##############ECHO OF PROBLEM################# ##############R:Temp/sing3postode.ode################# diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; ! #BEGIN FIRST INPUT BLOCK # Digits:=16; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(-2.0) x_end=c(-0.7) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=c(0.001) $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 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(0.0) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(2.0) # 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(1.0)/c(x)/c(x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -2.0 y[1] (closed_form) 0.25 y[1] (numeric) 0.25 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) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0000000000000013 Order of pole (three term test) 4.254547669924697e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.990000000000001 y[1] (closed_form) 0.2525188757859647 y[1] (numeric) 0.25251887578596505 absolute error 3.3306690738754696e-16 relative error 1.3189782599454262e-13% Desired digits 12 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.990000000000001 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9900000000000102 Order of pole (three term test) 3.66054555895079e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.9800000000000022 y[1] (closed_form) 0.25507601265176966 y[1] (numeric) 0.25507601265177027 absolute error 6.106226635438361e-16 relative error 2.3938850901572604e-13% Desired digits 12 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9800000000000022 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.98 Order of pole (three term test) 3.1470905000416404e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.9700000000000033 y[1] (closed_form) 0.25767218944059284 y[1] (numeric) 0.25767218944059384 absolute error 9.992007221626409e-16 relative error 3.8777980826410056e-13% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.9700000000000033 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9700000000000137 Order of pole (three term test) 2.703586747765104e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.9600000000000044 y[1] (closed_form) 0.26030820491461776 y[1] (numeric) 0.26030820491461903 absolute error 1.27675647831893e-15 relative error 4.904787687110023e-13% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.9600000000000044 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9600000000000144 Order of pole (three term test) 4.641578080018343e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.9500000000000055 y[1] (closed_form) 0.26298487836949225 y[1] (numeric) 0.26298487836949386 absolute error 1.609823385706477e-15 relative error 6.121353424148914e-13% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.9500000000000055 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9500000000000124 Order of pole (three term test) 3.981272102077787e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.9400000000000066 y[1] (closed_form) 0.2657030502710153 y[1] (numeric) 0.2657030502710171 absolute error 1.7763568394002505e-15 relative error 6.685496600766828e-13% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.9400000000000066 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.94000000000001 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.9300000000000077 y[1] (closed_form) 0.26846358291497546 y[1] (numeric) 0.2684635829149776 absolute error 2.1649348980190553e-15 relative error 8.064166001631243e-13% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.9300000000000077 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9300000000000053 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.9200000000000088 y[1] (closed_form) 0.2712673611111086 y[1] (numeric) 0.2712673611111111 absolute error 2.4980018054066022e-15 relative error 9.208633855450985e-13% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.9200000000000088 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.920000000000016 Order of pole (three term test) 5.0009254051877527e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.91000000000001 y[1] (closed_form) 0.2741152928921876 y[1] (numeric) 0.2741152928921904 absolute error 2.7755575615628914e-15 relative error 1.0125511540337689e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.91000000000001 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9100000000000197 Order of pole (three term test) 8.551543880544887e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.900000000000011 y[1] (closed_form) 0.2770083102493043 y[1] (numeric) 0.27700831024930733 absolute error 3.0531133177191805e-15 relative error 1.1021739076966369e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.900000000000011 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9000000000000192 Order of pole (three term test) 3.6527634120364176e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8900000000000121 y[1] (closed_form) 0.2799473698944563 y[1] (numeric) 0.2799473698944596 absolute error 3.3306690738754696e-15 relative error 1.1897482998790716e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8900000000000121 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8900000000000194 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8800000000000132 y[1] (closed_form) 0.2829334540516031 y[1] (numeric) 0.2829334540516068 absolute error 3.7192471324942744e-15 relative error 1.314530706508795e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8800000000000132 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8800000000000165 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8700000000000143 y[1] (closed_form) 0.2859675712774128 y[1] (numeric) 0.2859675712774168 absolute error 3.9968028886505635e-15 relative error 1.3976420021322368e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8700000000000143 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8700000000000168 Order of pole (three term test) 9.064037693127495e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8600000000000154 y[1] (closed_form) 0.28905075731297936 y[1] (numeric) 0.2890507573129838 absolute error 4.440892098500626e-15 relative error 1.536371030397302e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8600000000000154 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8600000000000207 Order of pole (three term test) 3.858618459903657e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8500000000000165 y[1] (closed_form) 0.2921840759678545 