##############ECHO OF PROBLEM################# ##############temp/arcsin_sqrt_sm_hpostode.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_h=0.000001; 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 SETTING H FOR MAX H 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 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 = 1e-06 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] = 0.0100009999999991 y[1] (analytic) = 0.6137003600865696 y[1] (numeric) = 0.6137003600865694 absolute error = 2.220446049250313e-16 relative error = 3.618127336501959e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 1e-06 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] = 0.02000099999999935 y[1] (analytic) = 0.6183555602099058 y[1] (numeric) = 0.6183555602098999 absolute error = 5.88418203051333e-15 relative error = 9.515855292893132e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 1e-06 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] = 0.03000000000000935 y[1] (analytic) = 0.6230227465023512 y[1] (numeric) = 0.6230227465023326 absolute error = 1.865174681370263e-14 relative error = 2.993750536142301e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.04000000000001935 y[1] (analytic) = 0.6277028295756644 y[1] (numeric) = 0.6277028295756422 absolute error = 2.220446049250313e-14 relative error = 3.537416026547729e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.05000000000002935 y[1] (analytic) = 0.632395320568568 y[1] (numeric) = 0.6323953205685442 absolute error = 2.375877272697835e-14 relative error = 3.756949483057139e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.06000000000003935 y[1] (analytic) = 0.6371001969629018 y[1] (numeric) = 0.6371001969628634 absolute error = 3.841371665203042e-14 relative error = 6.029462372661492e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.07000000000004934 y[1] (analytic) = 0.6418174364382452 y[1] (numeric) = 0.641817436438204 absolute error = 4.118927421359331e-14 relative error = 6.417599752691743e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.08000000000005934 y[1] (analytic) = 0.6465470168696008 y[1] (numeric) = 0.6465470168695547 absolute error = 4.6074255521944e-14 relative error = 7.126203403585807e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.09000000000006934 y[1] (analytic) = 0.6512889163251145 y[1] (numeric) = 0.6512889163250642 absolute error = 5.029310301551959e-14 relative error = 7.722087963556555e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.1000000000000793 y[1] (analytic) = 0.6560431130638325 y[1] (numeric) = 0.6560431130637807 absolute error = 5.173639294753229e-14 relative error = 7.886126981184906e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.1100000000000893 y[1] (analytic) = 0.6608095855334968 y[1] (numeric) = 0.6608095855334428 absolute error = 5.395683899678261e-14 relative error = 8.165262759198809e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.1200000000000993 y[1] (analytic) = 0.6655883123683846 y[1] (numeric) = 0.6655883123683244 absolute error = 6.017408793468348e-14 relative error = 9.04073686639179e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.1300000000001093 y[1] (analytic) = 0.6703792723871715 y[1] (numeric) = 0.6703792723871072 absolute error = 6.439293542825908e-14 relative error = 9.605448449943946e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.1400000000001193 y[1] (analytic) = 0.6751824445908428 y[1] (numeric) = 0.6751824445907679 absolute error = 7.482903185973555e-14 relative error = 1.108278695028594e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.1500000000001293 y[1] (analytic) = 0.6799978081606306 y[1] (numeric) = 0.6799978081605501 absolute error = 8.049116928532385e-14 relative error = 1.183697481364676e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.1600000000001393 y[1] (analytic) = 0.6848253424559938 y[1] (numeric) = 0.6848253424559052 absolute error = 8.859579736508749e-14 relative error = 1.293699164919274e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.1700000000001493 y[1] (analytic) = 0.6896650270126181 y[1] (numeric) = 0.6896650270125186 absolute error = 9.947598300641403e-14 relative error = 1.442381143166101e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.1800000000001593 y[1] (analytic) = 0.6945168415404668 y[1] (numeric) = 0.6945168415403623 absolute error = 1.044719866172272e-13 relative error = 1.504239787555102e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.1900000000001693 y[1] (analytic) = 0.6993807659218465 y[1] (numeric) = 0.6993807659217415 absolute error = 1.050270981295398e-13 relative error = 1.501715563926107e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.2000000000001793 y[1] (analytic) = 0.7042567802095183 y[1] (numeric) = 0.7042567802094102 absolute error = 1.081357225984902e-13 relative error = 1.535458736603424e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.2100000000001893 y[1] (analytic) = 0.7091448646248235 y[1] (numeric) = 0.7091448646247116 absolute error = 1.119104808822158e-13 relative error = 1.57810465061215e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.2200000000001993 y[1] (analytic) = 0.714044999555862 y[1] (numeric) = 0.714044999555745 absolute error = 1.170175067954915e-13 relative error = 1.638797370869857e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.2300000000002093 y[1] (analytic) = 0.718957165555675 y[1] (numeric) = 0.7189571655555512 absolute error = 1.23789867245705e-13 relative error = 1.721797530872774e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.2400000000002193 y[1] (analytic) = 0.7238813433404792 y[1] (numeric) = 0.7238813433403477 absolute error = 1.314504061156185e-13 relative error = 