##############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_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) * 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 = 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) = 0.609057172997582 y[1] (numeric) = 0.609057172997582 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) = 0.6137463854579579 y[1] (numeric) = 0.6137463854578273 absolute error = 1.305622276959184e-13 relative error = 2.127299333885234e-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 = 2.01 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) = 0.6184017089845004 y[1] (numeric) = 0.6184017089842401 absolute error = 2.603472992745992e-13 relative error = 4.210002907367847e-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) = 0.6230694858394505 y[1] (numeric) = 0.6230694858390594 absolute error = 3.911315715754426e-13 relative error = 6.277495214654558e-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) = 0.627702829575655 y[1] (numeric) = 0.6277028295751359 absolute error = 5.191402863147232e-13 relative error = 8.270478670068714e-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) = 0.6323953205685546 y[1] (numeric) = 0.6323953205679056 absolute error = 6.490363801958665e-13 relative error = 1.026314330745444e-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 = 2.05 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) = 0.6371001969628831 y[1] (numeric) = 0.6371001969621046 absolute error = 7.784883848671598e-13 relative error = 1.221924571014555e-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 = 2.06 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) = 0.6418174364382216 y[1] (numeric) = 0.6418174364373137 absolute error = 9.07940389538453e-13 relative error = 1.414639643598787e-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 = 2.07 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) = 0.6465470168695733 y[1] (numeric) = 0.6465470168685357 absolute error = 1.037614438814671e-12 relative error = 1.604855349636525e-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 = 2.08 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) = 0.6512889163250826 y[1] (numeric) = 0.6512889163239156 absolute error = 1.166955421183502e-12 relative error = 1.791763059270352e-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 = 2.09 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) = 0.6560431130637951 y[1] (numeric) = 0.6560431130624991 absolute error = 1.296074358947408e-12 relative error = 1.975593269921842e-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 = 2.1 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) = 0.6608095855334555 y[1] (numeric) = 0.6608095855320296 absolute error = 1.425859430526089e-12 relative error = 2.157746288403227e-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 = 2.11 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) = 0.6655883123683375 y[1] (numeric) = 0.6655883123667825 absolute error = 1.554978368289994e-12 relative error = 2.33624650462532e-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 = 2.12 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) = 0.67037927238712 y[1] (numeric) = 0.6703792723854353 absolute error = 1.684763439868675e-12 relative error = 2.513149659101907e-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 = 2.13 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) = 0.6751824445907855 y[1] (numeric) = 0.6751824445889727 absolute error = 1.812772154607956e-12 relative error = 2.68486269027128e-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 = 2.14 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) = 0.6800460232926793 y[1] (numeric) = 0.6800460232907366 absolute error = 1.942668248489099e-12 relative error = 2.856671728014811e-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 = 2.15 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) = 0.684873679191655 y[1] (numeric) = 0.6848736791895836 absolute error = 2.071343097043155e-12 relative error = 3.024416268249535e-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 = 2.16 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) = 0.689713485148133 y[1] (numeric) = 0.6897134851459331 absolute error = 2.199906923294748e-12 relative error = 3.189595347439471e-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 = 2.17 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) = 0.6945654208738086 y[1] (numeric) = 0.6945654208714801 absolute error = 2.328470749546341e-12 relative error = 3.352413868540955e-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 = 2.18 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) = 0.699429466252703 y[1] (numeric) = 0.6994294662502457 absolute error = 2.457256620402859e-12 relative error = 3.513230052442565e-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 = 2.19 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) = 0.7043056013392688 y[1] (numeric) = 0.7043056013366836 absolute error = 2.585154312839677e-12 relative error = 3.670500856338342e-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 = 2.2 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) = 0.7091938063565295 y[1] (numeric) = 0.7091938063538155 absolute error = 2.714051205998658e-12 relative error = 3.82695277605715e-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 = 2.21 