##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrtpostode.ode################# diff ( y , x , 1 ) = sqrt ( 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=0.1 x_end=0.5 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 #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=10.0 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(0.8 * (x + 2.0) * sqrt(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 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 0.4 estimated_steps 400000.00000000006 step_error 2.4999999999999997e-16 est_needed_step_err 2.4999999999999997e-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 8.415344990229178e-169 estimated_step_error 8.415344990229178e-169 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 5.647441192047533e-161 estimated_step_error 5.647441192047533e-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 3.789931974716501e-153 estimated_step_error 3.789931974716501e-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 2.5433780741975387e-145 estimated_step_error 2.5433780741975387e-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 1.7068291526464142e-137 estimated_step_error 1.7068291526464142e-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 1.1454296548628577e-129 estimated_step_error 1.1454296548628577e-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 7.6867946078048e-122 estimated_step_error 7.6867946078048e-122 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 5.15844848580879e-114 estimated_step_error 5.15844848580879e-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 3.4616794743432704e-106 estimated_step_error 3.4616794743432704e-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 2.3229639868712595e-98 estimated_step_error 2.3229639868712595e-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 1.5587405792957548e-90 estimated_step_error 1.5587405792957548e-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 1.0458194158671238e-82 estimated_step_error 1.0458194158671238e-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 7.015241008029888e-75 estimated_step_error 7.015241008029888e-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 4.7036474280256603e-67 estimated_step_error 4.7036474280256603e-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 3.150940825069223e-59 estimated_step_error 3.150940825069223e-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 2.1070531390336458e-51 estimated_step_error 2.1070531390336458e-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 1.4040499461688466e-43 estimated_step_error 1.4040499461688466e-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 9.291405850230925e-36 estimated_step_error 9.291405850230925e-36 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (analytic) 1.1372713678556832 y[1] (numeric) 1.1372713678556832 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0999999999999712 Order of pole (three term test) 1.2500000000002258 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11 y[1] (analytic) 1.144044864944275 y[1] (numeric) 1.144044864944275 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1099999999999888 Order of pole (three term test) 1.2500000000000362 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12 y[1] (analytic) 1.1508263922859747 y[1] (numeric) 1.1508263922859745 absolute error 2.220446049250313e-16 relative error 1.9294361548657836e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.119999999999997 Order of pole (three term test) 1.2499999999998785 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.13 y[1] (analytic) 1.1576159214548989 y[1] (numeric) 1.1576159214548989 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.130000000000003 Order of pole (three term test) 1.2499999999999956 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.14 y[1] (analytic) 1.164413424258851 y[1] (numeric) 1.164413424258851 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.139999999999998 Order of pole (three term test) 1.2499999999999858 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15000000000000002 y[1] (analytic) 1.171218872736315 y[1] (numeric) 1.171218872736315 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1499999999999977 Order of pole (three term test) 1.2499999999999887 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16000000000000003 y[1] (analytic) 1.1780322391535036 y[1] (numeric) 1.1780322391535034 absolute error 2.220446049250313e-16 relative error 1.8848771497508885e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1599999999999846 Order of pole (three term test) 1.2500000000001197 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17000000000000004 y[1] (analytic) 1.1848534960014563 y[1] (numeric) 1.1848534960014563 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1700000000000004 Order of pole (three term test) 1.2500000000000444 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000005 y[1] (analytic) 1.191682615993191 y[1] (numeric) 1.191682615993191 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1799999999999993 Order of pole (three term test) 1.250000000000016 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000006 y[1] (analytic) 1.1985195720608994 y[1] (numeric) 1.1985195720608994 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1899999999999937 Order of pole (three term test) 1.250000000000058 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20000000000000007 y[1] (analytic) 1.2053643373531946 y[1] (numeric) 1.2053643373531946 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1999999999999873 Order of pole (three term test) 1.2500000000000147 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.21000000000000008 y[1] (analytic) 1.2122168852324038 y[1] (numeric) 1.212216885232404 absolute error 2.220446049250313e-16 relative error 1.831723412122422e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2100000000000026 Order of pole (three term test) 1.2499999999998657 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.22000000000000008 y[1] (analytic) 1.2190771892719083 y[1] (numeric) 1.2190771892719083 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2199999999999775 Order of pole (three term test) 1.2500000000002303 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2300000000000001 y[1] (analytic) 1.225945223253526 y[1] (numeric) 1.225945223253526 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2299999999999844 Order of pole (three term test) 1.2500000000001814 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2400000000000001 y[1] (analytic) 1.232820961164941 y[1] (numeric) 1.232820961164941 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.240000000000011 Order of pole (three term test) 1.250000000000006 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y[1] (analytic) 1.2397043771971739 y[1] (numeric) 1.2397043771971739 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2499999999999805 Order of pole (three term test) 1.2500000000002702 