y[1] (numeric) 0.2921840759678593 absolute error 4.773959005888173e-15 relative error 1.6338874697652565e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8500000000000165 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8500000000000172 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8400000000000176 y[1] (closed_form) 0.2953686200378015 y[1] (numeric) 0.29536862003780673 absolute error 5.218048215738236e-15 relative error 1.7666224039203712e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8400000000000176 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8400000000000178 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8300000000000187 y[1] (closed_form) 0.29860551225775017 y[1] (numeric) 0.2986055122577558 absolute error 5.6066262743570405e-15 relative error 1.8776030730194676e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8300000000000187 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8300000000000254 Order of pole (three term test) 4.738121560345565e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8200000000000198 y[1] (closed_form) 0.30189590629150415 y[1] (numeric) 0.30189590629151014 absolute error 5.995204332975845e-15 relative error 1.985851483254962e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8200000000000198 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.820000000000017 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.810000000000021 y[1] (closed_form) 0.30524098775982933 y[1] (numeric) 0.3052409877598357 absolute error 6.38378239159465e-15 relative error 2.091390949310372e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.810000000000021 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.810000000000024 Order of pole (three term test) 3.40745989402625e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.800000000000022 y[1] (closed_form) 0.30864197530863446 y[1] (numeric) 0.3086419753086412 absolute error 6.716849298982197e-15 relative error 2.1762591728702848e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.800000000000022 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8000000000000262 Order of pole (three term test) 5.771366517289493e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.7900000000000231 y[1] (closed_form) 0.3121001217190394 y[1] (numeric) 0.31210012171904655 absolute error 7.16093850883226e-15 relative error 2.2944363076150037e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7900000000000231 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7900000000000365 Order of pole (three term test) 9.766173322021753e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.7800000000000242 y[1] (closed_form) 0.3156167150612211 y[1] (numeric) 0.31561671506122857 absolute error 7.494005416219807e-15 relative error 2.3744006760751482e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7800000000000242 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7800000000000367 Order of pole (three term test) 8.255313441228783e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.7700000000000253 y[1] (closed_form) 0.31919307989401874 y[1] (numeric) 0.3191930798940267 absolute error 7.93809462606987e-15 relative error 2.486925665401501e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7700000000000253 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7700000000000307 Order of pole (three term test) 3.48579219635657e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.7600000000000264 y[1] (closed_form) 0.322830578512387 y[1] (numeric) 0.3228305785123953 absolute error 8.326672684688674e-15 relative error 2.5792701308092412e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7600000000000264 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7600000000000326 Order of pole (three term test) 5.881844415897357e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.7500000000000275 y[1] (closed_form) 0.32653061224488766 y[1] (numeric) 0.3265306122448964 absolute error 8.715250743307479e-15 relative error 2.669045540138e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7500000000000275 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7500000000000357 Order of pole (three term test) 4.9576396748033454e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.7400000000000286 y[1] (closed_form) 0.3302946228035299 y[1] (numeric) 0.330294622803539 absolute error 9.103828801926284e-15 relative error 2.7562752080712925e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7400000000000286 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7400000000000369 Order of pole (three term test) 4.1745622987697043e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.7300000000000297 y[1] (closed_form) 0.33412409368838436 y[1] (numeric) 0.33412409368839396 absolute error 9.603429163007604e-15 relative error 2.874210314196645e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7300000000000297 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7300000000000277 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.7200000000000308 y[1] (closed_form) 0.3380205516495282 y[1] (numeric) 0.3380205516495381 absolute error 9.880984919163893e-15 relative error 2.9231905784855506e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7200000000000308 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7200000000000382 Order of pole (three term test) 2.951120244473521e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.710000000000032 y[1] (closed_form) 0.34198556820900883 y[1] (numeric) 0.3419855682090192 absolute error 1.0380585280245214e-14 relative error 3.0353869417966163e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.710000000000032 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7100000000000357 Order of pole (three term test) 2.4775179510658243e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.700000000000033 y[1] (closed_form) 0.3460207612456613 y[1] (numeric) 0.3460207612456721 absolute error 1.0824674490095276e-14 relative error 3.1283309276376564e-12% Desired digits 12 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.700000000000033 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7000000000000446 Order of pole (three term test) 8.311150196169288e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.6900000000000341 y[1] (closed_form) 0.35012779664576155 y[1] (numeric) 0.35012779664577287 absolute error 1.1324274851176597e-14 relative error 3.2343261402446784e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.6900000000000341 