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) = 0.7140940616942388 y[1] (numeric) = 0.7140940616913962 absolute error = 2.842615032250251e-12 relative error = 3.980729129025306e-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) = 0.7190063479070807 y[1] (numeric) = 0.7190063479041098 absolute error = 2.970956813896919e-12 relative error = 4.132031410494396e-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) = 0.7239306457128931 y[1] (numeric) = 0.7239306457097944 absolute error = 3.098743484031274e-12 relative error = 4.280442473850208e-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) = 0.728866935990919 y[1] (numeric) = 0.7288669359876923 absolute error = 3.226752198770555e-12 relative error = 4.42707995031175e-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) = 0.7338151997800888 y[1] (numeric) = 0.7338151997767333 absolute error = 3.355538069627073e-12 relative error = 4.572729034002931e-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) = 0.7387754182773252 y[1] (numeric) = 0.7387754182738416 absolute error = 3.483546784366354e-12 relative error = 4.715298720265057e-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) = 0.7437475728358804 y[1] (numeric) = 0.7437475728322683 absolute error = 3.612110610617947e-12 relative error = 4.856635157604764e-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) = 0.7487316449636947 y[1] (numeric) = 0.7487316449599548 absolute error = 3.739897280752302e-12 relative error = 4.994976913168464e-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) = 0.7537276163217848 y[1] (numeric) = 0.7537276163179164 absolute error = 3.868350084701433e-12 relative error = 5.132291826560776e-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) = 0.758735468722652 y[1] (numeric) = 0.758735468718655 absolute error = 3.996913910953026e-12 relative error = 5.267862220388774e-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) = 0.76375518412872 y[1] (numeric) = 0.7637551841245958 absolute error = 4.124256491877532e-12 relative error = 5.39997184645289e-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) = 0.768786744650797 y[1] (numeric) = 0.7687867446465451 absolute error = 4.251932139709425e-12 relative error = 5.53070428086109e-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) = 0.7738301325465557 y[1] (numeric) = 0.7738301325421753 absolute error = 4.380495965961018e-12 relative error = 5.660797869870329e-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) = 0.7788853302190413 y[1] (numeric) = 0.7788853302145338 absolute error = 4.507505479978136e-12 relative error = 5.78712334806783e-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) = 0.7839523202152039 y[1] (numeric) = 0.7839523202105687 absolute error = 4.635181127810029e-12 relative error = 5.912580406085945e-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) = 0.7890310852244493 y[1] (numeric) = 0.7890310852196859 absolute error = 4.763411887154234e-12 relative error = 6.037039574681933e-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) = 0.7941216080772131 y[1] (numeric) = 0.7941216080723213 absolute error = 4.891753668800902e-12 relative error = 6.159955375909218e-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) = 0.7992238717435547 y[1] (numeric) = 0.799223871738535 absolute error = 5.01965136123772e-12 relative error = 6.28065744618845e-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) = 0.8043378593317785 y[1] (numeric) = 0.8043378593266308 absolute error = 5.147660075977001e-12 relative error = 6.39987290944322e-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) = 0.8094635540870674 y[1] (numeric) = 0.8094635540817914 absolute error = 5.276001857623669e-12 relative error = 6.517899207425184e-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) = 0.814600939390143 y[1] (numeric) = 0.8146009393847401 absolute error = 5.402900349338324e-12 relative error = 6.632573187778602e-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) = 0.8197499987559462 y[1] (numeric) = 0.8197499987504147 absolute error = 5.53157519789238e-12 relative error = 6.747880703003484e-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) = 0.8249107158323259 y[1] (numeric) = 0.8249107158266676 absolute error = 5.65825164500211e-12 relative error = 6.859229170387241e-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) = 0.830083074398769 y[1] (numeric) = 0.8300830743929823 absolute error = 5.786704448951241e-12 relative error = 6.971235322612213e-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) = 0.8352670583651229 y[1] (numeric) = 0.835267058359209 absolute error = 5.913936007573284e-12 relative error = 7.08029359992802e-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) = 0.8404626517703595 y[1] (numeric) = 0.8404626517643176 absolute error = 6.041944722312564e-12 relative error = 7.188831900603492e-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) = 0.8456698387813435 y[1] (numeric) = 0.8456698387751738 absolute error = 6.16973139244692e-12 relative error = 7.295673925580508e-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) = 0.8508886036916219 y[1] (numeric) = 0.8508886036853246 absolute error = 6.29729601797635e-12 relative error = 7.400846586327779e-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 ) = arcsin ( 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 %