##############ECHO OF PROBLEM################# ##############R:Temp/lin_coshpostode.ode################# diff ( y , x , 1 ) = cosh ( 2.0 * x + 3.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(2.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_min_h=c(0.000000001) # 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=3 #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(sinh(c(2.0)*c(x)+c(3.0))/c(2)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 6.122941998282746 y[1] (numeric) 6.122941998282746 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 14 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999861961752493 Order of pole (three term test) 22.501661552686002 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11000000000000001 y[1] (closed_form) 6.24704128076929 y[1] (numeric) 6.247041280769288 absolute error 1.7763568394002505e-15 relative error 2.8435170500129965e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499987257461025 Order of pole (three term test) 22.50159640261216 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12000000000000002 y[1] (closed_form) 6.373639463063135 y[1] (numeric) 6.373639463063134 absolute error 8.881784197001252e-16 relative error 1.3935184518160237e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999882371516732 Order of pole (three term test) 22.501533807070928 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.13000000000000003 y[1] (closed_form) 6.5027871861251985 y[1] (numeric) 6.5027871861251985 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499989141520465 Order of pole (three term test) 22.501473665901994 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.14000000000000004 y[1] (closed_form) 6.634536110766698 y[1] (numeric) 6.634536110766697 absolute error 8.881784197001252e-16 relative error 1.3387197007772197e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999899763583713 Order of pole (three term test) 22.501415882871882 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15000000000000005 y[1] (closed_form) 6.768938938314164 y[1] (numeric) 6.768938938314164 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999907470111352 Order of pole (three term test) 22.501360365520057 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16000000000000006 y[1] (closed_form) 6.906049431690678 y[1] (numeric) 6.906049431690678 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499991458413511 Order of pole (three term test) 22.50130702501102 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17000000000000007 y[1] (closed_form) 7.045922436921756 y[1] (numeric) 7.045922436921756 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499992115120853 Order of pole (three term test) 22.50125577599223 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000008 y[1] (closed_form) 7.188613905074487 y[1] (numeric) 7.1886139050744875 absolute error 8.881784197001252e-16 relative error 1.2355350161081187e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999927213382872 Order of pole (three term test) 22.501206536457563 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000009 y[1] (closed_form) 7.334180914638711 y[1] (numeric) 7.334180914638713 absolute error 1.7763568394002505e-15 relative error 2.422024845139446e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999932809476408 Order of pole (three term test) 22.501159227616117 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2000000000000001 y[1] (closed_form) 7.482681694359174 y[1] (numeric) 7.482681694359177 absolute error 2.6645352591003757e-15 relative error 3.560936263143517e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999937975322947 Order of pole (three term test) 22.501113773766217 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2100000000000001 y[1] (closed_form) 7.6341756465278 y[1] (numeric) 7.634175646527801 absolute error 8.881784197001252e-16 relative error 1.1634241348692171e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499994274400127 Order of pole (three term test) 22.501070102174243 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2200000000000001 y[1] (closed_form) 7.788723370745403 y[1] (numeric) 7.788723370745403 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999947146046989 Order of pole (three term test) 22.501028142958347 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.23000000000000012 y[1] (closed_form) 7.946386688162335 y[1] (numeric) 7.946386688162333 absolute error 1.7763568394002505e-15 relative error 2.2354271307315995e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999951209648033 Order of pole (three term test) 22.500987828976598 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.24000000000000013 y[1] (closed_form) 8.107228666207765 y[1] (numeric) 8.107228666207762 absolute error 3.552713678800501e-15 relative error 4.3821555121650676e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999954960825174 Order of pole (three term test) 22.50094909571961 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y[1] (closed_form) 8.2713136438175 y[1] (numeric) 8.2713136438175 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999958423598617 Order of pole (three term test) 22.500911881207298 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y[1] (closed_form) 8.43870725717042 y[1] (numeric) 8.438707257170417 absolute error 1.7763568394002505e-15 relative error 2.1050106198326402e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999961620141806 Order of pole (three term test) 22.50087612588975 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (closed_form) 8.609476465943796 y[1] (numeric) 8.609476465943798 absolute error 1.7763568394002505e-15 relative error 2.063257674757487e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999964570923439 Order of pole (three term test) 22.50084177255191 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (closed_form) 8.78368958009811 y[1] (numeric) 8.783689580098109 absolute error 1.7763568394002505e-15 relative error 2.0223356292384015e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999967294838502 Order of pole (three term test) 22.500808766222107 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y[1] (closed_form) 8.961416287201878 y[1] (numeric) 8.96141628720188 absolute error 1.7763568394002505e-15 relative error 1.9822277890796456e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999969809329292 Order of pole (three term test) 22.50077705408402 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y[1] (closed_form) 9.14272768030768 y[1] (numeric) 9.142727680307676 absolute error 3.552713678800501e-15 relative error 3.8858356094895105e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999972130497072 Order of pole (three term test) 22.500746585392235 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y[1] (closed_form) 9.327696286390255 y[1] (numeric) 9.327696286390259 absolute error 3.552713678800501e-15 relative error 3.808779327414586e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999974273205175 Order of pole (three term test) 22.500717311391025 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y[1] (closed_form) 9.516396095358338 y[1] (numeric) 9.516396095358337 absolute error 1.7763568394002505e-15 relative error 1.866627683001421e-14% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499997625117422 Order of pole (three term test) 22.50068918523635 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y[1] (closed_form) 9.708902589651528 y[1] (numeric) 9.708902589651531 absolute error 3.552713678800501e-15 relative error 3.659233003931101e-14% Desired digits 12 Estimated correct digits 13 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999978077069912 Order of pole (three term test) 