##############ECHO OF PROBLEM################# ##############temp/ln_sqrtpostode.ode################# diff ( y , x , 1 ) = ln(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=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(5.0 * ln(0.1 * x + 0.2) * ( 0.1 * x + 0.2) - 0.5 * x - 1.0) 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 0.4 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 6.769774203019721e-168 estimated_step_error 6.769774203019721e-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 4.543117561442684e-160 estimated_step_error 4.543117561442684e-160 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 3.0488332413865504e-152 estimated_step_error 3.0488332413865504e-152 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 2.046035549286344e-144 estimated_step_error 2.046035549286344e-144 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 1.373068792528451e-136 estimated_step_error 1.373068792528451e-136 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 9.214476183597742e-129 estimated_step_error 9.214476183597742e-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 6.1836866667815736e-121 estimated_step_error 6.1836866667815736e-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 4.14974332605945e-113 estimated_step_error 4.14974332605945e-113 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 2.784767024780193e-105 estimated_step_error 2.784767024780193e-105 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 1.8687200556996822e-97 estimated_step_error 1.8687200556996822e-97 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 1.2539352791758713e-89 estimated_step_error 1.2539352791758713e-89 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 8.413118386750587e-82 estimated_step_error 8.413118386750587e-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 5.643401349000378e-74 estimated_step_error 5.643401349000378e-74 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 3.7838088921202467e-66 estimated_step_error 3.7838088921202467e-66 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 2.534701929020545e-58 estimated_step_error 2.534701929020545e-58 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 1.6949104517401106e-50 estimated_step_error 1.6949104517401106e-50 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 1.1293388539584937e-42 estimated_step_error 1.1293388539584937e-42 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 7.472612328186663e-35 estimated_step_error 7.472612328186663e-35 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (analytic) -2.688680135677902 y[1] (numeric) -2.688680135677902 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 2.3000000000000003 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] 0.11 y[1] (analytic) -2.6964714885089043 y[1] (numeric) -2.6964714885089047 absolute error 4.440892098500626e-16 relative error 1.646927148099145e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.310952380952381 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] 0.12 y[1] (analytic) -2.7042391445687324 y[1] (numeric) -2.7042391445687324 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 2.321904761904763 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] 0.13 y[1] (analytic) -2.711983215635438 y[1] (numeric) -2.7119832156354384 absolute error 4.440892098500626e-16 relative error 1.6375072208771366e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.3328571428571436 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] 0.14 y[1] (analytic) -2.7197038124375057 y[1] (numeric) -2.7197038124375057 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 2.343809523809525 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] 0.15000000000000002 y[1] (analytic) -2.72740104466856 y[1] (numeric) -2.72740104466856 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 2.3547619047619057 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] 0.16000000000000003 y[1] (analytic) -2.7350750210018098 y[1] (numeric) -2.7350750210018098 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 2.365714285714286 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] 0.17000000000000004 y[1] (analytic) -2.74272584910422 y[1] (numeric) -2.74272584910422 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 2.3766666666666665 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] 0.18000000000000005 y[1] (analytic) -2.7503536356504226 y[1] (numeric) -2.750353635650422 absolute error 4.440892098500626e-16 relative error 1.6146622168644917e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.3876190476190486 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] 0.19000000000000006 y[1] (analytic) -2.7579584863363715 y[1] (numeric) -2.7579584863363715 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 2.398571428571429 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] 0.20000000000000007 y[1] (analytic) -2.765540505892753 y[1] (numeric) -2.765540505892753 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 2.4095238095238085 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] 0.21000000000000008 y[1] (analytic) -2.7730997980981447 y[1] (numeric) -2.7730997980981447 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 2.420476190476191 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] 0.22000000000000008 y[1] (analytic) -2.7806364657919422 y[1] (numeric) -2.7806364657919422 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 2.431428571428573 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] 0.2300000000000001 y[1] (analytic) -2.78815061088705 y[1] (numeric) -2.7881506108870506 absolute error 4.440892098500626e-16 relative error 1.59277338934275e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.442380952380953 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.0931722549540468 Order of pole (six term test) -0.5000000000146425 TOP MAIN SOLVE Loop x[1] 0.2400000000000001 y[1] (analytic) -2.7956423343823493 y[1] (numeric) -2.795642334382349 absolute error 4.440892098500626e-16 relative error 1.5885050973381284e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.4533333333333336 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] 0.2500000000000001 y[1] (analytic) -2.8031117363749316 y[1] (numeric) -2.8031117363749316 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 2.4642857142857153 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] 0.2600000000000001 y[1] (analytic) -2.8105589160721323 y[1] (numeric) -2.810558916072132 absolute error 4.440892098500626e-16 relative error 1.580074366385085e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.4752380952380957 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.8531093599642863 Order of pole (six term test) -0.499999999994321 