##############ECHO OF PROBLEM################# ##############R:Temp/sqrt_sqrt_tzeropostode.ode################# diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.0) x_end=c(0.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_min_h=c(0.001) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(-2.0) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(0.5) # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=c(0.0) #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=12 $glob_max_minutes=(3.0) $glob_subiter_method=2 $glob_max_iter=1000000 $glob_upper_ratio_limit=c(1.000001) $glob_lower_ratio_limit=c(0.999999) $glob_look_poles=true $glob_h=c(0.001) $glob_display_interval=c(0.01) $glob_h_reason=1 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(c(0.8) * (c(x) + c(2.0)) * sqrt(sqrt(c(0.1) * c(x) + c(0.2)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (closed_form) 1.0699844879622753 y[1] (numeric) 1.0699844879622753 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 14 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9999999999999978 Order of pole (three term test) 1.2500000000002283 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.010000000000000002 y[1] (closed_form) 1.0766760654258092 y[1] (numeric) 1.0766760654258096 absolute error 4.440892098500626e-16 relative error 4.124631577785023e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 h 0.001 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 2.0099999999999953 Order of pole (three term test) 1.2499999999999698 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.02000000000000001 y[1] (closed_form) 1.0833759709550181 y[1] (numeric) 1.0833759709550186 absolute error 4.440892098500626e-16 relative error 4.099123681491559e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 h 0.001 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 2.0200000000000014 Order of pole (three term test) 1.2499999999999503 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.03000000000000002 y[1] (closed_form) 1.0900841736094704 y[1] (numeric) 1.0900841736094709 absolute error 4.440892098500626e-16 relative error 4.073898333736935e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 h 0.001 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 2.030000000000036 Order of pole (three term test) 1.2499999999993892 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.04000000000000003 y[1] (closed_form) 1.09680064271563 y[1] (numeric) 1.09680064271563 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 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 2.0400000000000236 Order of pole (three term test) 1.2499999999994877 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.05000000000000004 y[1] (closed_form) 1.1035253478632558 y[1] (numeric) 1.1035253478632558 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 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 2.050000000000001 Order of pole (three term test) 1.2500000000001432 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.060000000000000046 y[1] (closed_form) 1.1102582589018688 y[1] (numeric) 1.1102582589018688 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 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 2.060000000000037 Order of pole (three term test) 1.2499999999995457 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.07000000000000005 y[1] (closed_form) 1.116999345937281 y[1] (numeric) 1.1169993459372807 absolute error 2.220446049250313e-16 relative error 1.9878669198209096e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 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 2.069999999999992 Order of pole (three term test) 1.2500000000002118 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.08000000000000006 y[1] (closed_form) 1.1237485793281883 y[1] (numeric) 1.123748579328188 absolute error 2.220446049250313e-16 relative error 1.9759277921203376e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 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 2.0800000000000134 Order of pole (three term test) 1.2499999999999813 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09000000000000007 y[1] (closed_form) 1.130505929682826 y[1] (numeric) 1.130505929682826 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 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 2.090000000000009 Order of pole (three term test) 1.2499999999999254 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10000000000000007 y[1] (closed_form) 1.1372713678556832 y[1] (numeric) 1.1372713678556832 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 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 2.1000000000000196 Order of pole (three term test) 1.2499999999997322 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11000000000000008 y[1] (closed_form) 1.144044864944275 y[1] (numeric) 1.1440448649442754 absolute error 4.440892098500626e-16 relative error 3.881746454687279e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.109999999999983 Order of pole (three term test) 1.2500000000004416 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12000000000000009 y[1] (closed_form) 1.1508263922859747 y[1] (numeric) 1.150826392285975 absolute error 2.220446049250313e-16 relative error 1.929436154865784e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 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 2.1200000000000254 Order of pole (three term test) 1.2499999999994231 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1300000000000001 y[1] (closed_form) 1.1576159214548989 y[1] (numeric) 1.1576159214548996 absolute error 6.661338147750939e-16 relative error 5.754359476482431e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.130000000000052 Order of pole (three term test) 1.249999999999398 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1400000000000001 y[1] (closed_form) 1.164413424258851 y[1] (numeric) 1.164413424258852 absolute error 8.881784197001252e-16 relative error 7.627689626349427e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.140000000000042 Order of pole (three term test) 1.2499999999994393 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1500000000000001 y[1] (closed_form) 1.171218872736315 y[1] (numeric) 1.171218872736316 absolute error 8.881784197001252e-16 relative error 