22.50066216192088 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y[1] (closed_form) 9.905292774434347 y[1] (numeric) 9.905292774434347 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499997976258419 Order of pole (three term test) 22.50063619820204 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y[1] (closed_form) 10.105645208399265 y[1] (numeric) 10.105645208399265 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499998131851008 Order of pole (three term test) 22.500611252532746 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y[1] (closed_form) 10.310040035191282 y[1] (numeric) 10.31004003519128 absolute error 1.7763568394002505e-15 relative error 1.7229388376155744e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999982754810782 Order of pole (three term test) 22.50058728499499 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y[1] (closed_form) 10.518559015466401 y[1] (numeric) 10.518559015466403 absolute error 1.7763568394002505e-15 relative error 1.6887834510300415e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499998408068352 Order of pole (three term test) 22.500564257235926 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y[1] (closed_form) 10.731285559597039 y[1] (numeric) 10.731285559597035 absolute error 3.552713678800501e-15 relative error 3.310613308228754e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999985304618372 Order of pole (three term test) 22.50054213240651 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y[1] (closed_form) 10.948304761037221 y[1] (numeric) 10.948304761037221 absolute error 0.0 relative error 0.0% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999986434452698 Order of pole (three term test) 22.500520875102566 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y[1] (closed_form) 11.169703430361173 y[1] (numeric) 11.169703430361164 absolute error 8.881784197001252e-15 relative error 7.95167414459639e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999987477421273 Order of pole (three term test) 22.5005004513081 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y[1] (closed_form) 11.395570129988622 y[1] (numeric) 11.39557012998862 absolute error 1.7763568394002505e-15 relative error 1.55881348553644e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999988440202656 Order of pole (three term test) 22.500480828340894 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y[1] (closed_form) 11.625995209611037 y[1] (numeric) 11.625995209611032 absolute error 5.329070518200751e-15 relative error 4.5837542697379474e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499998932896192 Order of pole (three term test) 22.50046197480019 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y[1] (closed_form) 11.861070842332625 y[1] (numeric) 11.861070842332623 absolute error 1.7763568394002505e-15 relative error 1.497636143492511e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999990149390158 Order of pole (three term test) 22.50044386051646 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y[1] (closed_form) 12.100891061540876 y[1] (numeric) 12.100891061540871 absolute error 5.329070518200751e-15 relative error 4.403866203818358e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999990906740893 Order of pole (three term test) 22.50042645650313 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y[1] (closed_form) 12.345551798521097 y[1] (numeric) 12.345551798521095 absolute error 1.7763568394002505e-15 relative error 1.4388638664276186e-14% Desired digits 12 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999991605863753 Order of pole (three term test) 22.50040973491019 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y[1] (closed_form) 12.595150920830289 y[1] (numeric) 12.59515092083028 absolute error 8.881784197001252e-15 relative error 7.051748925304464e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999992251235525 Order of pole (three term test) 22.500393668979648 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y[1] (closed_form) 12.849788271445387 y[1] (numeric) 12.849788271445382 absolute error 5.329070518200751e-15 relative error 4.1472049232460385e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999284698876 Order of pole (three term test) 22.500378233002674 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y[1] (closed_form) 13.10956570870187 y[1] (numeric) 13.109565708701858 absolute error 1.2434497875801753e-14 relative error 9.485057058410395e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999993396938325 Order of pole (three term test) 22.500363402278502 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y[1] (closed_form) 13.374587147038362 y[1] (numeric) 13.374587147038357 absolute error 5.329070518200751e-15 relative error 3.984474780128678e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999993904605772 Order of pole (three term test) 22.500349153074897 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5000000000000003 y[1] (closed_form) 13.644958598563889 y[1] (numeric) 13.644958598563875 absolute error 1.4210854715202004e-14 relative error 1.041472908294326e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999994373241896 Order of pole (three term test) 22.50033546259015 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5100000000000003 y[1] (closed_form) 13.920788215464034 y[1] (numeric) 13.920788215464025 absolute error 8.881784197001252e-15 relative error 6.38023081705592e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999994805847572 Order of pole (three term test) 22.500322308916637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5200000000000004 y[1] (closed_form) 14.202186333263363 y[1] (numeric) 14.202186333263345 absolute error 1.7763568394002505e-14 relative error 1.2507629443220248e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999995205192949 Order of pole (three term test) 22.50030967100572 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y[1] (closed_form) 14.489265514960993 y[1] (numeric) 14.48926551496098 absolute error 1.2434497875801753e-14 relative error 8.58186901396929e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999995573835201 Order of pole (three term test) 22.500297528634103 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5400000000000004 y[1] (closed_form) 14.782140596057404 y[1] (numeric) 14.782140596057387 absolute error 1.7763568394002505e-14 relative error 1.2016912082909214e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999995914134898 Order of pole (three term test) 22.500285862371438 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y[1] (closed_form) 15.08092873049006 y[1] (numeric) 15.080928730490049 absolute error 1.0658141036401503e-14 relative error 7.067297529795543e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999996228271104 Order of pole (three term test) 22.50027465354925 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5600000000000004 y[1] (closed_form) 15.385749437496656 y[1] (numeric) 15.385749437496635 absolute error 2.1316282072803006e-14 relative error 1.3854562079928996e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999651825539 Order of pole (three term test) 22.500263884231085 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y[1] (closed_form) 15.696724649424299 y[1] (numeric) 15.696724649424285 absolute error 1.4210854715202004e-14 relative error 9.053388546076845e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999996785944617 Order of pole (three term test) 22.500253537183735 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5800000000000004 y[1] (closed_form) 16.013978760504177 y[1] (numeric) 16.01397876050416 absolute error 1.7763568394002505e-14 relative error 1.109253899962288e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999997033052918 