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (analytic) -2.8179839718033337 y[1] (numeric) -2.8179839718033337 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 2.486190476190476 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.6678703257318748 Order of pole (six term test) -0.5000000000043237 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (analytic) -2.825387001031574 y[1] (numeric) -2.825387001031574 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 2.497142857142857 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] 0.29000000000000015 y[1] (analytic) -2.8327681003649428 y[1] (numeric) -2.8327681003649428 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 2.5080952380952395 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9185501480704144 Order of pole (six term test) -0.5000000000267057 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y[1] (analytic) -2.840127365567783 y[1] (numeric) -2.840127365567783 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 2.5190476190476208 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] 0.31000000000000016 y[1] (analytic) -2.847464891571697 y[1] (numeric) -2.847464891571697 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 2.5300000000000002 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] 0.3200000000000002 y[1] (analytic) -2.8547807724863596 y[1] (numeric) -2.8547807724863596 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 2.5409523809523815 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] 0.3300000000000002 y[1] (analytic) -2.8620751016101487 y[1] (numeric) -2.8620751016101487 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 2.551904761904763 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] 0.3400000000000002 y[1] (analytic) -2.8693479714405896 y[1] (numeric) -2.8693479714405896 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 2.5628571428571445 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] 0.3500000000000002 y[1] (analytic) -2.8765994736846245 y[1] (numeric) -2.876599473684624 absolute error 4.440892098500626e-16 relative error 1.543799245993849e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.573809523809524 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 7.626444418455966 Order of pole (six term test) -0.500000000051406 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y[1] (analytic) -2.883829699268702 y[1] (numeric) -2.8838296992687016 absolute error 4.440892098500626e-16 relative error 1.539928692608573e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.584761904761905 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] 0.3700000000000002 y[1] (analytic) -2.891038738348702 y[1] (numeric) -2.8910387383487017 absolute error 4.440892098500626e-16 relative error 1.5360887557795804e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.595714285714286 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] 0.3800000000000002 y[1] (analytic) -2.8982266803196888 y[1] (numeric) -2.898226680319688 absolute error 8.881784197001252e-16 relative error 3.064558151131763e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.6066666666666674 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] 0.39000000000000024 y[1] (analytic) -2.9053936138254985 y[1] (numeric) -2.905393613825498 absolute error 4.440892098500626e-16 relative error 1.528499297777885e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.617619047619048 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] 0.40000000000000024 y[1] (analytic) -2.912539626768175 y[1] (numeric) -2.9125396267681745 absolute error 4.440892098500626e-16 relative error 1.52474907386182e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.628571428571429 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] 0.41000000000000025 y[1] (analytic) -2.919664806317236 y[1] (numeric) -2.9196648063172352 absolute error 8.881784197001252e-16 relative error 3.04205612157391e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.63952380952381 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] 0.42000000000000026 y[1] (analytic) -2.9267692389187956 y[1] (numeric) -2.9267692389187947 absolute error 8.881784197001252e-16 relative error 3.0346718418710565e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.65047619047619 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] 0.43000000000000027 y[1] (analytic) -2.9338530103045306 y[1] (numeric) -2.9338530103045297 absolute error 8.881784197001252e-16 relative error 3.027344643990645e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.661428571428572 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] 0.4400000000000003 y[1] (analytic) -2.940916205500501 y[1] (numeric) -2.9409162055005007 absolute error 4.440892098500626e-16 relative error 1.5100369368548027e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.672380952380952 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.0922178613076983 Order of pole (six term test) -0.49999999997890576 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y[1] (analytic) -2.947958908835828 y[1] (numeric) -2.947958908835827 absolute error 8.881784197001252e-16 relative error 3.012858887001495e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.6833333333333345 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] 0.4600000000000003 y[1] (analytic) -2.954981203951223 y[1] (numeric) -2.9549812039512218 absolute error 1.3322676295501878e-15 relative error 4.508548574754925e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.694285714285715 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.649822618319593 Order of pole (six term test) -0.49999999996492406 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y[1] (analytic) -2.961983173807387 y[1] (numeric) -2.9619831738073867 absolute error 4.440892098500626e-16 relative error 1.499296868993426e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.705238095238096 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] 0.4800000000000003 y[1] (analytic) -2.968964900693272 y[1] (numeric) -2.9689649006932712 absolute error 8.881784197001252e-16 relative error 2.9915423368350696e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.716190476190478 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] 0.4900000000000003 y[1] (analytic) -2.9759264662342 y[1] (numeric) -2.9759264662341987 absolute error 1.3322676295501878e-15 relative error 4.47681636178352e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.7271428571428586 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.4991482999501207 Order of pole (six term test) -0.5000000000109157 Finished! diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2)); Iterations 40 Total Elapsed Time 0.0 Seconds Elapsed Time(since restart) 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 102.50000000000009%