##############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_max_iter=1000000; glob_display_interval=0.1; glob_max_minutes=10; glob_max_h=0.0001; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; glob_max_minutes=30.0; 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 = 2e-16 est_needed_step_err = 2e-16 opt_iter = 1 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 best_h = 2e-06 opt_iter = 2 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 best_h = 4e-06 opt_iter = 3 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 best_h = 8e-06 opt_iter = 4 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 best_h = 1.6e-05 opt_iter = 5 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 best_h = 3.2e-05 opt_iter = 6 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 best_h = 6.4e-05 opt_iter = 7 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 best_h = 0.000128 opt_iter = 8 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 best_h = 0.0001 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 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.01009999999999999 y[1] (analytic) = 2.543711311032464 y[1] (numeric) = 2.543711311032595 absolute error = 1.310063169057685e-13 relative error = 5.150203811948866e-12 % Correct digits = 14 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.02009999999999993 y[1] (analytic) = 2.55476395077387 y[1] (numeric) = 2.554763950774132 absolute error = 2.62456723021387e-13 relative error = 1.027322790200972e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.03009999999999987 y[1] (analytic) = 2.565804137186869 y[1] (numeric) = 2.565804137187261 absolute error = 3.916866830877552e-13 relative error = 1.526565014885345e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.04000000000000012 y[1] (analytic) = 2.576721677085934 y[1] (numeric) = 2.576721677086455 absolute error = 5.204725539442734e-13 relative error = 2.019902104960308e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.05000000000000041 y[1] (analytic) = 2.587737149360984 y[1] (numeric) = 2.587737149361636 absolute error = 6.514788708500419e-13 relative error = 2.517561998176353e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.06000000000000069 y[1] (analytic) = 2.598740236234605 y[1] (numeric) = 2.598740236235387 absolute error = 7.820410985459603e-13 relative error = 3.009308462776887e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.07000000000000098 y[1] (analytic) = 2.609730960027216 y[1] (numeric) = 2.609730960028128 absolute error = 9.126033262418787e-13 relative error = 3.496924932953095e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.08000000000000126 y[1] (analytic) = 2.620709342863814 y[1] (numeric) = 2.620709342864856 absolute error = 1.042277375518097e-12 relative error = 3.977081160702602e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.09000000000000155 y[1] (analytic) = 2.631675406676254 y[1] (numeric) = 2.631675406677425 absolute error = 1.171063246374615e-12 relative error = 4.449877228034142e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.1000000000000018 y[1] (analytic) = 2.64262917320549 y[1] (numeric) = 2.642629173206789 absolute error = 1.298960938811433e-12 relative error = 4.915411333463041e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.1100000000000021 y[1] (analytic) = 2.653570664003779 y[1] (numeric) = 2.653570664005207 absolute error = 1.427746809667951e-12 relative error = 5.380474049685672e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.1200000000000024 y[1] (analytic) = 2.664499900436847 y[1] (numeric) = 2.664499900438403 absolute error = 1.556088591314619e-12 relative error = 5.840077498443506e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.130000000000002 y[1] (analytic) = 2.675416903686013 y[1] (numeric) = 2.6754169036877 absolute error = 1.686650819010538e-12 relative error = 6.304254176935121e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.1400000000000009 y[1] (analytic) = 2.686321694750295 y[1] (numeric) = 2.686321694752112 absolute error = 1.816768957496606e-12 relative error = 6.763035719240181e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.1500999999999998 y[1] (analytic) = 2.697323158949027 y[1] (numeric) = 2.697323158950977 absolute error = 1.949995720451625e-12 relative error = 7.22937373663233e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.1600999999999987 y[1] (analytic) = 2.708203466317999 y[1] (numeric) = 2.708203466320079 absolute error = 2.080113858937693e-12 relative error = 7.680788702946904e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.1700999999999976 y[1] (analytic) = 2.719071623629468 y[1] (numeric) = 2.719071623631681 absolute error = 2.212896532682862e-12 relative error = 8.138426783068869e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.1800999999999965 y[1] (analytic) = 2.72992765117174 y[1] (numeric) = 2.729927651174083 absolute error = 2.34257058195908e-12 relative error = 8.581072033002786e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.1900999999999954 y[1] (analytic) = 2.740771569060793 y[1] (numeric) = 2.740771569063264 absolute error = 2.470912363605748e-12 relative error = 9.015389649756475e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.2000999999999943 y[1] (analytic) = 2.751603397242174 y[1] (numeric) = 2.751603397244776 absolute error = 2.601474591301667e-12 relative error = 9.454395186126839e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.2100999999999932 y[1] (analytic) = 2.76242315549286 y[1] (numeric) = 2.762423155495592 absolute error = 2.731148640577885e-12 relative error = 9.886785937003213e-11 % Correct digits = 13 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.2200999999999921 y[1] (analytic) = 2.773230863423099 y[1] (numeric) = 2.773230863425959 absolute error = 2.860378600644253e-12 relative error = 1.031424624026283e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.230099999999991 y[1] (analytic) = 2.784026540478204 y[1] (numeric) = 