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.690000000000037 Order of pole (three term test) 3.4814858324292844e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.6800000000000352 y[1] (closed_form) 0.3543083900226609 y[1] (numeric) 0.3543083900226725 absolute error 1.1601830607332886e-14 relative error 3.274500670613771e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.6800000000000352 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6800000000000423 Order of pole (three term test) 8.741041864949897e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.6700000000000363 y[1] (closed_form) 0.3585643085087154 y[1] (numeric) 0.35856430850872756 absolute error 1.2156942119645464e-14 relative error 3.3904495877480715e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.6700000000000363 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6700000000000355 Order of pole (three term test) 2.435889751493088e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.6600000000000374 y[1] (closed_form) 0.3628973726230058 y[1] (numeric) 0.3628973726230184 absolute error 1.2601031329495527e-14 relative error 3.472340193155944e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.6600000000000374 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6600000000000512 Order of pole (three term test) 4.068516959230799e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.6500000000000385 y[1] (closed_form) 0.36730945821853195 y[1] (numeric) 0.36730945821854505 absolute error 1.3100631690576847e-14 relative error 3.566646977759713e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.6500000000000385 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6500000000000417 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.6400000000000396 y[1] (closed_form) 0.37180249851277203 y[1] (numeric) 0.3718024985127855 absolute error 1.3489209749195652e-14 relative error 3.628057854143838e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.6400000000000396 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6400000000000459 Order of pole (three term test) 2.8281922697127065e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.6300000000000407 y[1] (closed_form) 0.3763784862057097 y[1] (numeric) 0.3763784862057236 absolute error 1.3933298959045715e-14 relative error 3.701938200429041e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.6300000000000407 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6300000000000456 Order of pole (three term test) 2.3540821895507794e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.6200000000000419 y[1] (closed_form) 0.3810394756896618 y[1] (numeric) 0.3810394756896763 absolute error 1.4488410471358293e-14 relative error 3.8023384441034665e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.6200000000000419 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6200000000000494 Order of pole (three term test) 7.828957167961674e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.610000000000043 y[1] (closed_form) 0.3857875853554827 y[1] (numeric) 0.38578758535549773 absolute error 1.504352198367087e-14 relative error 3.899431333387534e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.610000000000043 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6100000000000492 Order of pole (three term test) 3.250871222785224e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.600000000000044 y[1] (closed_form) 0.3906249999999785 y[1] (numeric) 0.39062499999999406 absolute error 1.554312234475219e-14 relative error 3.97903932025678e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.600000000000044 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.600000000000051 Order of pole (three term test) 5.3932799074841315e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.5900000000000452 y[1] (closed_form) 0.3955539733396397 y[1] (numeric) 0.39555397333965586 absolute error 1.6153745008296028e-14 relative error 4.083828275547551e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.5900000000000452 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5900000000000498 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.5800000000000463 y[1] (closed_form) 0.40057683063609256 y[1] (numeric) 0.4005768306361092 absolute error 1.6653345369377348e-14 relative error 4.157341138011604e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.5800000000000463 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.580000000000051 Order of pole (three term test) 3.697993039768497e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.5700000000000474 y[1] (closed_form) 0.4056959714389791 y[1] (numeric) 0.40569597143899633 absolute error 1.7208456881689926e-14 relative error 4.2417125367680065e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.5700000000000474 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5700000000000498 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.5600000000000485 y[1] (closed_form) 0.4109138724523084 y[1] (numeric) 0.4109138724523263 absolute error 1.787459069646502e-14 relative error 4.349960391891998e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.5600000000000485 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5600000000000531 Order of pole (three term test) 2.5234309849375423e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.5500000000000496 y[1] (closed_form) 0.41623309053067054 y[1] (numeric) 0.41623309053068897 absolute error 1.84297022087776e-14 relative error 4.4277359556591016e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.5500000000000496 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5500000000000533 Order of pole (three term test) 4.161351694799955e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.5400000000000507 y[1] (closed_form) 0.42165626581208226 y[1] (numeric) 0.42165626581210125 absolute error 1.8984813721090177e-14 relative error 4.502438422094042e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.5400000000000507 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.540000000000059 Order of pole (three term test) 3.4269289592648016e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.5300000000000518 y[1] (closed_form) 0.42718612499463127 y[1] (numeric) 0.427186124994651 absolute error 1.970645868709653e-14 relative error 4.613084914062739e-12% Desired digits 12 Estimated correct digits 13 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.5300000000000518 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5300000000000598 Order of pole (three term test) 