Order of pole (three term test) 22.500243595849767 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y[1] (closed_form) 16.33763867661081 y[1] (numeric) 16.337638676610798 absolute error 1.0658141036401503e-14 relative error 6.523672880377655e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999726116264 Order of pole (three term test) 22.500234044320948 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6000000000000004 y[1] (closed_form) 16.667833866026182 y[1] (numeric) 16.667833866026168 absolute error 1.4210854715202004e-14 relative error 8.525915742517565e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999997471734456 Order of pole (three term test) 22.50022486731281 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6100000000000004 y[1] (closed_form) 17.004696411228704 y[1] (numeric) 17.004696411228693 absolute error 1.0658141036401503e-14 relative error 6.267763198267755e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999997666116736 Order of pole (three term test) 22.500216050140196 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6200000000000004 y[1] (closed_form) 17.34836106172804 y[1] (numeric) 17.348361061728024 absolute error 1.4210854715202004e-14 relative error 8.191468153468606e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.249999978455542 Order of pole (three term test) 22.50020757869377 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y[1] (closed_form) 17.698965287966615 y[1] (numeric) 17.698965287966608 absolute error 7.105427357601002e-15 relative error 4.014600425501668e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999998011195856 Order of pole (three term test) 22.500199439417433 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y[1] (closed_form) 18.05664933630974 y[1] (numeric) 18.056649336309725 absolute error 1.4210854715202004e-14 relative error 7.870150463976554e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999998164102383 Order of pole (three term test) 22.500191619286603 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y[1] (closed_form) 18.42155628514591 y[1] (numeric) 18.421556285145904 absolute error 7.105427357601002e-15 relative error 3.857126535682771e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999998305252893 Order of pole (three term test) 22.50018410578743 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y[1] (closed_form) 18.793832102120184 y[1] (numeric) 18.79383210212016 absolute error 2.4868995751603507e-14 relative error 1.3232530553892714e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999998435551238 Order of pole (three term test) 22.500176886896707 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y[1] (closed_form) 19.173625702523054 y[1] (numeric) 19.173625702523037 absolute error 1.7763568394002505e-14 relative error 9.26458494058586e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999998555831773 Order of pole (three term test) 22.500169951062688 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y[1] (closed_form) 19.5610890088587 y[1] (numeric) 19.56108900885868 absolute error 2.1316282072803006e-14 relative error 1.0897288010472945e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999998666864703 Order of pole (three term test) 22.50016328718657 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y[1] (closed_form) 19.956377011615878 y[1] (numeric) 19.956377011615864 absolute error 1.4210854715202004e-14 relative error 7.120959233697773e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999998769361004 Order of pole (three term test) 22.500156884604724 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y[1] (closed_form) 20.359647831266287 y[1] (numeric) 20.359647831266265 absolute error 2.1316282072803006e-14 relative error 1.0469867774464948e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999886397703 Order of pole (three term test) 22.500150733071674 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y[1] (closed_form) 20.77106278151478 y[1] (numeric) 20.771062781514765 absolute error 1.4210854715202004e-14 relative error 6.841659892265581e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999998951318622 Order of pole (three term test) 22.500144822743643 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7200000000000005 y[1] (closed_form) 21.19078643382709 y[1] (numeric) 21.190786433827064 absolute error 2.4868995751603507e-14 relative error 1.1735758759714953e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999031945075 Order of pole (three term test) 22.500139144162866 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7300000000000005 y[1] (closed_form) 21.6189866832605 y[1] (numeric) 21.618986683260484 absolute error 1.4210854715202004e-14 relative error 6.573321369500365e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999106372672 Order of pole (three term test) 22.5001336882424 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7400000000000005 y[1] (closed_form) 22.05583481562423 y[1] (numeric) 22.055834815624205 absolute error 2.4868995751603507e-14 relative error 1.12754724359771e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999917507801 Order of pole (three term test) 22.500128446251615 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7500000000000006 y[1] (closed_form) 22.501505575995914 y[1] (numeric) 22.501505575995893 absolute error 2.1316282072803006e-14 relative error 9.473269244500121e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999923850102 Order of pole (three term test) 22.500123409802203 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7600000000000006 y[1] (closed_form) 22.956177238622086 y[1] (numeric) 22.956177238622054 absolute error 3.197442310920451e-14 relative error 1.3928461510311868e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999297047842 Order of pole (three term test) 22.500118570834786 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7700000000000006 y[1] (closed_form) 23.42003167823013 y[1] (numeric) 23.42003167823011 absolute error 2.1316282072803006e-14 relative error 9.101730674693047e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999351093372 Order of pole (three term test) 22.500113921605973 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7800000000000006 y[1] (closed_form) 23.893254442780744 y[1] (numeric) 23.893254442780716 absolute error 2.842170943040401e-14 relative error 1.1895285968040875e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999400983686 Order of pole (three term test) 22.500109454676025 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7900000000000006 y[1] (closed_form) 24.376034827689423 y[1] (numeric) 24.37603482768941 absolute error 1.4210854715202004e-14 relative error 5.829846739084691e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999447038254 Order of pole (three term test) 22.500105162896887 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y[1] (closed_form) 24.86856595154733 y[1] (numeric) 24.868565951547303 absolute error 2.4868995751603507e-14 relative error 1.0000172828645213e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999948955197 Order of pole (three term test) 22.500101039400803 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y[1] (closed_form) 25.37104483337113 y[1] (numeric) 25.371044833371116 absolute error 1.4210854715202004e-14 relative error 5.601209886519981e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999528797076 Order of pole (three term test) 22.50009707758931 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y[1] (closed_form) 25.883672471413412 y[1] (numeric) 25.883672471413384 absolute error 2.842170943040401e-14 relative error 1.0980555198182819e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999956502488 Order