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y[1] (analytic) 1.2465954457420958 y[1] (numeric) 1.2465954457420956 absolute error 2.220446049250313e-16 relative error 1.7812082154114447e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2599999999999816 Order of pole (three term test) 1.2500000000002252 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (analytic) 1.2534941413899818 y[1] (numeric) 1.2534941413899818 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2699999999999783 Order of pole (three term test) 1.2500000000000975 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (analytic) 1.260400438927108 y[1] (numeric) 1.260400438927108 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2799999999999985 Order of pole (three term test) 1.2500000000000349 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y[1] (analytic) 1.267314313333384 y[1] (numeric) 1.267314313333384 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.289999999999987 Order of pole (three term test) 1.2500000000000946 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y[1] (analytic) 1.274235739780028 y[1] (numeric) 1.2742357397800277 absolute error 2.220446049250313e-16 relative error 1.7425708445704323e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2999999999999905 Order of pole (three term test) 1.2500000000001008 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y[1] (analytic) 1.2811646936272763 y[1] (numeric) 1.2811646936272763 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.309999999999996 Order of pole (three term test) 1.250000000000004 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y[1] (analytic) 1.2881011504221347 y[1] (numeric) 1.2881011504221345 absolute error 2.220446049250313e-16 relative error 1.7238134198720587e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.319999999999984 Order of pole (three term test) 1.2500000000000702 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y[1] (analytic) 1.29504508589616 y[1] (numeric) 1.2950450858961597 absolute error 2.220446049250313e-16 relative error 1.714570460466852e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3299999999999725 Order of pole (three term test) 1.2500000000002272 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y[1] (analytic) 1.3019964759632834 y[1] (numeric) 1.301996475963283 absolute error 4.440892098500626e-16 relative error 3.410832656221306e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3400000000000007 Order of pole (three term test) 1.250000000000047 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y[1] (analytic) 1.3089552967176639 y[1] (numeric) 1.3089552967176636 absolute error 2.220446049250313e-16 relative error 1.6963497949993428e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3500000000000156 Order of pole (three term test) 1.2499999999998472 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y[1] (analytic) 1.3159215244315805 y[1] (numeric) 1.3159215244315803 absolute error 2.220446049250313e-16 relative error 1.6873696554279306e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.359999999999982 Order of pole (three term test) 1.2500000000001743 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y[1] (analytic) 1.3228951355533531 y[1] (numeric) 1.322895135553353 absolute error 2.220446049250313e-16 relative error 1.6784747253012793e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.36999999999998 Order of pole (three term test) 1.2500000000002789 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y[1] (analytic) 1.3298761067053002 y[1] (numeric) 1.3298761067053 absolute error 2.220446049250313e-16 relative error 1.669663841657667e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3800000000000194 Order of pole (three term test) 1.2499999999999354 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y[1] (analytic) 1.3368644146817266 y[1] (numeric) 1.3368644146817263 absolute error 2.220446049250313e-16 relative error 1.660935862204803e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3899999999999935 Order of pole (three term test) 1.2500000000000637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y[1] (analytic) 1.3438600364469442 y[1] (numeric) 1.343860036446944 absolute error 2.220446049250313e-16 relative error 1.6522896648679206e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3999999999999844 Order of pole (three term test) 1.2500000000001033 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y[1] (analytic) 1.350862949133322 y[1] (numeric) 1.350862949133322 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.409999999999966 Order of pole (three term test) 1.250000000000374 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y[1] (analytic) 1.3578731300393687 y[1] (numeric) 1.3578731300393685 absolute error 2.220446049250313e-16 relative error 1.6352382267008522e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.419999999999984 Order of pole (three term test) 1.250000000000042 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y[1] (analytic) 1.3648905566278418 y[1] (numeric) 1.3648905566278418 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.429999999999986 Order of pole (three term test) 1.2500000000001477 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y[1] (analytic) 1.37191520652389 y[1] (numeric) 1.37191520652389 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4399999999999697 Order of pole (three term test) 1.2500000000003582 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y[1] (analytic) 1.3789470575132206 y[1] (numeric) 1.3789470575132206 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.449999999999953 Order of pole (three term test) 1.2500000000003262 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y[1] (analytic) 1.385986087540297 y[1] (numeric) 1.3859860875402967 absolute error 2.220446049250313e-16 relative error 1.6020695079204786e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.46000000000001 Order of pole (three term test) 1.2499999999999585 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y[1] (analytic) 1.3930322747065624 y[1] (numeric) 1.3930322747065622 absolute error 2.220446049250313e-16 relative error 1.5939659759268985e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.470000000000018 Order of pole (three term test) 1.249999999999816 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y[1] (analytic) 1.4000855972686923 y[1] (numeric) 1.4000855972686919 absolute error 4.440892098500626e-16 relative error 3.1718718535238016e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.479999999999993 Order of pole (three term test) 1.2500000000000895 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y[1] (analytic) 1.4071460336368704 y[1] (numeric) 1.4071460336368704 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.48999999999998 Order of pole (three term test) 1.2500000000002622 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 40 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 10 Minutes 0.0 Seconds Percent Done 102.50000000000009%