5.637108534640929e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.5200000000000529 y[1] (closed_form) 0.43282548476451277 y[1] (numeric) 0.4328254847645332 absolute error 2.042810365310288e-14 relative error 4.719709068013218e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.5200000000000529 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.520000000000058 Order of pole (three term test) 4.630427731763702e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.510000000000054 y[1] (closed_form) 0.43857725538350445 y[1] (numeric) 0.43857725538352543 absolute error 2.098321516541546e-14 relative error 4.78438288986672e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.510000000000054 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.510000000000056 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.500000000000055 y[1] (closed_form) 0.44444444444441183 y[1] (numeric) 0.4444444444444333 absolute error 2.148281552649678e-14 relative error 4.83363349346213e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.500000000000055 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.500000000000054 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.4900000000000562 y[1] (closed_form) 0.4504301608035335 y[1] (numeric) 0.4504301608035555 absolute error 2.2037927038809357e-14 relative error 4.892640181886434e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.4900000000000562 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4900000000000642 Order of pole (three term test) 5.092505657353903e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.4800000000000573 y[1] (closed_form) 0.4565376186997456 y[1] (numeric) 0.4565376186997683 absolute error 2.270406085358445e-14 relative error 4.973097489369523e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.4800000000000573 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.480000000000064 Order of pole (three term test) 4.1609733055891353e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.4700000000000584 y[1] (closed_form) 0.46277014207039685 y[1] (numeric) 0.46277014207042033 absolute error 2.348121697082206e-14 relative error 5.074056175225343e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.4700000000000584 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4700000000000613 Order of pole (three term test) 3.3951855215326365e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.4600000000000595 y[1] (closed_form) 0.4691311690748351 y[1] (numeric) 0.4691311690748593 absolute error 2.4202861936828413e-14 relative error 5.159082050454765e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.4600000000000595 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4600000000000632 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.4500000000000606 y[1] (closed_form) 0.47562425683705895 y[1] (numeric) 0.4756242568370838 absolute error 2.4868995751603507e-14 relative error 5.228706356775074e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.4500000000000606 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4500000000000655 Order of pole (three term test) 4.5020833434430505e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.4400000000000617 y[1] (closed_form) 0.48225308641971176 y[1] (numeric) 0.48225308641973735 absolute error 2.5590640717609858e-14 relative error 5.3064752592040345e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.4400000000000617 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4400000000000626 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.4300000000000628 y[1] (closed_form) 0.48902146804240415 y[1] (numeric) 0.4890214680424304 absolute error 2.6256774532384952e-14 relative error 5.36924782412787e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.4300000000000628 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.430000000000069 Order of pole (three term test) 5.935872761573851e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.4200000000000639 y[1] (closed_form) 0.49593334655817795 y[1] (numeric) 0.495933346558205 absolute error 2.7033930649622562e-14 relative error 5.451121776190384e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.4200000000000639 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4200000000000688 Order of pole (three term test) 4.8089890765402026e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.410000000000065 y[1] (closed_form) 0.5029928072028106 y[1] (numeric) 0.5029928072028385 absolute error 2.786659791809143e-14 relative error 5.540158332096268e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.410000000000065 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4100000000000663 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.400000000000066 y[1] (closed_form) 0.5102040816326049 y[1] (numeric) 0.5102040816326334 absolute error 2.853273173286652e-14 relative error 5.592415419642367e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.400000000000066 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.400000000000073 Order of pole (three term test) 6.284554909485683e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3900000000000672 y[1] (closed_form) 0.5175715542673274 y[1] (numeric) 0.5175715542673567 absolute error 2.930988785010413e-14 relative error 5.6629634315191674e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.3900000000000672 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3900000000000683 Order of pole (three term test) 5.0684767935903485e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3800000000000683 y[1] (closed_form) 0.5250997689560497 y[1] (numeric) 0.5250997689560799 absolute error 3.019806626980426e-14 relative error 5.750919740422092e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.3800000000000683 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3800000000000703 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3700000000000694 y[1] (closed_form) 0.5327934359848147 y[1] (numeric) 0.5327934359848456 absolute error 3.097522238704187e-14 relative error 5.813739489824477e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.3700000000000694 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3700000000000716 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3600000000000705 y[1] (closed_form) 0.5406574394463107 y[1] (numeric) 0.5406574394463424 absolute error 3.164135620181696e-14 relative error 5.852385243088672e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.3600000000000705 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.360000000000074 