of pole (three term test) 22.500093271122658 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8300000000000006 y[1] (closed_form) 26.406653923564473 y[1] (numeric) 26.40665392356445 absolute error 2.4868995751603507e-14 relative error 9.417700487001571e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999598467357 Order of pole (three term test) 22.500089613909683 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y[1] (closed_form) 26.940198389378395 y[1] (numeric) 26.940198389378356 absolute error 3.907985046680551e-14 relative error 1.450614798820983e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999629338643 Order of pole (three term test) 22.500086100098077 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y[1] (closed_form) 27.48451929375548 y[1] (numeric) 27.484519293755454 absolute error 2.4868995751603507e-14 relative error 9.04836482159387e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999965783645 Order of pole (three term test) 22.500082724064992 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y[1] (closed_form) 28.039834372315234 y[1] (numeric) 28.039834372315195 absolute error 3.907985046680551e-14 relative error 1.393726152155538e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999968414323 Order of pole (three term test) 22.500079480408044 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y[1] (closed_form) 28.606365758493332 y[1] (numeric) 28.606365758493304 absolute error 2.842170943040401e-14 relative error 9.935449217964886e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999708427453 Order of pole (three term test) 22.500076363936707 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y[1] (closed_form) 29.18434007239815 y[1] (numeric) 29.18434007239811 absolute error 3.907985046680551e-14 relative error 1.3390691847017743e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999973084462 Order of pole (three term test) 22.50007336966396 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y[1] (closed_form) 29.773988511461624 y[1] (numeric) 29.773988511461592 absolute error 3.197442310920451e-14 relative error 1.0739045961845459e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999751538268 Order of pole (three term test) 22.500070492798308 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y[1] (closed_form) 30.375546942921517 y[1] (numeric) 30.375546942921467 absolute error 4.973799150320701e-14 relative error 1.637435256611818e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999977064091 Order of pole (three term test) 22.50006772873618 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y[1] (closed_form) 30.989255998171238 y[1] (numeric) 30.98925599817121 absolute error 2.842170943040401e-14 relative error 9.171472019877228e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999788274874 Order of pole (three term test) 22.500065073054472 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y[1] (closed_form) 31.61536116901585 y[1] (numeric) 31.615361169015806 absolute error 4.263256414560601e-14 relative error 1.3484762649932147e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999804553075 Order of pole (three term test) 22.50006252150353 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y[1] (closed_form) 32.25411290587181 y[1] (numeric) 32.25411290587177 absolute error 3.552713678800501e-14 relative error 1.1014761711687738e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999981957975 Order of pole (three term test) 22.50006007000033 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y[1] (closed_form) 32.90576671795071 y[1] (numeric) 32.90576671795066 absolute error 4.973799150320701e-14 relative error 1.5115281138875272e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999833451123 Order of pole (three term test) 22.500057714621942 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y[1] (closed_form) 33.57058327546618 y[1] (numeric) 33.570583275466134 absolute error 4.263256414560601e-14 relative error 1.269938141848207e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999846256007 Order of pole (three term test) 22.500055451599266 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y[1] (closed_form) 34.24882851390561 y[1] (numeric) 34.24882851390555 absolute error 5.684341886080802e-14 relative error 1.6597186335213953e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999858076405 Order of pole (three term test) 22.50005327731097 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y[1] (closed_form) 34.94077374040771 y[1] (numeric) 34.940773740407664 absolute error 4.263256414560601e-14 relative error 1.2201379529355709e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999868988013 Order of pole (three term test) 22.500051188277737 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y[1] (closed_form) 35.64669574228919 y[1] (numeric) 35.64669574228914 absolute error 4.973799150320701e-14 relative error 1.39530440248353e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999987906069 Order of pole (three term test) 22.500049181156665 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9900000000000008 y[1] (closed_form) 36.36687689776317 y[1] (numeric) 36.36687689776315 absolute error 2.1316282072803006e-14 relative error 5.861455228264079e-14% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999888358945 Order of pole (three term test) 22.50004725273594 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0000000000000007 y[1] (closed_form) 37.10160528889445 y[1] (numeric) 37.101605288894405 absolute error 4.263256414560601e-14 relative error 1.1490759985624431e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999989694232 Order of pole (three term test) 22.500045399929668 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0099999999999996 y[1] (closed_form) 37.851174816835844 y[1] (numeric) 37.85117481683589 absolute error 4.973799150320701e-14 relative error 1.3140408915678893e-13% Desired digits 12 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999904865763 Order of pole (three term test) 22.50004361977297 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0199999999999985 y[1] (closed_form) 38.61588531939304 y[1] (numeric) 38.61588531939317 absolute error 1.3500311979441904e-13 relative error 3.496051396408617e-13% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999912180035 Order of pole (three term test) 22.50004190941722 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0299999999999974 y[1] (closed_form) 39.39604269096332 y[1] (numeric) 39.39604269096355 absolute error 2.2737367544323206e-13 relative error 5.77148515212131e-13% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999918931956 Order of pole (three term test) 22.500040266125463 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0399999999999963 y[1] (closed_form) 40.191959004897555 y[1] (numeric) 40.191959004897875 absolute error 3.197442310920451e-13 relative error 7.955427876831854e-13% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999925164768 Order of pole (three term test) 22.500038687268113 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0499999999999952 y[1] (closed_form) 41.00395263833368 y[1] (numeric) 41.00395263833409 absolute error 4.121147867408581e-13 relative error 1.0050611227064515e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999930918365 Order of pole (three term test) 22.500037170318627 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.059999999999994 y[1] (closed_form) 41.83234839955179 y[1] (numeric) 41.832348399552295 absolute error 5.044853423896711e-13 relative error 1.2059694511319293e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999993622962 Order of pole (three term test) 22.500035712849602 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.069999999999993 