##############ECHO OF PROBLEM################# ##############temp/arcsin_sqrtpostode.ode################# diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2)); ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb 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 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (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 #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 desired_abs_gbl_error 1.0e-10 range 0.5 estimated_steps 500000.0 step_error 2.0e-16 est_needed_step_err 2.0e-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 1.172096533994529e-168 estimated_step_error 1.172096533994529e-168 best_h 2.0e-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 7.865804904946755e-161 estimated_step_error 7.865804904946755e-161 best_h 4.0e-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 5.278649921019754e-153 estimated_step_error 5.278649921019754e-153 best_h 8.0e-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 3.5424387818267094e-145 estimated_step_error 3.5424387818267094e-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 2.377286109685046e-137 estimated_step_error 2.377286109685046e-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 1.59536391118642e-129 estimated_step_error 1.59536391118642e-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 1.070622824928351e-121 estimated_step_error 1.070622824928351e-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 7.184723836425154e-114 estimated_step_error 7.184723836425154e-114 best_h 0.000256 opt_iter 9 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.821446539804459e-106 estimated_step_error 4.821446539804459e-106 best_h 0.000512 opt_iter 10 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.235430101625355e-98 estimated_step_error 3.235430101625355e-98 best_h 0.001024 opt_iter 11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.171008236243644e-90 estimated_step_error 2.171008236243644e-90 best_h 0.002048 opt_iter 12 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.4566006524607436e-82 estimated_step_error 1.4566006524607436e-82 best_h 0.004096 opt_iter 13 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.770543937362864e-75 estimated_step_error 9.770543937362864e-75 best_h 0.008192 opt_iter 14 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.550819349617228e-67 estimated_step_error 6.550819349617228e-67 best_h 0.016384 opt_iter 15 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.388040640368087e-59 estimated_step_error 4.388040640368087e-59 best_h 0.032768 opt_iter 16 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.9339006397091225e-51 estimated_step_error 2.9339006397091225e-51 best_h 0.065536 opt_iter 17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9544915641618e-43 estimated_step_error 1.9544915641618e-43 best_h 0.131072 opt_iter 18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.292731496281798e-35 estimated_step_error 1.292731496281798e-35 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (analytic) 0.609057172997582 y[1] (numeric) 0.609057172997582 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.243627707756313 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.01 y[1] (analytic) 0.6136998951900665 y[1] (numeric) 0.6136998951900672 absolute error 6.661338147750939e-16 relative error 1.0854390232033334e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.2548444947098796 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.02 y[1] (analytic) 0.6183550940668945 y[1] (numeric) 0.6183550940668949 absolute error 4.440892098500626e-16 relative error 7.181782993478832e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.2660612684944903 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.03 y[1] (analytic) 0.6230227465023472 y[1] (numeric) 0.6230227465023473 absolute error 1.1102230246251565e-16 relative error 1.7819943667513812e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.2772780291141688 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.04 y[1] (analytic) 0.627702829575655 y[1] (numeric) 0.6277028295756554 absolute error 3.3306690738754696e-16 relative error 5.306124039821673e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.288494776572927 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.05 y[1] (analytic) 0.6323953205685546 y[1] (numeric) 0.6323953205685546 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.2997115108747788 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.060000000000000005 y[1] (analytic) 0.6371001969628827 y[1] (numeric) 0.6371001969628832 absolute error 5.551115123125783e-16 relative error 8.713095914250972e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.3109282320237368 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.07 y[1] (analytic) 0.6418174364382216 y[1] (numeric) 0.6418174364382216 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.3221449400238074 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.08 y[1] (analytic) 0.6465470168695724 y[1] (numeric) 0.6465470168695728 absolute error 4.440892098500626e-16 relative error 6.868629786589032e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.333361634879001 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09 y[1] (analytic) 0.6512889163250812 y[1] (numeric) 0.6512889163250818 absolute error 5.551115123125783e-16 relative error 8.523275897965728e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.3445783165933207 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09999999999999999 y[1] (analytic) 0.6560431130637943 