1.815910954535964e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.2500000000002293 y[1] (analytic) = 0.7288175137879112 y[1] (numeric) = 0.7288175137877732 absolute error = 1.38000721960907e-13 relative error = 1.893488004201086e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.2600009999999617 y[1] (analytic) = 0.7337661533477062 y[1] (numeric) = 0.733766153347705 absolute error = 1.221245327087672e-15 relative error = 1.66435222109375e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 1e-06 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] = 0.2700009999996942 y[1] (analytic) = 0.7387262535848445 y[1] (numeric) = 0.7387262535849726 absolute error = 1.281197370417431e-13 relative error = 1.734333068846703e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.2800009999994266 y[1] (analytic) = 0.7436982900671425 y[1] (numeric) = 0.743698290067404 absolute error = 2.614575222992244e-13 relative error = 3.515639686029391e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.2900009999991591 y[1] (analytic) = 0.7486822443010186 y[1] (numeric) = 0.7486822443014102 absolute error = 3.915756607852927e-13 relative error = 5.230198308641256e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.3000009999988915 y[1] (analytic) = 0.7536780979459787 y[1] (numeric) = 0.7536780979465048 absolute error = 5.260236690673992e-13 relative error = 6.97942092918697e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.310000999998624 y[1] (analytic) = 0.7586858328130361 y[1] (numeric) = 0.7586858328136922 absolute error = 6.56030785251005e-13 relative error = 8.646936015907806e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.3200009999983564 y[1] (analytic) = 0.7637054308631366 y[1] (numeric) = 0.7637054308639238 absolute error = 7.872591467616985e-13 relative error = 1.030841362319424e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.3300009999980889 y[1] (analytic) = 0.7687368742056249 y[1] (numeric) = 0.7687368742065452 absolute error = 9.203748874142548e-13 relative error = 1.197256068099147e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.3400009999978213 y[1] (analytic) = 0.7737801450967274 y[1] (numeric) = 0.7737801450977813 absolute error = 1.053823694974199e-12 relative error = 1.361916174319081e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.3500009999975537 y[1] (analytic) = 0.7788352259380602 y[1] (numeric) = 0.7788352259392474 absolute error = 1.18716148023168e-12 relative error = 1.524278102344197e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.3600009999972862 y[1] (analytic) = 0.7839020992751538 y[1] (numeric) = 0.7839020992764738 absolute error = 1.320055176279311e-12 relative error = 1.683954128327911e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.3700009999970186 y[1] (analytic) = 0.7889807477960109 y[1] (numeric) = 0.7889807477974647 absolute error = 1.453837050746642e-12 relative error = 1.842677473192956e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.3800009999967511 y[1] (analytic) = 0.7940711543296768 y[1] (numeric) = 0.7940711543312694 absolute error = 1.592614928824787e-12 relative error = 2.005632518120129e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.3900009999964835 y[1] (analytic) = 0.7991733018448373 y[1] (numeric) = 0.7991733018465664 absolute error = 1.729172360853681e-12 relative error = 2.163701360971399e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.400000999996216 y[1] (analytic) = 0.8042871734484338 y[1] (numeric) = 0.8042871734502988 absolute error = 1.864952636765338e-12 relative error = 2.318764613352258e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.4100009999959484 y[1] (analytic) = 0.8094127523843007 y[1] (numeric) = 0.8094127523863027 absolute error = 2.002065180306545e-12 relative error = 2.473478672542566e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.4200009999956809 y[1] (analytic) = 0.8145500220318254 y[1] (numeric) = 0.8145500220339645 absolute error = 2.139177723847752e-12 relative error = 2.626207925833401e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.4300009999954133 y[1] (analytic) = 0.8196989659046254 y[1] (numeric) = 0.8196989659069008 absolute error = 2.275402088969258e-12 relative error = 2.775899670018626e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.4400009999951457 y[1] (analytic) = 0.824859567649241 y[1] (numeric) = 0.8248595676516526 absolute error = 2.411626454090765e-12 relative error = 2.92368125275389e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.4500009999948782 y[1] (analytic) = 0.83003181104386 y[1] (numeric) = 0.8300318110464103 absolute error = 2.550293309866447e-12 relative error = 3.072524782705811e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.4600009999946106 y[1] (analytic) = 0.8352156799970469 y[1] (numeric) = 0.8352156799997356 absolute error = 2.688627098734742e-12 relative error = 3.219081206358875e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.4700009999943431 y[1] (analytic) = 0.8404111585465022 y[1] (numeric) = 0.8404111585493331 absolute error = 2.830957690491687e-12 relative error = 3.368538913009973e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.4800009999940755 y[1] (analytic) = 0.8456182308578288 y[1] (numeric) = 0.8456182308608021 absolute error = 2.973288282248632e-12 relative error = 3.516111850181387e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.490000999993808 y[1] (analytic) = 0.8508368812233273 y[1] (numeric) = 0.8508368812264411 absolute error = 3.113731494863714e-12 relative error = 3.659610394870063e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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 = 500001 Total Elapsed Time = 13.0 Seconds Elapsed Time(since restart) = 13.0 Seconds Time to Timeout = 9 Minutes 47.0 Seconds Percent Done = 100 %