y[1] (closed_form) 42.677477657901804 y[1] (numeric) 42.6774776579024 absolute error 5.968558980384842e-13 relative error 1.3985266486993881e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999941132517 Order of pole (three term test) 22.50003431252874 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0799999999999919 y[1] (closed_form) 43.53967847635559 y[1] (numeric) 43.539678476356286 absolute error 6.963318810448982e-13 relative error 1.5993041414466215e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999945658458 Order of pole (three term test) 22.50003296711524 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0899999999999908 y[1] (closed_form) 44.41929574673671 y[1] (numeric) 44.41929574673751 absolute error 8.029132914089132e-13 relative error 1.8075777157450761e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999949836443 Order of pole (three term test) 22.50003167445617 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0999999999999897 y[1] (closed_form) 45.316681327681685 y[1] (numeric) 45.316681327682595 absolute error 9.094947017729282e-13 relative error 2.0069755223169083e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.249999999536932 Order of pole (three term test) 22.50003043248298 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1099999999999886 y[1] (closed_form) 46.23219418538821 y[1] (numeric) 46.23219418538922 absolute error 1.0089706847793423e-12 relative error 2.1823984402155624e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999995725344 Order of pole (three term test) 22.500029239208256 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1199999999999875 y[1] (closed_form) 47.16620053720636 y[1] (numeric) 47.166200537207466 absolute error 1.1084466677857563e-12 relative error 2.35008683158902e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999960539948 Order of pole (three term test) 22.500028092722506 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1299999999999863 y[1] (closed_form) 48.119073998130446 y[1] (numeric) 48.119073998131654 absolute error 1.2079226507921703e-12 relative error 2.5102782543967936e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999963573782 Order of pole (three term test) 22.500026991191103 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1399999999999852 y[1] (closed_form) 49.091195730249986 y[1] (numeric) 49.0911957302513 absolute error 1.3145040611561853e-12 relative error 2.6776778230850635e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999966374364 Order of pole (three term test) 22.50002593285136 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1499999999999841 y[1] (closed_form) 50.082954595219626 y[1] (numeric) 50.08295459522103 absolute error 1.4068746168049984e-12 relative error 2.8090886972935965e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999968959621 Order of pole (three term test) 22.500024916009718 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.159999999999983 y[1] (closed_form) 51.09474730980898 y[1] (numeric) 51.094747309810494 absolute error 1.5134560271690134e-12 relative error 2.9620579547879783e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999971346112 Order of pole (three term test) 22.500023939039 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.169999999999982 y[1] (closed_form) 52.12697860459464 y[1] (numeric) 52.12697860459626 absolute error 1.6200374375330284e-12 relative error 3.107867520620566e-12% Desired digits 12 Estimated correct digits 12 Correct digits 14 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999997354914 Order of pole (three term test) 22.500023000375855 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1799999999999808 y[1] (closed_form) 53.18006138585778 y[1] (numeric) 53.18006138585952 absolute error 1.7337242752546445e-12 relative error 3.2601020571888532e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999997558277 Order of pole (three term test) 22.500022098518222 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1899999999999797 y[1] (closed_form) 54.2544169007522 y[1] (numeric) 54.25441690075405 absolute error 1.8545165403338615e-12 relative error 3.4181853686241538e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999997746006 Order of pole (three term test) 22.50002123202293 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1999999999999786 y[1] (closed_form) 55.35047490580878 y[1] (numeric) 55.350474905810756 absolute error 1.9753088054130785e-12 relative error 3.5687296428341554e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999997919301 Order of pole (three term test) 22.500020399503402 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2099999999999775 y[1] (closed_form) 56.468673838843856 y[1] (numeric) 56.46867383884595 absolute error 2.0961010704922955e-12 relative error 3.711971484356735e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999980792725 Order of pole (three term test) 22.500019599627432 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2199999999999764 y[1] (closed_form) 57.60946099434015 y[1] (numeric) 57.60946099434237 absolute error 2.2239987629291136e-12 relative error 3.860474867396539e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999982269455 Order of pole (three term test) 22.50001883111505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2299999999999753 y[1] (closed_form) 58.77329270237057 y[1] (numeric) 58.77329270237291 absolute error 2.3447910280083306e-12 relative error 3.9895519209420704e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999983632648 Order of pole (three term test) 22.50001809273647 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2399999999999742 y[1] (closed_form) 59.96063451113628 y[1] (numeric) 59.96063451113876 absolute error 2.4797941478027496e-12 relative error 4.1357036462684294e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999984891028 Order of pole (three term test) 22.500017383310123 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2499999999999731 y[1] (closed_form) 61.17196137319222 y[1] (numeric) 61.17196137319484 absolute error 2.6219026949547697e-12 relative error 4.286118404736623e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999986052657 Order of pole (three term test) 22.500016701700783 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.259999999999972 y[1] (closed_form) 62.40775783543447 y[1] (numeric) 62.407757835437216 absolute error 2.7498003873915877e-12 relative error 4.406183594422102e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999987124985 Order of pole (three term test) 22.500016046817738 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.269999999999971 y[1] (closed_form) 63.66851823292541 y[1] (numeric) 63.6685182329283 absolute error 2.8919089345436078e-12 relative error 4.542133247021433e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999988114854 Order of pole (three term test) 22.50001541761301 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2799999999999698 y[1] (closed_form) 64.95474688663441 y[1] (numeric) 64.95474688663745 absolute error 3.0411229090532288e-12 relative error 4.68191018334796e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999998902863 Order of pole (three term test) 22.50001481307976 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2899999999999687 y[1] (closed_form) 66.2669583051729 y[1] (numeric) 66.26695830517609 absolute error 3.183231456205249e-12 relative error 4.8036480587290824e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999989872154 Order of pole (three term test) 22.500014232250592 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2999999999999676 y[1] (closed_form) 67.60567739060468 y[1] (numeric) 67.60567739060801 absolute error 3.325340003357269e-12 