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3500000000000716 y[1] (closed_form) 0.5486968449930831 y[1] (numeric) 0.5486968449931154 absolute error 3.2307490016592055e-14 relative error 5.8880400555245265e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.3500000000000716 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3500000000000698 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3400000000000727 y[1] (closed_form) 0.5569169079972663 y[1] (numeric) 0.5569169079972995 absolute error 3.319566843629218e-14 relative error 5.9606142244212704e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.3400000000000727 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.340000000000079 Order of pole (three term test) 3.377593664739286e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3300000000000738 y[1] (closed_form) 0.5653230821413812 y[1] (numeric) 0.565323082141415 absolute error 3.3861802251067274e-14 relative error 5.989814200191954e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.3300000000000738 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3300000000000767 Order of pole (three term test) 5.395636390815429e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.320000000000075 y[1] (closed_form) 0.5739210284664179 y[1] (numeric) 0.5739210284664528 absolute error 3.4861002973229915e-14 relative error 6.0741811580562696e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.320000000000075 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3200000000000764 Order of pole (three term test) 4.302405918093686e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.310000000000076 y[1] (closed_form) 0.582716624905241 y[1] (numeric) 0.5827166249052769 absolute error 3.5860203695392556e-14 relative error 6.15396955616703e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.310000000000076 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3100000000000778 Order of pole (three term test) 3.424777138370139e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.300000000000077 y[1] (closed_form) 0.5917159763312908 y[1] (numeric) 0.5917159763313278 absolute error 3.697042672001771e-14 relative error 6.248002115683734e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.300000000000077 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3000000000000775 Order of pole (three term test) 2.7214102443661045e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.2900000000000782 y[1] (closed_form) 0.6009254251546654 y[1] (numeric) 0.6009254251547036 absolute error 3.8191672047105385e-14 relative error 6.355476145359578e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.2900000000000782 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2900000000000784 Order of pole (three term test) 4.317325079361939e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.2800000000000793 y[1] (closed_form) 0.6103515624999244 y[1] (numeric) 0.6103515624999637 absolute error 3.930189507173054e-14 relative error 6.43922248855313e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.2800000000000793 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2800000000000793 Order of pole (three term test) 3.41839725596407e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.2700000000000804 y[1] (closed_form) 0.6200012400024015 y[1] (numeric) 0.6200012400024418 absolute error 4.030109579389318e-14 relative error 6.500163740597854e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.2700000000000804 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2700000000000886 Order of pole (three term test) 5.403374465132195e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.2600000000000815 y[1] (closed_form) 0.6298815822624532 y[1] (numeric) 0.6298815822624945 absolute error 4.1300296516055823e-14 relative error 6.556835074889872e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.2600000000000815 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2600000000000824 Order of pole (three term test) 4.2625529897189324e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.2500000000000826 y[1] (closed_form) 0.6399999999999154 y[1] (numeric) 0.6399999999999578 absolute error 4.241051954068098e-14 relative error 6.626643678232279e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.2500000000000826 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2500000000000844 Order of pole (three term test) 3.3562463262094e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.2400000000000837 y[1] (closed_form) 0.6503642039541265 y[1] (numeric) 0.65036420395417 absolute error 4.3520742565306136e-14 relative error 6.691749376842375e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.2400000000000837 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.240000000000084 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.2300000000000848 y[1] (closed_form) 0.6609822195782021 y[1] (numeric) 0.660982219578247 absolute error 4.4853010194856324e-14 relative error 6.78581191238075e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.2300000000000848 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2300000000000872 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.220000000000086 y[1] (closed_form) 0.671862402579857 y[1] (numeric) 0.671862402579903 absolute error 4.6074255521943996e-14 relative error 6.85769219188711e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.220000000000086 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2200000000000877 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.210000000000087 y[1] (closed_form) 0.6830134553649725 y[1] (numeric) 0.6830134553650197 absolute error 4.718447854656915e-14 relative error 6.9082795040041825e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.210000000000087 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2100000000000863 Order of pole (three term test) 2.530139941501143e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.200000000000088 y[1] (closed_form) 0.6944444444443425 y[1] (numeric) 0.6944444444443908 absolute error 4.829470157119431e-14 relative error 6.954437026253002e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.200000000000088 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2000000000000877 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.1900000000000892 y[1] (closed_form) 0.706164818868618 y[1] (numeric) 0.7061648188686674 absolute error 4.9404924595819466e-14 relative error 6.996231372015044e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.1900000000000892 