7.583368406838226e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.1500000000000337 Order of pole (three term test) 1.2499999999997677 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16000000000000011 y[1] (closed_form) 1.1780322391535036 y[1] (numeric) 1.178032239153504 absolute error 4.440892098500626e-16 relative error 3.769754299501777e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.1600000000000317 Order of pole (three term test) 1.24999999999974 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17000000000000012 y[1] (closed_form) 1.1848534960014563 y[1] (numeric) 1.1848534960014567 absolute error 4.440892098500626e-16 relative error 3.74805164814669e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.1699999999999857 Order of pole (three term test) 1.2500000000001372 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000013 y[1] (closed_form) 1.191682615993191 y[1] (numeric) 1.1916826159931915 absolute error 4.440892098500626e-16 relative error 3.7265728633621354e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.180000000000027 Order of pole (three term test) 1.2499999999994573 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000014 y[1] (closed_form) 1.1985195720608994 y[1] (numeric) 1.1985195720609 absolute error 6.661338147750939e-16 relative error 5.5579719372429755e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.189999999999996 Order of pole (three term test) 1.2499999999999944 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20000000000000015 y[1] (closed_form) 1.2053643373531946 y[1] (numeric) 1.2053643373531953 absolute error 6.661338147750939e-16 relative error 5.5264105144991033e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.200000000000017 Order of pole (three term test) 1.2499999999998455 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.21000000000000016 y[1] (closed_form) 1.2122168852324038 y[1] (numeric) 1.2122168852324045 absolute error 6.661338147750939e-16 relative error 5.4951702363672663e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.209999999999991 Order of pole (three term test) 1.2500000000001075 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.22000000000000017 y[1] (closed_form) 1.2190771892719083 y[1] (numeric) 1.2190771892719086 absolute error 2.220446049250313e-16 relative error 1.8214154680200934e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 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 2.2200000000000237 Order of pole (three term test) 1.2499999999998501 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.23000000000000018 y[1] (closed_form) 1.225945223253526 y[1] (numeric) 1.2259452232535262 absolute error 2.220446049250313e-16 relative error 1.8112114694304935e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 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 2.230000000000014 Order of pole (three term test) 1.2499999999998523 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.24000000000000019 y[1] (closed_form) 1.232820961164941 y[1] (numeric) 1.232820961164941 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 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 2.2400000000000393 Order of pole (three term test) 1.2499999999995433 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.25000000000000017 y[1] (closed_form) 1.2397043771971739 y[1] (numeric) 1.239704377197174 absolute error 2.220446049250313e-16 relative error 1.7911093080678485e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 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 2.249999999999998 Order of pole (three term test) 1.250000000000245 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2600000000000002 y[1] (closed_form) 1.2465954457420958 y[1] (numeric) 1.2465954457420958 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 2.2600000000000002 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2599999999999842 Order of pole (three term test) 1.2500000000002827 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2700000000000002 y[1] (closed_form) 1.2534941413899818 y[1] (numeric) 1.253494141389982 absolute error 2.220446049250313e-16 relative error 1.7714052071979308e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 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 2.2700000000000022 Order of pole (three term test) 1.2500000000001348 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2800000000000002 y[1] (closed_form) 1.260400438927108 y[1] (numeric) 1.2604004389271082 absolute error 2.220446049250313e-16 relative error 1.7616988860622945e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 2.2800000000000002 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2800000000000415 Order of pole (three term test) 1.2499999999992906 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2900000000000002 y[1] (closed_form) 1.267314313333384 y[1] (numeric) 1.2673143133333846 absolute error 6.661338147750939e-16 relative error 5.2562636416768574e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.290000000000008 Order of pole (three term test) 1.2499999999997953 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3000000000000002 y[1] (closed_form) 1.274235739780028 y[1] (numeric) 1.2742357397800286 absolute error 6.661338147750939e-16 relative error 5.2277125337112973e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.3000000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.299999999999983 Order of pole (three term test) 1.2500000000000904 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3100000000000002 y[1] (closed_form) 1.2811646936272763 y[1] (numeric) 1.2811646936272774 absolute error 1.1102230246251565e-15 relative error 8.665732283660237e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.309999999999994 Order of pole (three term test) 1.250000000000032 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.32000000000000023 y[1] (closed_form) 1.2881011504221347 y[1] (numeric) 1.2881011504221358 absolute error 1.1102230246251565e-15 relative error 8.619067099360293e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.3200000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3199999999999967 Order of pole (three term test) 1.250000000000136 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.33000000000000024 y[1] (closed_form) 