relative error 4.918728917017551e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999990650815 Order of pole (three term test) 22.500013674196065 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3099999999999665 y[1] (closed_form) 68.97143964841376 y[1] (numeric) 68.97143964841723 absolute error 3.467448550509289e-12 relative error 5.027368673446321e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999991369617 Order of pole (three term test) 22.500013138023167 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3199999999999654 y[1] (closed_form) 70.36479140171363 y[1] (numeric) 70.36479140171726 absolute error 3.623767952376511e-12 relative error 5.149973275254049e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999992033145 Order of pole (three term test) 22.500012622873907 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3299999999999643 y[1] (closed_form) 71.78629000978393 y[1] (numeric) 71.78629000978769 absolute error 3.765876499528531e-12 relative error 5.2459550410186554e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999992645666 Order of pole (three term test) 22.500012127923945 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3399999999999632 y[1] (closed_form) 73.23650409102143 y[1] (numeric) 73.23650409102534 absolute error 3.907985046680551e-12 relative error 5.336116319565912e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.249999999932111 Order of pole (three term test) 22.500011652381243 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3499999999999621 y[1] (closed_form) 74.71601375039506 y[1] (numeric) 74.71601375039913 absolute error 4.064304448547773e-12 relative error 5.4396698171364676e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999993733057 Order of pole (three term test) 22.50001119548484 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.359999999999961 y[1] (closed_form) 76.22541081149565 y[1] (numeric) 76.2254108114999 absolute error 4.249045559845399e-12 relative error 5.574316379026448e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999994214883 Order of pole (three term test) 22.500010756503602 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.36999999999996 y[1] (closed_form) 77.7652990532732 y[1] (numeric) 77.76529905327762 absolute error 4.419575816427823e-12 relative error 5.683223584596759e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999994659666 Order of pole (three term test) 22.500010334735066 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3799999999999588 y[1] (closed_form) 79.33629445155651 y[1] (numeric) 79.3362944515611 absolute error 4.590106073010247e-12 relative error 5.785632042359893e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999995070246 Order of pole (three term test) 22.500009929504305 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3899999999999577 y[1] (closed_form) 80.93902542545182 y[1] (numeric) 80.93902542545658 absolute error 4.760636329592671e-12 relative error 5.881756426604635e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999995449257 Order of pole (three term test) 22.500009540162868 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3999999999999566 y[1] (closed_form) 82.5741330887187 y[1] (numeric) 82.57413308872364 absolute error 4.945377440890297e-12 relative error 5.9890152713767174e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999995799135 Order of pole (three term test) 22.500009166087732 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4099999999999555 y[1] (closed_form) 84.24227150622417 y[1] (numeric) 84.2422715062293 absolute error 5.130118552187923e-12 relative error 6.089720113742291e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999612212 Order of pole (three term test) 22.50000880668029 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4199999999999544 y[1] (closed_form) 85.94410795557738 y[1] (numeric) 85.9441079555827 absolute error 5.314859663485549e-12 relative error 6.184088461576311e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999996420266 Order of pole (three term test) 22.50000846136542 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4299999999999533 y[1] (closed_form) 87.68032319404954 y[1] (numeric) 87.68032319405505 absolute error 5.5138116294983774e-12 relative error 6.2885393536877095e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999669548 Order of pole (three term test) 22.500008129590537 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4399999999999522 y[1] (closed_form) 89.45161173088587 y[1] (numeric) 89.45161173089159 absolute error 5.7127635955112055e-12 relative error 6.3864289138780284e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999996949548 Order of pole (three term test) 22.500007810824734 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.449999999999951 y[1] (closed_form) 91.25868210511862 y[1] (numeric) 91.2586821051245 absolute error 5.8832938520936295e-12 relative error 6.446831924788053e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999997184083 Order of pole (three term test) 22.500007504557917 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.45999999999995 y[1] (closed_form) 93.10225716899205 y[1] (numeric) 93.10225716899814 absolute error 6.0822458181064576e-12 relative error 6.532866122747629e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999740058 Order of pole (three term test) 22.500007210299987 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.469999999999949 y[1] (closed_form) 94.98307437711306 y[1] (numeric) 94.98307437711935 absolute error 6.295408638834488e-12 relative error 6.627926796557154e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999997600428 Order of pole (three term test) 22.500006927580078 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4799999999999478 y[1] (closed_form) 96.90188608144277 y[1] (numeric) 96.90188608144929 absolute error 6.52278231427772e-12 relative error 6.731326476757678e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999997784922 Order of pole (three term test) 22.500006655945786 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4899999999999467 y[1] (closed_form) 98.85945983224742 y[1] (numeric) 98.85945983225416 absolute error 6.73594513500575e-12 relative error 6.813657637251747e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999795522 Order of pole (three term test) 22.500006394962416 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4999999999999456 y[1] (closed_form) 100.85657868512868 y[1] (numeric) 100.85657868513566 absolute error 6.977529665164184e-12 relative error 6.918269245428034e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999998112435 Order of pole (three term test) 22.500006144212353 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5099999999999445 y[1] (closed_form) 102.8940415142563 y[1] (numeric) 102.89404151426349 absolute error 7.190692485892214e-12 relative error 6.988444014900435e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999998257558 Order of pole (three term test) 22.50000590329434 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5199999999999434 y[1] (closed_form) 104.97266333192844 y[1] (numeric) 104.97266333193586 absolute error 7.418066161335446e-12 relative error 7.066664716202518e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999839152 Order of pole (three term test) 22.50000567182286 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5299999999999423 y[1] (closed_form) 107.09327561458754 y[1] (numeric) 107.09327561459517 absolute error 7.631228982063476e-12 relative error 7.125777914877786e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999998515185 Order of pole (three term test) 22.5000054494275 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5399999999999412 y[1] (closed_form) 