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1900000000000934 Order of pole (three term test) 3.0691793711730654e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.1800000000000903 y[1] (closed_form) 0.7181844297614528 y[1] (numeric) 0.7181844297615034 absolute error 5.062616992290714e-14 relative error 7.0491879000666686e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.1800000000000903 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1800000000000979 Order of pole (three term test) 9.530893995361015e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.1700000000000914 y[1] (closed_form) 0.7305135510262574 y[1] (numeric) 0.7305135510263094 absolute error 5.206945985491984e-14 relative error 7.1277883595410915e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.1700000000000914 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1700000000000947 Order of pole (three term test) 3.691639436825081e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.1600000000000925 y[1] (closed_form) 0.7431629013078481 y[1] (numeric) 0.7431629013079017 absolute error 5.362377208939506e-14 relative error 7.215614772350151e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.1600000000000925 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1600000000000994 Order of pole (three term test) 5.70706865259961e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.1500000000000936 y[1] (closed_form) 0.7561436672966633 y[1] (numeric) 0.756143667296718 absolute error 5.473399511402022e-14 relative error 7.238570853830352e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.1500000000000936 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1500000000001014 Order of pole (three term test) 4.4015803140784134e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.1400000000000947 y[1] (closed_form) 0.7694675284701707 y[1] (numeric) 0.7694675284702267 absolute error 5.595524044110789e-14 relative error 7.271943047727589e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.1400000000000947 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.140000000000097 Order of pole (three term test) 3.387029351304228e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.1300000000000958 y[1] (closed_form) 0.7831466833736631 y[1] (numeric) 0.7831466833737206 absolute error 5.750955267558311e-14 relative error 7.343394781146453e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.1300000000000958 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.130000000000096 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.120000000000097 y[1] (closed_form) 0.7971938775508824 y[1] (numeric) 0.7971938775509417 absolute error 5.928590951498336e-14 relative error 7.436824489560801e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.120000000000097 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1200000000001018 Order of pole (three term test) 7.966619803186177e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.110000000000098 y[1] (closed_form) 0.8116224332439115 y[1] (numeric) 0.8116224332439725 absolute error 6.106226635438361e-14 relative error 7.523481837524933e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.110000000000098 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1100000000001014 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.1000000000000991 y[1] (closed_form) 0.8264462809915866 y[1] (numeric) 0.8264462809916493 absolute error 6.272760089132134e-14 relative error 7.590039707851251e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.1000000000000991 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1000000000001044 Order of pole (three term test) 2.3199785551522004e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.0900000000001002 y[1] (closed_form) 0.8416799932664053 y[1] (numeric) 0.8416799932664697 absolute error 6.439293542825908e-14 relative error 7.650524658232869e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.0900000000001002 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0900000000001053 Order of pole (three term test) 3.5279981572692714e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.0800000000001013 y[1] (closed_form) 0.8573388203016225 y[1] (numeric) 0.8573388203016885 absolute error 6.605826996519681e-14 relative error 7.705036608742003e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.0800000000001013 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0800000000001058 Order of pole (three term test) 8.027260016396198e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.0700000000001024 y[1] (closed_form) 0.8734387282730444 y[1] (numeric) 0.8734387282731123 absolute error 6.794564910705958e-14 relative error 7.779097366268741e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.0700000000001024 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0700000000001084 Order of pole (three term test) 4.0483377443404275e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.0600000000001035 y[1] (closed_form) 0.8899964400140661 y[1] (numeric) 0.8899964400141358 absolute error 6.972200594645983e-14 relative error 7.833964588145757e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.0600000000001035 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0600000000001049 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.0500000000001046 y[1] (closed_form) 0.9070294784578692 y[1] (numeric) 0.9070294784579408 absolute error 7.16093850883226e-14 relative error 7.89493470598914e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.0500000000001046 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.050000000000104 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.0400000000001057 y[1] (closed_form) 0.9245562130175634 y[1] (numeric) 0.9245562130176371 absolute error 7.37188088351104e-14 relative error 7.973426363607163e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.0400000000001057 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0400000000001113 Order of pole (three term test) 3.449797329742344e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.0300000000001068 y[1] (closed_form) 0.9425959091335588 y[1] (numeric) 0.9425959091336342 absolute error 7.538414337204813e-14 relative error 7.997503770342245e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.0300000000001068 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.030000000000108 Order of pole (three term test) 2.581725972781943e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.020000000000108 y[1] (closed_form) 0.9611687812377819 