##############ECHO OF PROBLEM################# ##############temp/diff2postode.ode################# diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(-1.0) x_end=c(1.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $array_y_init[1 + 1] = exact_soln_yp(x_start) $array_y_init[2 + 1] = exact_soln_ypp(x_start) $glob_look_poles=true # 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=8 $glob_max_minutes=(3.0) $glob_subiter_method=3 $glob_max_iter=100000 $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) #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(neg(cos(c(x)))) end def exact_soln_yp (x) x = c(x) return(sin(c(x))) end def exact_soln_ypp (x) x = c(x) return(cos(c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -1.0 y[1] (closed_form) -0.5403023058681398 y[1] (numeric) -0.5403023058681398 absolute error 0.0 relative error 0.0% Desired digits 8 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 0.4546487134128409 Order of pole (three term test) 32.70807341827358 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.99 y[1] (closed_form) -0.5486898605815875 y[1] (numeric) -0.5486898605815874 absolute error 1.1102230246251565e-16 relative error 2.0234072185120535e-14% Desired digits 8 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 0.4587189776409048 Order of pole (three term test) 32.69893943689496 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.98 y[1] (closed_form) -0.5570225467662173 y[1] (numeric) -0.5570225467662171 absolute error 2.220446049250313e-16 relative error 3.9862767892270536e-14% Desired digits 8 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 0.462605760394084 Order of pole (three term test) 32.689725882394086 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.97 y[1] (closed_form) -0.5652995311603544 y[1] (numeric) -0.5652995311603539 absolute error 4.440892098500626e-16 relative error 7.855821301293297e-14% Desired digits 8 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 0.4663075070111 Order of pole (three term test) 32.680436440069876 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.96 y[1] (closed_form) -0.5735199860724567 y[1] (numeric) -0.5735199860724564 absolute error 3.3306690738754696e-16 relative error 5.807415878711301e-14% Desired digits 8 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 0.4698227368426624 Order of pole (three term test) 32.671074825575445 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.95 y[1] (closed_form) -0.5816830894638836 y[1] (numeric) -0.5816830894638831 absolute error 4.440892098500626e-16 relative error 7.63455596172417e-14% Desired digits 8 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 0.4731500438437071 Order of pole (three term test) 32.66164478343175 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.94 y[1] (closed_form) -0.5897880250310983 y[1] (numeric) -0.5897880250310978 absolute error 4.440892098500626e-16 relative error 7.529641006642119e-14% Desired digits 8 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 0.4762880971357977 Order of pole (three term test) 32.65215008552991 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9299999999999999 y[1] (closed_form) -0.5978339822872983 y[1] (numeric) -0.597833982287298 absolute error 3.3306690738754696e-16 relative error 5.5712274185759903e-14% Desired digits 8 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 0.479235641539457 Order of pole (three term test) 32.642594529622514 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9199999999999999 y[1] (closed_form) -0.6058201566434629 y[1] (numeric) -0.6058201566434627 absolute error 2.220446049250313e-16 relative error 3.665190114427126e-14% Desired digits 8 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 0.48199149807622416 Order of pole (three term test) 32.632981937804495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9099999999999999 y[1] (closed_form) -0.6137457494888117 y[1] (numeric) -0.6137457494888114 absolute error 2.220446049250313e-16 relative error 3.617859758865492e-14% Desired digits 8 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 0.4845545644402282 Order of pole (three term test) 32.623316154984416 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8999999999999999 y[1] (closed_form) -0.6216099682706645 y[1] (numeric) -0.6216099682706642 absolute error 3.3306690738754696e-16 relative error 5.358133305264521e-14% Desired digits 8 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 0.4869238154390974 Order of pole (three term test) 32.61360104734654 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8899999999999999 y[1] (closed_form) -0.629412026573697 y[1] (numeric) -0.6294120265736965 absolute error 4.440892098500626e-16 relative error 7.055620024732158e-14% Desired digits 8 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 0.4890983034040223 Order of pole (three term test) 32.60384050080439 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8799999999999999 y[1] (closed_form) -0.6371511441985803 y[1] (numeric) -0.63715114419858 absolute error 3.3306690738754696e-16 relative error 5.2274395238901166e-14% Desired digits 8 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 