109.25672663542183 y[1] (numeric) 109.25672663542969 absolute error 7.858602657506708e-12 relative error 7.19278610984753e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999862934 Order of pole (three term test) 22.500005235752397 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.54999999999994 y[1] (closed_form) 111.46388180368605 y[1] (numeric) 111.46388180369416 absolute error 8.114398042380344e-12 relative error 7.279845193864408e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999998734726 Order of pole (three term test) 22.500005030455608 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.559999999999939 y[1] (closed_form) 113.71562401087665 y[1] (numeric) 113.71562401088501 absolute error 8.355982572538778e-12 relative error 7.348139400562536e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999998832 Order of pole (three term test) 22.50000483320862 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.569999999999938 y[1] (closed_form) 116.01285398390013 y[1] (numeric) 116.01285398390874 absolute error 8.611777957412414e-12 relative error 7.423123957115586e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.249999999989218 Order of pole (three term test) 22.5000046436958 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5799999999999368 y[1] (closed_form) 118.35649064537584 y[1] (numeric) 118.3564906453847 absolute error 8.853362487570848e-12 relative error 7.480250926075212e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.249999999990047 Order of pole (three term test) 22.50000446161388 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5899999999999357 y[1] (closed_form) 120.74747148121727 y[1] (numeric) 120.74747148122638 absolute error 9.109157872444484e-12 relative error 7.543974015109251e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999081224 Order of pole (three term test) 22.5000042866715 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5999999999999346 y[1] (closed_form) 123.18675291563892 y[1] (numeric) 123.1867529156483 absolute error 9.379164112033322e-12 relative error 7.613776554737494e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999151862 Order of pole (three term test) 22.50000411858871 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6099999999999335 y[1] (closed_form) 125.67531069373877 y[1] (numeric) 125.67531069374841 absolute error 9.64917035162216e-12 relative error 7.677856771037917e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999217065 Order of pole (three term test) 22.500003957096535 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6199999999999324 y[1] (closed_form) 128.21414027180924 y[1] (numeric) 128.21414027181916 absolute error 9.919176591210999e-12 relative error 7.73641391673548e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999277256 Order of pole (three term test) 22.50000380193656 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6299999999999313 y[1] (closed_form) 130.8042572155331 y[1] (numeric) 130.80425721554332 absolute error 1.0203393685515039e-11 relative error 7.800505811292033e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999332834 Order of pole (three term test) 22.5000036528605 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6399999999999302 y[1] (closed_form) 133.44669760622318 y[1] (numeric) 133.44669760623367 absolute error 1.0487610779819079e-11 relative error 7.859026089027772e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999938413 Order of pole (three term test) 22.50000350962979 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.649999999999929 y[1] (closed_form) 136.14251845526874 y[1] (numeric) 136.14251845527954 absolute error 1.0800249583553523e-11 relative error 7.933046711709006e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999431474 Order of pole (three term test) 22.500003372015232 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.659999999999928 y[1] (closed_form) 138.8927981269542 y[1] (numeric) 138.8927981269653 absolute error 1.1084466677857563e-11 relative error 7.980591382229816e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999475184 Order of pole (three term test) 22.500003239796627 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6699999999999269 y[1] (closed_form) 141.6986367698191 y[1] (numeric) 141.69863676983047 absolute error 1.1368683772161603e-11 relative error 8.023142657772596e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999515538 Order of pole (three term test) 22.500003112762382 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6799999999999258 y[1] (closed_form) 144.56115675673226 y[1] (numeric) 144.56115675674394 absolute error 1.1681322575896047e-11 relative error 8.080540331835747e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999552783 Order of pole (three term test) 22.50000299070923 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6899999999999247 y[1] (closed_form) 147.48150313385588 y[1] (numeric) 147.48150313386788 absolute error 1.1993961379630491e-11 relative error 8.132519078507517e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999587166 Order of pole (three term test) 22.500002873441836 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6999999999999236 y[1] (closed_form) 150.4608440786793 y[1] (numeric) 150.46084407869157 absolute error 1.2278178473934531e-11 relative error 8.160381226835336e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999618908 Order of pole (three term test) 22.500002760772578 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7099999999999225 y[1] (closed_form) 153.5003713673055 y[1] (numeric) 153.50037136731808 absolute error 1.2590817277668975e-11 relative error 8.202466981360497e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999648206 Order of pole (three term test) 22.500002652521125 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7199999999999214 y[1] (closed_form) 156.60130085117754 y[1] (numeric) 156.60130085119047 absolute error 1.2931877790833823e-11 relative error 8.25783548447234e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999675251 Order of pole (three term test) 22.50000254851429 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7299999999999203 y[1] (closed_form) 159.7648729434352 y[1] (numeric) 159.76487294344847 absolute error 1.3272938303998671e-11 relative error 8.307795111318343e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999700218 Order of pole (three term test) 22.500002448585608 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7399999999999192 y[1] (closed_form) 162.99235311509693 y[1] (numeric) 162.99235311511057 absolute error 1.3642420526593924e-11 relative error 8.369975809208876e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999723269 Order of pole (three term test) 22.500002352575198 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.749999999999918 y[1] (closed_form) 166.28503240126503 y[1] (numeric) 166.28503240127904 absolute error 1.4011902749189176e-11 relative error 8.426436551052191e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999744543 Order of pole (three term test) 22.500002260329403 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.759999999999917 y[1] (closed_form) 169.64422791755698 y[1] (numeric) 169.64422791757133 absolute error 1.4352963262354024e-11 relative error 8.460625768728907e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999764186 Order of pole (three term test) 22.500002171700626 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7699999999999159 y[1] (closed_form) 173.0712833869691 y[1] (numeric) 173.07128338698382 absolute error 1.4722445484949276e-11 relative error 8.50657902156503e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999978231 Order of pole (three term test) 22.50000208654702 