y[1] (numeric) 0.9611687812378596 absolute error 7.771561172376096e-14 relative error 8.085532243741801e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.020000000000108 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0200000000001113 Order of pole (three term test) 3.853262103531257e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.010000000000109 y[1] (closed_form) 0.9802960494067092 y[1] (numeric) 0.9802960494067892 absolute error 7.993605777301127e-14 relative error 8.15427725342664e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.010000000000109 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.010000000000111 Order of pole (three term test) 2.8672437310793636e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.0000000000001101 y[1] (closed_form) 0.9999999999997797 y[1] (numeric) 0.9999999999998618 absolute error 8.204548151979907e-14 relative error 8.204548151981715e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 1.0000000000001101 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0000000000001157 Order of pole (three term test) 4.254547669938773e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9900000000001101 y[1] (closed_form) 1.020304050606854 y[1] (numeric) 1.020304050606936 absolute error 8.215650382226158e-14 relative error 8.052158939621649e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.9900000000001101 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9900000000001125 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9800000000001101 y[1] (closed_form) 1.0412328196582417 y[1] (numeric) 1.0412328196583234 absolute error 8.171241461241152e-14 relative error 7.847660299377767e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.9800000000001101 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.980000000000108 Order of pole (three term test) 2.3207890400168227e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9700000000001101 y[1] (closed_form) 1.062812201083827 y[1] (numeric) 1.062812201083909 absolute error 8.193445921733655e-14 relative error 7.709213267760947e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.9700000000001101 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9700000000001101 Order of pole (three term test) 3.412207378198867e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9600000000001101 y[1] (closed_form) 1.0850694444441957 y[1] (numeric) 1.0850694444442772 absolute error 8.149037000748649e-14 relative error 7.510152499891676e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.9600000000001101 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.960000000000113 Order of pole (three term test) 2.5004627026021307e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9500000000001101 y[1] (closed_form) 1.108033240996973 y[1] (numeric) 1.1080332409970546 absolute error 8.149037000748649e-14 relative error 7.35450589317736e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.9500000000001101 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9500000000001155 Order of pole (three term test) 3.6527634120484834e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9400000000001101 y[1] (closed_form) 1.1317338162061632 y[1] (numeric) 1.1317338162062442 absolute error 8.104628079763643e-14 relative error 7.161249371280832e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.9400000000001101 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.940000000000111 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9300000000001101 y[1] (closed_form) 1.156203029251663 y[1] (numeric) 1.156203029251744 absolute error 8.104628079763643e-14 relative error 7.0096928261892335e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.9300000000001101 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.930000000000114 Order of pole (three term test) 7.717236919832805e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9200000000001101 y[1] (closed_form) 1.181474480150946 y[1] (numeric) 1.181474480151027 absolute error 8.104628079763643e-14 relative error 6.859757206713589e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.9200000000001101 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9200000000001111 Order of pole (three term test) 2.7898329635503156e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.91000000000011 y[1] (closed_form) 1.2075836251657506 y[1] (numeric) 1.2075836251658318 absolute error 8.126832540256146e-14 relative error 6.729830026587743e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.91000000000011 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9100000000001156 Order of pole (three term test) 8.039798088460846e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.90000000000011 y[1] (closed_form) 1.234567901234266 y[1] (numeric) 1.2345679012343471 absolute error 8.104628079763643e-14 relative error 6.564748744610156e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.90000000000011 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9000000000001147 Order of pole (three term test) 5.771366517308563e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.89000000000011 y[1] (closed_form) 1.2624668602446063 y[1] (numeric) 1.2624668602446873 absolute error 8.104628079763643e-14 relative error 6.41967590198237e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.89000000000011 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8900000000001125 Order of pole (three term test) 4.1276567206279984e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.88000000000011 y[1] (closed_form) 1.291322314049264 y[1] (numeric) 1.2913223140493446 absolute error 8.060219158778636e-14 relative error 6.241833716559735e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.88000000000011 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8800000000001109 Order of pole (three term test) 2.940922207958376e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.87000000000011 y[1] (closed_form) 1.321178491213829 y[1] (numeric) 1.3211784912139097 absolute error 8.08242361927114e-14 relative error 6.1175864374278725e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.87000000000011 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8700000000001147 Order of pole (three term test) 8.34912459756696e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.86000000000011 y[1] (closed_form) 1.3520822065978153 y[1] (numeric) 1.352082206597896 absolute error 8.060219158778636e-14 relative error 5.9613380898342046e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.86000000000011 