0.4910771585688092 Order of pole (three term test) 32.59403841944644 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8699999999999999 y[1] (closed_form) -0.6448265472400013 y[1] (numeric) -0.644826547240001 absolute error 3.3306690738754696e-16 relative error 5.165217046555329e-14% Desired digits 8 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 0.49285958941777674 Order of pole (three term test) 32.58419872397454 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8599999999999999 y[1] (closed_form) -0.6524374681640519 y[1] (numeric) -0.6524374681640517 absolute error 2.220446049250313e-16 relative error 3.403308604422445e-14% Desired digits 8 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 0.49444488300235084 Order of pole (three term test) 32.57432535013569 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8499999999999999 y[1] (closed_form) -0.6599831458849823 y[1] (numeric) -0.6599831458849821 absolute error 2.220446049250313e-16 relative error 3.364398110913697e-14% Desired digits 8 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 0.49583240522623434 Order of pole (three term test) 32.56442224714776 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8399999999999999 y[1] (closed_form) -0.6674628258413082 y[1] (numeric) -0.6674628258413081 absolute error 1.1102230246251565e-16 relative error 1.6633481021594994e-14% Desired digits 8 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 0.497021601099038 Order of pole (three term test) 32.554493376119936 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8299999999999998 y[1] (closed_form) -0.6748757600712673 y[1] (numeric) -0.6748757600712672 absolute error 1.1102230246251565e-16 relative error 1.6450776428952143e-14% Desired digits 8 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 0.4980119949582684 Order of pole (three term test) 32.54454270846823 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8199999999999998 y[1] (closed_form) -0.6822212072876137 y[1] (numeric) -0.6822212072876136 absolute error 1.1102230246251565e-16 relative error 1.627365160692086e-14% Desired digits 8 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 0.4988031906595869 Order of pole (three term test) 32.53457422432703 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8099999999999998 y[1] (closed_form) -0.6894984329517472 y[1] (numeric) -0.6894984329517471 absolute error 1.1102230246251565e-16 relative error 1.610189337011666e-14% Desired digits 8 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 0.499394871735262 Order of pole (three term test) 32.524591910957085 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7999999999999998 y[1] (closed_form) -0.6967067093471655 y[1] (numeric) -0.6967067093471655 absolute error 0.0 relative error 0.0% Desired digits 8 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 0.4997868015207526 Order of pole (three term test) 32.51459976115065 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7899999999999998 y[1] (closed_form) -0.7038453156522362 y[1] (numeric) -0.7038453156522362 absolute error 0.0 relative error 0.0% Desired digits 8 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 0.49997882324937 Order of pole (three term test) 32.504601771634405 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7799999999999998 y[1] (closed_form) -0.7109135380122775 y[1] (numeric) -0.7109135380122775 absolute error 0.0 relative error 0.0% Desired digits 8 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 0.49997086011498315 Order of pole (three term test) 32.49460194147087 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7699999999999998 y[1] (closed_form) -0.7179106696109435 y[1] (numeric) -0.7179106696109435 absolute error 0.0 relative error 0.0% Desired digits 8 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 0.49976291530273953 Order of pole (three term test) 32.48460427045877 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7599999999999998 y[1] (closed_form) -0.7248360107409053 y[1] (numeric) -0.7248360107409053 absolute error 0.0 relative error 0.0% Desired digits 8 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 0.4993550719877915 Order of pole (three term test) 32.474612757533215 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7499999999999998 y[1] (closed_form) -0.731688868873821 y[1] (numeric) -0.7316888688738209 absolute error 1.1102230246251565e-16 relative error 1.517343056392202e-14% Desired digits 8 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 0.49874749330202717 Order of pole (three term test) 32.464631399166144 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7399999999999998 y[1] (closed_form) -0.738468558729588 y[1] (numeric) -0.738468558729588 absolute error 0.0 relative error 0.0% Desired digits 8 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 0.49794042226882 Order of pole (three term test) 32.45466418776785 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7299999999999998 y[1] (closed_form) -0.7451744023448705 y[1] (numeric) -0.7451744023448703 absolute error 2.220446049250313e-16 relative error 2.9797669408170024e-14% Desired digits 8 