y[1] (numeric) 0.6560431130637945 absolute error 2.220446049250313e-16 relative error 3.384603854585994e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.3557949851707742 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10999999999999999 y[1] (analytic) 0.660809585533455 y[1] (numeric) 0.6608095855334546 absolute error 4.440892098500626e-16 relative error 6.720380871768991e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.367011640615358 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11999999999999998 y[1] (analytic) 0.665588312368337 y[1] (numeric) 0.6655883123683372 absolute error 1.1102230246251565e-16 relative error 1.668032632175726e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.378228282931078 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12999999999999998 y[1] (analytic) 0.6703792723871183 y[1] (numeric) 0.6703792723871193 absolute error 9.992007221626409e-16 relative error 1.4905006215431448e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.389444912121931 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.13999999999999999 y[1] (analytic) 0.675182444590785 y[1] (numeric) 0.6751824445907854 absolute error 3.3306690738754696e-16 relative error 4.9329912241633055e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.4006615281919172 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15 y[1] (analytic) 0.6799978081605684 y[1] (numeric) 0.6799978081605688 absolute error 3.3306690738754696e-16 relative error 4.898058543578417e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.4118781311450337 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16 y[1] (analytic) 0.6848253424559259 y[1] (numeric) 0.684825342455926 absolute error 1.1102230246251565e-16 relative error 1.621176898395241e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.423094720985276 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17 y[1] (analytic) 0.6896650270125453 y[1] (numeric) 0.6896650270125456 absolute error 3.3306690738754696e-16 relative error 4.829401148994153e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.434311297716641 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000002 y[1] (analytic) 0.6945168415403891 y[1] (numeric) 0.6945168415403892 absolute error 1.1102230246251565e-16 relative error 1.5985545032468338e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.445527861343124 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000003 y[1] (analytic) 0.6993807659217648 y[1] (numeric) 0.6993807659217645 absolute error 3.3306690738754696e-16 relative error 4.762311513508294e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.4567444118687223 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20000000000000004 y[1] (analytic) 0.7042567802094295 y[1] (numeric) 0.7042567802094301 absolute error 5.551115123125783e-16 relative error 7.882231707410769e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.467960949297429 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.21000000000000005 y[1] (analytic) 0.7091448646247316 y[1] (numeric) 0.709144864624731 absolute error 5.551115123125783e-16 relative error 7.827900052640649e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.4791774736332437 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.22000000000000006 y[1] (analytic) 0.7140449995557643 y[1] (numeric) 0.714044999555764 absolute error 3.3306690738754696e-16 relative error 4.66450864574027e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.4903939848801655 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.23000000000000007 y[1] (analytic) 0.7189571655555724 y[1] (numeric) 0.7189571655555725 absolute error 1.1102230246251565e-16 relative error 1.544213032173112e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.5016104830421892 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.24000000000000007 y[1] (analytic) 0.7238813433403708 y[1] (numeric) 0.7238813433403712 absolute error 4.440892098500626e-16 relative error 6.134834305865662e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.5128269681233184 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.25000000000000006 y[1] (analytic) 0.7288175137877979 y[1] (numeric) 0.7288175137877979 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.524043440127557 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.26000000000000006 y[1] (analytic) 0.7337656579351934 y[1] (numeric) 0.7337656579351935 absolute error 1.1102230246251565e-16 relative error 1.51304849527751e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.5352598990589095 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2700000000000001 y[1] (analytic) 0.7387257569779107 y[1] (numeric) 0.7387257569779102 absolute error 4.440892098500626e-16 relative error 6.011557139510188e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.5464763449213885 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2800000000000001 y[1] (analytic) 0.7436977922676444 y[1] (numeric) 0.7436977922676447 absolute error 2.220446049250313e-16 relative error 2.985683260508069e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.5576927777190077 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2900000000000001 y[1] (analytic) 0.7486817453107992 y[1] (numeric) 0.7486817453107988 absolute error 4.440892098500626e-16 relative error 5.931615304253325e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.5689091974557874 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3000000000000001 y[1] (analytic) 0.7536775977668664 y[1] (numeric) 0.7536775977668656 absolute error 