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8600000000001096 Order of pole (three term test) 2.951120244483243e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.85000000000011 y[1] (closed_form) 1.3840830449823407 y[1] (numeric) 1.3840830449824213 absolute error 8.060219158778636e-14 relative error 5.823508342219073e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.85000000000011 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8500000000001126 Order of pole (three term test) 4.1555750980983375e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.84000000000011 y[1] (closed_form) 1.4172335600903319 y[1] (numeric) 1.4172335600904122 absolute error 8.038014698286133e-14 relative error 5.671623171112181e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.84000000000011 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8400000000001123 Order of pole (three term test) 5.827361243319142e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.83000000000011 y[1] (closed_form) 1.4515894904917042 y[1] (numeric) 1.4515894904917845 absolute error 8.038014698286133e-14 relative error 5.537388325650784e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.83000000000011 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8300000000001095 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.82000000000011 y[1] (closed_form) 1.4872099940507613 y[1] (numeric) 1.4872099940508412 absolute error 7.993605777301127e-14 relative error 5.374900524658719e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.82000000000011 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.820000000000113 Order of pole (three term test) 5.656384539444061e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.81000000000011 y[1] (closed_form) 1.5241579027583119 y[1] (numeric) 1.524157902758392 absolute error 8.01581023779363e-14 relative error 5.259173097017829e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.81000000000011 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8100000000001113 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.80000000000011 y[1] (closed_form) 1.5624999999995703 y[1] (numeric) 1.5624999999996503 absolute error 7.993605777301127e-14 relative error 5.1159076974741285e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.80000000000011 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.800000000000112 Order of pole (three term test) 5.3932799075019055e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.79000000000011 y[1] (closed_form) 1.6023073225440179 y[1] (numeric) 1.6023073225440978 absolute error 7.993605777301127e-14 relative error 4.9888093656150225e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.79000000000011 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7900000000001103 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7800000000001099 y[1] (closed_form) 1.6436554898088727 y[1] (numeric) 1.643655489808952 absolute error 7.926992395823618e-14 relative error 4.822782173620449e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.7800000000001099 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7800000000001122 Order of pole (three term test) 5.04686196989172e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7700000000001099 y[1] (closed_form) 1.6866250632479582 y[1] (numeric) 1.6866250632480375 absolute error 7.926992395823618e-14 relative error 4.699913791485165e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.7700000000001099 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7700000000001127 Order of pole (three term test) 6.853857918552181e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7600000000001099 y[1] (closed_form) 1.7313019390576712 y[1] (numeric) 1.7313019390577502 absolute error 7.904787935331115e-14 relative error 4.565805511448572e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.7600000000001099 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7600000000001135 Order of pole (three term test) 4.630427731778967e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7500000000001099 y[1] (closed_form) 1.7777777777772565 y[1] (numeric) 1.7777777777773358 absolute error 7.926992395823618e-14 relative error 4.458933222652093e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.7500000000001099 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7500000000001122 Order of pole (three term test) 3.112083520005983e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7400000000001099 y[1] (closed_form) 1.8261504747985808 y[1] (numeric) 1.8261504747986599 absolute error 7.904787935331115e-14 relative error 4.328661873388605e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.7400000000001099 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7400000000001112 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7300000000001099 y[1] (closed_form) 1.8765246762989285 y[1] (numeric) 1.876524676299007 absolute error 7.860379014346108e-14 relative error 4.188795976746302e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.7300000000001099 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7300000000001103 Order of pole (three term test) 2.766490233084476e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7200000000001099 y[1] (closed_form) 1.9290123456784236 y[1] (numeric) 1.929012345678502 absolute error 7.838174553853605e-14 relative error 4.063309688718949e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.7200000000001099 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7200000000001113 Order of pole (three term test) 3.658038114904969e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7100000000001099 y[1] (closed_form) 1.9837333862322764 y[1] (numeric) 1.9837333862323545 absolute error 7.815970093361102e-14 relative error 3.940030524064551e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.7100000000001099 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7100000000001102 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7000000000001099 y[1] (closed_form) 2.0408163265299715 y[1] (numeric) 2.0408163265300496 absolute error 7.815970093361102e-14 relative error 3.829825345748143e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 Radius of convergence (given) for eq 1 0.7000000000001099 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7000000000001111 Order of pole (three term test) 6.284554909506351e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; Iterations 1301 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.1538461538377%