356987061474e-14 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 = 2.532535480592211 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-10 range = 0.5 estimated_steps = 125000 step_error = 2.387697349229713e-14 est_needed_step_err = 2.387697349229713e-14 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 = 2.532535480592211 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-10 range = 0.5 estimated_steps = 62500 step_error = 3.376713974122948e-14 est_needed_step_err = 3.376713974122948e-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 = 2.532535480592211 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-10 range = 0.5 estimated_steps = 31250 step_error = 4.775394698459425e-14 est_needed_step_err = 4.775394698459425e-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 = 2.532535480592211 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-10 range = 0.5 estimated_steps = 15625 step_error = 6.753427948245896e-14 est_needed_step_err = 6.753427948245896e-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 = 2.532535480592211 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-10 range = 0.5 estimated_steps = 7812.5 step_error = 9.550789396918851e-14 est_needed_step_err = 9.550789396918851e-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 = 2.532535480592211 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-10 range = 0.5 estimated_steps = 3906.25 step_error = 1.350685589649179e-13 est_needed_step_err = 1.350685589649179e-13 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 = 2.532535480592211 glob_desired_digits_correct = 10 estimated_h = 0.000256 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-10 range = 0.5 estimated_steps = 1953.125 step_error = 1.91015787938377e-13 est_needed_step_err = 1.91015787938377e-13 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 = 2.532535480592211 glob_desired_digits_correct = 10 estimated_h = 0.000512 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-10 range = 0.5 estimated_steps = 976.5625 step_error = 2.701371179298358e-13 est_needed_step_err = 2.701371179298358e-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 = 2.532535480592211 glob_desired_digits_correct = 10 estimated_h = 0.001024 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-10 range = 0.5 estimated_steps = 488.28125 step_error = 3.82031575876754e-13 est_needed_step_err = 3.82031575876754e-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 = 2.532535480592211 glob_desired_digits_correct = 10 estimated_h = 0.002048 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-10 range = 0.5 estimated_steps = 244.140625 step_error = 5.402742358596717e-13 est_needed_step_err = 5.402742358596717e-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 = 2.532535480592211 glob_desired_digits_correct = 10 estimated_h = 0.004096 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-10 range = 0.5 estimated_steps = 122.0703125 step_error = 7.640631517535081e-13 est_needed_step_err = 7.640631517535081e-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 = 2.532535480592211 glob_desired_digits_correct = 10 estimated_h = 0.008192 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-10 range = 0.5 estimated_steps = 61.03515625 step_error = 1.080548471719343e-12 est_needed_step_err = 1.080548471719343e-12 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) = 2.532535480592211 y[1] (numeric) = 2.532535480592211 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) = 2.543600721667676 y[1] (numeric) = 2.543600722968743 absolute error = 1.301066809844542e-09 relative error = 5.115059131574377e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 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) = 2.554653486058796 y[1] (numeric) = 2.554653488660137 absolute error = 2.601340920449502e-09 relative error = 1.018275447001125e-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) = 2.565693796891293 y[1] (numeric) = 2.565693800792133 absolute error = 3.900839207204854e-09 relative error = 1.520383769852537e-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) = 2.576721677085934 y[1] (numeric) = 2.576721682285517 absolute error = 5.19958209821425e-09 relative error = 2.017905986685594e-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) = 2.587737149360984 y[1] (numeric) = 2.587737155858573 absolute error = 6.497588689313716e-09 relative error = 2.510915256952674e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.598740236234604 y[1] (numeric) = 2.598740244029483 absolute error = 7.794878520428483e-09 relative error = 2.999483523494724e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.609730960027214 y[1] (numeric) = 2.609730969118684 absolute error = 9.091469355126947e-09 relative error = 3.483680691373696e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.620709342863813 y[1] (numeric) = 2.620709353251192 absolute error = 1.038737984515592e-08 relative error = 3.963575691230597e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.631675406676253 y[1] (numeric) = 2.631675418358882 absolute error = 1.168262908635143e-08 relative error = 4.439236334661167e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.642629173205489 y[1] (numeric) = 2.642629186182725 absolute error = 1.297723617454949e-08 relative error = 4.910729173101576e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.653570664003778 y[1] (numeric) = 2.653570678274995 absolute error = 1.427121754105087e-08 relative error = 5.378118523332665e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.664499900436843 y[1] (numeric) = 2.664499916001436 absolute error = 1.556459272578081e-08 relative error = 5.841468683571355e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.675416903686012 y[1] (numeric) = 2.675416920543389 absolute error = 1.685737682777244e-08 relative error = 6.30084111547156e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.686321694750294 y[1] (numeric) = 2.686321712899886 absolute error = 1.814959160739704e-08 relative error = 6.75629863797237e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.69721429444846 y[1] (numeric) = 2.697214313889712 absolute error = 1.944125216368775e-08 relative error = 7.207900463712765e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.708094723421051 y[1] (numeric) = 2.708094744153427 absolute error = 2.073237626021296e-08 relative error = 7.655705718455224e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.718963002132381 y[1] (numeric) = 2.718963024155362 absolute error = 2.202298121645185e-08 relative error = 8.099772302594797e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.729819150872486 y[1] (numeric) = 2.72981917418557 absolute error = 2.331308435188362e-08 relative error = 8.540157081260293e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.74066318975906 y[1] (numeric) = 2.740663214361761 absolute error = 2.460270165371981e-08 relative error = 8.976915421658473e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.751495138739343 y[1] (numeric) = 2.751495164631194 absolute error = 2.589185132961802e-08 relative error = 9.410102516656065e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.762315017591991 y[1] (numeric) = 2.76231504477254 absolute error = 2.718054981087903e-08 relative error = 9.839771944104077e-07 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 9 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) = 2.773122845928907 y[1] (numeric) = 2.77312287439772 absolute error = 2.846881308471438e-08 relative error = 1.026597618151252e-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) = 2.783918643197048 y[1] (numeric) = 2.783918672953705 absolute error = 2.975665758242485e-08 relative error = 1.068876694911327e-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) = 2.794702428680198 y[1] (numeric) = 2.794702459724298 absolute error = 3.10441001794004e-08 relative error = 1.110819522708935e-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) = 2.80547422150072 y[1] (numeric) = 2.805474253831878 absolute error = 3.23311573069418e-08 relative error = 1.152431095575957e-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) = 2.816234040621273 y[1] (numeric) = 2.816234074239118 absolute error = 3.361784495226061e-08 relative error = 1.193716305795536e-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) = 2.826981904846505 y[1] (numeric) = 2.826981939750683 absolute error = 3.490417821438996e-08 relative error = 1.234679930372074e-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) = 2.83771783282472 y[1] (numeric) = 2.837717869014893 absolute error = 3.61901730805414e-08 relative error = 1.275326696048458e-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) = 2.848441843049515 y[1] (numeric) = 2.848441880525361 absolute error = 3.747584642610491e-08 relative error = 1.315661280483916e-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) = 2.859153953861397 y[1] (numeric) = 2.85915399262261 absolute error = 3.876121335011362e-08 relative error = 1.355688220208119e-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) = 2.869854183449371 y[1] (numeric) = 2.86985422349566 absolute error = 4.004628850751146e-08 relative error = 1.395411959898901e-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) = 2.880542549852506 y[1] (numeric) = 2.880542591183594 absolute error = 4.133108788550999e-08 relative error = 1.434836915970093e-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) = 2.89121907096147 y[1] (numeric) = 2.891219113577097 absolute error = 4.261562702723154e-08 relative error = 1.473967415864471e-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) = 2.90188376452005 y[1] (numeric) = 2.901883808419972 absolute error = 4.389992147579846e-08 relative error = 1.512807715200101e-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) = 2.912536648126649 y[1] (numeric) = 2.912536693310634 absolute error = 4.518398455388706e-08 relative error = 1.551361923049089e-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) = 2.923177739235748 y[1] (numeric) = 2.923177785703581 absolute error = 4.64678335809765e-08 relative error = 1.589634217491179e-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) = 2.933807055159358 y[1] (numeric) = 2.933807102910841 absolute error = 4.775148232383231e-08 relative error = 1.627628587226182e-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) = 2.944424613068448 y[1] (numeric) = 2.944424662103394 absolute error = 4.903494632557681e-08 relative error = 1.66534901616912e-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) = 2.955030429994348 y[1] (numeric) = 2.955030480312587 absolute error = 5.031823935297552e-08 relative error = 1.702799363493248e-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) = 2.965624522830128 y[1] (numeric) = 2.965624574431504 absolute error = 5.160137606097237e-08 relative error = 1.739983455887012e-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) = 2.976206908331969 y[1] (numeric) = 2.976206961216339 absolute error = 5.288437066042206e-08 relative error = 1.77690504354287e-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) = 2.986777603120494 y[1] (numeric) = 2.986777657287734 absolute error = 5.416724002671458e-08 relative error = 1.813567905763131e-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) = 2.997336623682104 y[1] (numeric) = 2.997336679132099 absolute error = 5.544999481799096e-08 relative error = 1.849975554293029e-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) = 3.007883986370268 y[1] (numeric) = 3.007884043102919 absolute error = 5.673265146555195e-08 relative error = 1.886131636812678e-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) = 3.018419707406812 y[1] (numeric) = 3.018419765422036 absolute error = 5.801522373616308e-08 relative error = 1.922039655181193e-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) = 3.028943802883184 y[1] (numeric) = 3.02894386218091 absolute error = 5.929772628476826e-08 relative error = 1.957703085422849e-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) = 3.039456288761698 y[1] (numeric) = 3.039456349341871 absolute error = 6.058017243404379e-08 relative error = 1.99312530527375e-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) = 3.049957180876763 y[1] (numeric) = 3.04995724273934 absolute error = 6.18625772830228e-08 relative error = 2.028309697949246e-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) = 3.060446494936092 y[1] (numeric) = 3.060446558081044 absolute error = 6.314495237802475e-08 relative error = 2.063259478069828e-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 ) = arccos ( 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 %