7.771561172376096e-16 relative error 1.0311519402199424e-13% Correct digits 15 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.580125604135755 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3100000000000001 y[1] (analytic) 0.7586853314468405 y[1] (numeric) 0.75868533144684 absolute error 4.440892098500626e-16 relative error 5.85340445429686e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.591341997762941 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3200000000000001 y[1] (analytic) 0.7637049283116548 y[1] (numeric) 0.7637049283116547 absolute error 1.1102230246251565e-16 relative error 1.4537329581983444e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.6025583783413917 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3300000000000001 y[1] (analytic) 0.7687363704706405 y[1] (numeric) 0.7687363704706403 absolute error 2.220446049250313e-16 relative error 2.88843631515821e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.613774745875156 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.34000000000000014 y[1] (analytic) 0.7737796401800079 y[1] (numeric) 0.7737796401800082 absolute error 3.3306690738754696e-16 relative error 4.304415496252448e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.624991100368294 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.35000000000000014 y[1] (analytic) 0.7788347198413588 y[1] (numeric) 0.7788347198413587 absolute error 1.1102230246251565e-16 relative error 1.4254924650140128e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.6362074418248866 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.36000000000000015 y[1] (analytic) 0.783901592000209 y[1] (numeric) 0.7839015920002093 absolute error 2.220446049250313e-16 relative error 2.8325571371587685e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.647423770249018 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.37000000000000016 y[1] (analytic) 0.7889802393445478 y[1] (numeric) 0.7889802393445479 absolute error 1.1102230246251565e-16 relative error 1.407162016563918e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.6586400856447967 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.38000000000000017 y[1] (analytic) 0.7940706447034058 y[1] (numeric) 0.7940706447034063 absolute error 4.440892098500626e-16 relative error 5.592565508021454e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.6698563880163455 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3900000000000002 y[1] (analytic) 0.7991727910454558 y[1] (numeric) 0.7991727910454558 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.6810726773678093 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4000000000000002 y[1] (analytic) 0.8042866614776245 y[1] (numeric) 0.8042866614776243 absolute error 2.220446049250313e-16 relative error 2.760764483114689e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.6922889537033567 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4100000000000002 y[1] (analytic) 0.8094122392437333 y[1] (numeric) 0.8094122392437333 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.703505217027185 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4200000000000002 y[1] (analytic) 0.8145495077231564 y[1] (numeric) 0.814549507723156 absolute error 3.3306690738754696e-16 relative error 4.088970703800947e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.714721467343514 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4300000000000002 y[1] (analytic) 0.8196984504294957 y[1] (numeric) 0.8196984504294953 absolute error 4.440892098500626e-16 relative error 5.4177143999402964e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.7259377046566047 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4400000000000002 y[1] (analytic) 0.8248590510092804 y[1] (numeric) 0.8248590510092808 absolute error 4.440892098500626e-16 relative error 5.383819324121913e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.7371539289707516 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.45000000000000023 y[1] (analytic) 0.8300312932406859 y[1] (numeric) 0.8300312932406857 absolute error 2.220446049250313e-16 relative error 2.6751353440917144e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.748370140290292 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.46000000000000024 y[1] (analytic) 0.8352151610322625 y[1] (numeric) 0.8352151610322626 absolute error 1.1102230246251565e-16 relative error 1.3292658903042484e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.7595863386196084 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.47000000000000025 y[1] (analytic) 0.8404106384216976 y[1] (numeric) 0.8404106384216972 absolute error 4.440892098500626e-16 relative error 5.284193102125267e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.770802523963137 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.48000000000000026 y[1] (analytic) 0.8456177095745812 y[1] (numeric) 0.8456177095745809 absolute error 2.220446049250313e-16 relative error 2.6258272788153756e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.7820186963253755 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.49000000000000027 y[1] (analytic) 0.850836358783202 y[1] (numeric) 0.8508363587832014 absolute error 5.551115123125783e-16 relative error 6.524304075421204e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.7932348557108804 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2)); Iterations 50 Total Elapsed Time 0.0 Seconds Elapsed Time(since restart) 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 102.00000000000004%