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7799999999999148 y[1] (closed_form) 176.56756967738391 y[1] (numeric) 176.56756967739898 absolute error 1.5063505998114124e-11 relative error 8.531298259152269e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999799052 Order of pole (three term test) 22.500002004732345 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7899999999999137 y[1] (closed_form) 180.1344853499353 y[1] (numeric) 180.13448534995078 absolute error 1.5489831639570184e-11 relative error 8.599037330069875e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999814498 Order of pole (three term test) 22.500001926125666 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7999999999999126 y[1] (closed_form) 183.77345721845177 y[1] (numeric) 183.77345721846768 absolute error 1.5916157281026244e-11 relative error 8.660748685870716e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999828765 Order of pole (three term test) 22.5000018506012 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8099999999999115 y[1] (closed_form) 187.48594092020107 y[1] (numeric) 187.4859409202174 absolute error 1.63140612130519e-11 relative error 8.701485099619065e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999841924 Order of pole (three term test) 22.500001778038083 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8199999999999104 y[1] (closed_form) 191.27342149816434 y[1] (numeric) 191.2734214981811 absolute error 1.6768808563938364e-11 relative error 8.766930832624488e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999854083 Order of pole (three term test) 22.500001708320212 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8299999999999093 y[1] (closed_form) 195.13741399507308 y[1] (numeric) 195.13741399509033 absolute error 1.7251977624255233e-11 relative error 8.840937917057166e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.249999999998653 Order of pole (three term test) 22.500001641336024 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8399999999999082 y[1] (closed_form) 199.07946405944676 y[1] (numeric) 199.0794640594644 absolute error 1.764988155628089e-11 relative error 8.865746971777305e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999987566 Order of pole (three term test) 22.500001576978317 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.849999999999907 y[1] (closed_form) 203.10114856387244 y[1] (numeric) 203.10114856389052 absolute error 1.807620719773695e-11 relative error 8.900100922891747e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999885214 Order of pole (three term test) 22.500001515144113 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.859999999999906 y[1] (closed_form) 207.20407623577506 y[1] (numeric) 207.20407623579356 absolute error 1.850253283919301e-11 relative error 8.929618169354543e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999894038 Order of pole (three term test) 22.500001455734463 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8699999999999048 y[1] (closed_form) 211.38988830092984 y[1] (numeric) 211.38988830094883 absolute error 1.8985701899509877e-11 relative error 8.981367108951902e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999902187 Order of pole (three term test) 22.500001398654298 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8799999999999037 y[1] (closed_form) 215.66025913997441 y[1] (numeric) 215.66025913999385 absolute error 1.944044925039634e-11 relative error 9.014386483593395e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999909706 Order of pole (three term test) 22.50000134381228 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8899999999999026 y[1] (closed_form) 220.0168969581834 y[1] (numeric) 220.01689695820338 absolute error 1.9980461729574017e-11 relative error 9.081330573156626e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999916653 Order of pole (three term test) 22.500001291120647 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8999999999999015 y[1] (closed_form) 224.46154446877335 y[1] (numeric) 224.46154446879382 absolute error 2.0463630789890885e-11 relative error 9.116764672684388e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999992306 Order of pole (three term test) 22.50000124049508 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9099999999999004 y[1] (closed_form) 228.99597959001133 y[1] (numeric) 228.99597959003225 absolute error 2.091837814077735e-11 relative error 9.134823317959158e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999992897 Order of pole (three term test) 22.500001191854576 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9199999999998993 y[1] (closed_form) 233.62201615640572 y[1] (numeric) 233.62201615642718 absolute error 2.1458390619955026e-11 relative error 9.185089219326411e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999934436 Order of pole (three term test) 22.500001145121285 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9299999999998982 y[1] (closed_form) 238.3415046442644 y[1] (numeric) 238.3415046442864 absolute error 2.1998403099132702e-11 relative error 9.22978275729455e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999939473 Order of pole (three term test) 22.500001100220434 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9399999999998971 y[1] (closed_form) 243.15633291190986 y[1] (numeric) 243.15633291193237 absolute error 2.2509993868879974e-11 relative error 9.25741624711656e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999994413 Order of pole (three term test) 22.50000105708018 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.949999999999896 y[1] (closed_form) 248.06842695484775 y[1] (numeric) 248.06842695487077 absolute error 2.3021584638627246e-11 relative error 9.280336446369908e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999994842 Order of pole (three term test) 22.500001015631472 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.959999999999895 y[1] (closed_form) 253.07975167619065 y[1] (numeric) 253.07975167621424 absolute error 2.3590018827235326e-11 relative error 9.321179853779127e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999995239 Order of pole (three term test) 22.50000097580799 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9699999999998938 y[1] (closed_form) 258.1923116726457 y[1] (numeric) 258.19231167266986 absolute error 2.4158453015843406e-11 relative error 9.356767000278918e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999995605 Order of pole (three term test) 22.500000937546012 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9799999999998927 y[1] (closed_form) 263.4081520363799 y[1] (numeric) 263.40815203640454 absolute error 2.467004378559068e-11 relative error 9.365710056757638e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999959427 Order of pole (three term test) 22.500000900784308 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9899999999998916 y[1] (closed_form) 268.72935917308405 y[1] (numeric) 268.7293591731094 absolute error 2.5352164811920375e-11 relative error 9.434088217949968e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2499999999996255 Order of pole (three term test) 22.500000865464052 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9999999999998905 y[1] (closed_form) 274.1580616365634 y[1] (numeric) 274.15806163658925 absolute error 2.5863755581667647e-11 relative error 9.43388475512124e-12% Desired digits 12 Estimated correct digits 12 Correct digits 13 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999999999965428 Order of pole (three term test) 22.50000083152872 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = cosh ( 2.0 * x + 3.0 ) ; Iterations 1901 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.10526315788897%