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 0.4969341817058225 Order of pole (three term test) 32.444715110089966 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7199999999999998 y[1] (closed_form) -0.7518057291408952 y[1] (numeric) -0.7518057291408948 absolute error 3.3306690738754696e-16 relative error 4.430225714935025e-14% Desired digits 8 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 0.4957291740958433 Order of pole (three term test) 32.434788145630925 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7099999999999997 y[1] (closed_form) -0.7583618759905083 y[1] (numeric) -0.758361875990508 absolute error 3.3306690738754696e-16 relative error 4.3919257801893467e-14% Desired digits 8 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 0.4943258814258598 Order of pole (three term test) 32.424887265044156 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6999999999999997 y[1] (closed_form) -0.7648421872844886 y[1] (numeric) -0.7648421872844882 absolute error 4.440892098500626e-16 relative error 5.806285495662394e-14% Desired digits 8 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 0.4927248649942301 Order of pole (three term test) 32.415016428549876 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6899999999999997 y[1] (closed_form) -0.7712460149971068 y[1] (numeric) -0.7712460149971061 absolute error 6.661338147750939e-16 relative error 8.637111917882556e-14% Desired digits 8 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 0.49092676518618 Order of pole (three term test) 32.40517958435109 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6799999999999997 y[1] (closed_form) -0.7775727187509281 y[1] (numeric) -0.7775727187509275 absolute error 6.661338147750939e-16 relative error 8.566836241955008e-14% Desired digits 8 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 0.48893230121765824 Order of pole (three term test) 32.3953806670543 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6699999999999997 y[1] (closed_form) -0.7838216658808494 y[1] (numeric) -0.7838216658808488 absolute error 6.661338147750939e-16 relative error 8.498537917123032e-14% Desired digits 8 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 0.48674227084765975 Order of pole (three term test) 32.38562359609577 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6599999999999997 y[1] (closed_form) -0.7899922314973653 y[1] (numeric) -0.7899922314973645 absolute error 7.771561172376096e-16 relative error 9.837515943221038e-14% Desired digits 8 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 0.484357550059133 Order of pole (three term test) 32.375912274173814 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6499999999999997 y[1] (closed_form) -0.796083798549056 y[1] (numeric) -0.7960837985490552 absolute error 7.771561172376096e-16 relative error 9.762240088971236e-14% Desired digits 8 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 0.48177909270859676 Order of pole (three term test) 32.36625058568771 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6399999999999997 y[1] (closed_form) -0.8020957578842928 y[1] (numeric) -0.8020957578842921 absolute error 6.661338147750939e-16 relative error 8.30491631737551e-14% Desired digits 8 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 0.47900793014461285 Order of pole (three term test) 32.35664239518402 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6299999999999997 y[1] (closed_form) -0.8080275083121521 y[1] (numeric) -0.8080275083121515 absolute error 5.551115123125783e-16 relative error 6.869958096749982e-14% Desired digits 8 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 0.4760451707952583 Order of pole (three term test) 32.347091545810855 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6199999999999997 y[1] (closed_form) -0.8138784566625341 y[1] (numeric) -0.8138784566625337 absolute error 4.440892098500626e-16 relative error 5.456456135614355e-14% Desired digits 8 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 0.47289199972476986 Order of pole (three term test) 32.33760185778061 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6099999999999997 y[1] (closed_form) -0.8196480178454797 y[1] (numeric) -0.8196480178454792 absolute error 4.440892098500626e-16 relative error 5.4180477495375636e-14% Desired digits 8 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 0.469549678159534 Order of pole (three term test) 32.32817712684197 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5999999999999996 y[1] (closed_form) -0.8253356149096785 y[1] (numeric) -0.8253356149096781 absolute error 4.440892098500626e-16 relative error 5.3807106082373774e-14% Desired digits 8 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 0.4660195429836136 Order of pole (three term test) 32.31882112276167 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5899999999999996 y[1] (closed_form) -0.8309406791001637 y[1] (numeric) -0.8309406791001633 absolute error 3.3306690738754696e-16 relative error 4.008311492803907e-14% Desired digits 8 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 0.46230300620401055 Order of pole (three term test) 32.30953758781656 