2.784026540481195 absolute error = 2.991384917550022e-12 relative error = 1.074481465624319e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.2400999999999899 y[1] (analytic) = 2.794810205940339 y[1] (numeric) = 2.79481020594346 absolute error = 3.12105896682624e-12 relative error = 1.116733780416453e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.2500999999999888 y[1] (analytic) = 2.80558187893026 y[1] (numeric) = 2.80558187893351 absolute error = 3.250288926892608e-12 relative error = 1.158507955623063e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.2600999999999877 y[1] (analytic) = 2.816341578409037 y[1] (numeric) = 2.816341578412419 absolute error = 3.382183422218077e-12 relative error = 1.200913784090311e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.2700999999999866 y[1] (analytic) = 2.827089323179748 y[1] (numeric) = 2.827089323183259 absolute error = 3.510525203864745e-12 relative error = 1.241745414650113e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.2800999999999855 y[1] (analytic) = 2.83782513188914 y[1] (numeric) = 2.837825131892781 absolute error = 3.641087431560663e-12 relative error = 1.28305560150452e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.2900999999999844 y[1] (analytic) = 2.848549023029273 y[1] (numeric) = 2.848549023033047 absolute error = 3.773870105305832e-12 relative error = 1.324839444501654e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.3000999999999833 y[1] (analytic) = 2.85926101493913 y[1] (numeric) = 2.859261014943036 absolute error = 3.905764600631301e-12 relative error = 1.366004915334548e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.3100999999999822 y[1] (analytic) = 2.869961125806211 y[1] (numeric) = 2.869961125810244 absolute error = 4.033662293068119e-12 relative error = 1.405476282169156e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.3200999999999811 y[1] (analytic) = 2.88064937366809 y[1] (numeric) = 2.880649373672253 absolute error = 4.162892253134487e-12 relative error = 1.445122857084702e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.33009999999998 y[1] (analytic) = 2.891325776413959 y[1] (numeric) = 2.891325776418253 absolute error = 4.293010391620555e-12 relative error = 1.484789582218947e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.3400999999999789 y[1] (analytic) = 2.901990351786148 y[1] (numeric) = 2.901990351790572 absolute error = 4.423572619316474e-12 relative error = 1.52432368239743e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.3500999999999778 y[1] (analytic) = 2.91264311738161 y[1] (numeric) = 2.912643117386162 absolute error = 4.551470311753292e-12 relative error = 1.562659800162865e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.3600999999999767 y[1] (analytic) = 2.923284090653395 y[1] (numeric) = 2.923284090658077 absolute error = 4.68203253944921e-12 relative error = 1.60163446119351e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.3700999999999756 y[1] (analytic) = 2.933913288912096 y[1] (numeric) = 2.933913288916909 absolute error = 4.812594767145129e-12 relative error = 1.640332993252726e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.3800999999999745 y[1] (analytic) = 2.94453072932728 y[1] (numeric) = 2.944530729332223 absolute error = 4.942712905631197e-12 relative error = 1.678608022800438e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.3900999999999734 y[1] (analytic) = 2.955136428928886 y[1] (numeric) = 2.95513642893396 absolute error = 5.074163311746815e-12 relative error = 1.717065669819511e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.4000999999999723 y[1] (analytic) = 2.965730404608609 y[1] (numeric) = 2.965730404613811 absolute error = 5.201616914973783e-12 relative error = 1.753907538895211e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.4100999999999712 y[1] (analytic) = 2.976312673121268 y[1] (numeric) = 2.976312673126596 absolute error = 5.328626428990901e-12 relative error = 1.790344971854975e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.4200999999999701 y[1] (analytic) = 2.986883251086139 y[1] (numeric) = 2.986883251091597 absolute error = 5.45785638905727e-12 relative error = 1.827274764446382e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.430099999999969 y[1] (analytic) = 2.997442154988283 y[1] (numeric) = 2.997442154993871 absolute error = 5.587530438333488e-12 relative error = 1.86409950531817e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.4400999999999679 y[1] (analytic) = 3.00798940117985 y[1] (numeric) = 3.007989401185568 absolute error = 5.717204487609706e-12 relative error = 1.900673082613654e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.4500999999999667 y[1] (analytic) = 3.018525005881355 y[1] (numeric) = 3.018525005887204 absolute error = 5.848654893725325e-12 relative error = 1.937587027548119e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.4600999999999656 y[1] (analytic) = 3.029048985182948 y[1] (numeric) = 3.029048985188926 absolute error = 5.977884853791693e-12 relative error = 1.973518712649885e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.4700999999999645 y[1] (analytic) = 3.039561355045658 y[1] (numeric) = 3.039561355051767 absolute error = 6.108891170697461e-12 relative error = 2.009793669917776e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.4800999999999634 y[1] (analytic) = 3.050062131302622 y[1] (numeric) = 3.050062131308859 absolute error = 6.23767704155398e-12 relative error = 2.045098353091578e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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] = 0.4900999999999623 y[1] (analytic) = 3.060551329660291 y[1] (numeric) = 3.060551329666658 absolute error = 6.367351090830198e-12 relative error = 2.080458847111363e-10 % Correct digits = 12 h = 0.0001 NO INFO (given) for Equation 1 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 = 5001 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 30 Minutes 0.0 Seconds Percent Done = 100 %