1.29504508589616 y[1] (numeric) 1.295045085896161 absolute error 1.1102230246251565e-15 relative error 8.572852302334261e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.3300000000000014 Order of pole (three term test) 1.2500000000000304 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.34000000000000025 y[1] (closed_form) 1.3019964759632834 y[1] (numeric) 1.3019964759632843 absolute error 8.881784197001252e-16 relative error 6.821665312442612e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.3400000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3400000000000296 Order of pole (three term test) 1.2499999999995464 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.35000000000000026 y[1] (closed_form) 1.3089552967176639 y[1] (numeric) 1.3089552967176648 absolute error 8.881784197001252e-16 relative error 6.785399179997371e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.35000000000001 Order of pole (three term test) 1.2499999999996936 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.36000000000000026 y[1] (closed_form) 1.3159215244315805 y[1] (numeric) 1.3159215244315814 absolute error 8.881784197001252e-16 relative error 6.749478621711722e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.3600000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3600000000000376 Order of pole (three term test) 1.2499999999997247 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3700000000000003 y[1] (closed_form) 1.3228951355533531 y[1] (numeric) 1.322895135553354 absolute error 8.881784197001252e-16 relative error 6.713898901205117e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.3700000000000583 Order of pole (three term test) 1.249999999999379 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3800000000000003 y[1] (closed_form) 1.3298761067053002 y[1] (numeric) 1.3298761067053013 absolute error 1.1102230246251565e-15 relative error 8.348319208288335e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.3800000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3800000000000243 Order of pole (three term test) 1.249999999999655 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3900000000000003 y[1] (closed_form) 1.3368644146817266 y[1] (numeric) 1.3368644146817275 absolute error 8.881784197001252e-16 relative error 6.643743448819214e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.390000000000033 Order of pole (three term test) 1.2499999999996125 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4000000000000003 y[1] (closed_form) 1.3438600364469442 y[1] (numeric) 1.3438600364469453 absolute error 1.1102230246251565e-15 relative error 8.261448324339604e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.4000000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4000000000000505 Order of pole (three term test) 1.249999999999465 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4100000000000003 y[1] (closed_form) 1.350862949133322 y[1] (numeric) 1.3508629491333233 absolute error 1.3322676295501878e-15 relative error 9.8623448840975e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.410000000000021 Order of pole (three term test) 1.249999999999703 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4200000000000003 y[1] (closed_form) 1.3578731300393687 y[1] (numeric) 1.3578731300393696 absolute error 8.881784197001252e-16 relative error 6.540952906803409e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.4200000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4199999999999924 Order of pole (three term test) 1.2500000000003921 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4300000000000003 y[1] (closed_form) 1.3648905566278418 y[1] (numeric) 1.3648905566278424 absolute error 6.661338147750939e-16 relative error 4.880492516710448e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.429999999999974 Order of pole (three term test) 1.25000000000045 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.44000000000000034 y[1] (closed_form) 1.37191520652389 y[1] (numeric) 1.3719152065238909 absolute error 8.881784197001252e-16 relative error 6.474003753851232e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 2.4400000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.439999999999963 Order of pole (three term test) 1.2500000000005635 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.45000000000000034 y[1] (closed_form) 1.3789470575132206 y[1] (numeric) 1.3789470575132212 absolute error 6.661338147750939e-16 relative error 4.830742494033041e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 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 2.4499999999999997 Order of pole (three term test) 1.2500000000000133 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.46000000000000035 y[1] (closed_form) 1.385986087540297 y[1] (numeric) 1.3859860875402972 absolute error 2.220446049250313e-16 relative error 1.602069507920479e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 2.4600000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.460000000000002 Order of pole (three term test) 1.2500000000000273 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.47000000000000036 y[1] (closed_form) 1.3930322747065624 y[1] (numeric) 1.3930322747065624 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 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 2.469999999999973 Order of pole (three term test) 1.250000000000391 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.48000000000000037 y[1] (closed_form) 1.4000855972686923 y[1] (numeric) 1.400085597268692 absolute error 2.220446049250313e-16 relative error 1.5859359267619008e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 2.4800000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4799999999999724 Order of pole (three term test) 1.2500000000003526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4900000000000004 y[1] (closed_form) 1.4071460336368704 y[1] (numeric) 1.4071460336368706 absolute error 2.220446049250313e-16 relative error 1.57797840179488e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 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 2.4900000000000144 Order of pole (three term test) 1.2499999999999625 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 500 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.20000000000007%