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5799999999999996 y[1] (closed_form) -0.8364626499151872 y[1] (numeric) -0.8364626499151867 absolute error 4.440892098500626e-16 relative error 5.30913376580641e-14% Desired digits 8 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 0.45840155438588387 Order of pole (three term test) 32.30033023529686 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5699999999999996 y[1] (closed_form) -0.8419009751622689 y[1] (numeric) -0.8419009751622686 absolute error 3.3306690738754696e-16 relative error 3.9561292505137114e-14% Desired digits 8 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 0.4543167480579419 Order of pole (three term test) 32.29120274802082 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5599999999999996 y[1] (closed_form) -0.8472551110134163 y[1] (numeric) -0.8472551110134159 absolute error 4.440892098500626e-16 relative error 5.241505233516738e-14% Desired digits 8 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 0.45005022108825293 Order of pole (three term test) 32.28215877686164 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5499999999999996 y[1] (closed_form) -0.8525245220595059 y[1] (numeric) -0.8525245220595056 absolute error 3.3306690738754696e-16 relative error 3.90683081564543e-14% Desired digits 8 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 0.445603680030718 Order of pole (three term test) 32.27320193928721 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5399999999999996 y[1] (closed_form) -0.8577086813638244 y[1] (numeric) -0.8577086813638239 absolute error 4.440892098500626e-16 relative error 5.1776228864085386e-14% Desired digits 8 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 0.44097890344247437 Order of pole (three term test) 32.26433581791313 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5299999999999996 y[1] (closed_form) -0.8628070705147612 y[1] (numeric) -0.8628070705147609 absolute error 3.3306690738754696e-16 relative error 3.8602709547666916e-14% Desired digits 8 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 0.4361777411724937 Order of pole (three term test) 32.25556395906973 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5199999999999996 y[1] (closed_form) -0.8678191796776501 y[1] (numeric) -0.8678191796776497 absolute error 4.440892098500626e-16 relative error 5.117301164224312e-14% Desired digits 8 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 0.43120211362166977 Order of pole (three term test) 32.246889871383615 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5099999999999996 y[1] (closed_form) -0.8727445076457515 y[1] (numeric) -0.8727445076457512 absolute error 3.3306690738754696e-16 relative error 3.8163162812218966e-14% Desired digits 8 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 0.42605401097468193 Order of pole (three term test) 32.23831702437417 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.49999999999999956 y[1] (closed_form) -0.877582561890373 y[1] (numeric) -0.8775825618903728 absolute error 2.220446049250313e-16 relative error 2.5301847890725178e-14% Desired digits 8 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 0.4207354924039488 Order of pole (three term test) 32.22984884706593 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.48999999999999955 y[1] (closed_form) -0.8823328586101217 y[1] (numeric) -0.8823328586101216 absolute error 1.1102230246251565e-16 relative error 1.2582814000308394e-14% Desired digits 8 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 0.415248685245986 Order of pole (three term test) 32.2214887266169 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.47999999999999954 y[1] (closed_form) -0.8869949227792844 y[1] (numeric) -0.8869949227792842 absolute error 2.220446049250313e-16 relative error 2.503335692489458e-14% Desired digits 8 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 0.4095957841504996 Order of pole (three term test) 32.21324000696377 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.46999999999999953 y[1] (closed_form) -0.8915682881953292 y[1] (numeric) -0.891568288195329 absolute error 2.220446049250313e-16 relative error 2.4904946470727845e-14% Desired digits 8 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 0.4037790502025577 Order of pole (three term test) 32.20510598748445 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.4599999999999995 y[1] (closed_form) -0.8960524975255254 y[1] (numeric) -0.8960524975255253 absolute error 1.1102230246251565e-16 relative error 1.2390156019776399e-14% Desired digits 8 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 0.3978008100181835 Order of pole (three term test) 32.19708992167827 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.4499999999999995 y[1] (closed_form) -0.9004471023526771 y[1] (numeric) -0.9004471023526769 absolute error 2.220446049250313e-16 relative error 2.4659372476725828e-14% Desired digits 8 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 0.3916634548137422 Order of pole (three term test) 32.18919501586467 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.4399999999999995 y[1] (closed_form) -0.9047516632199636 y[1] (numeric) -0.9047516632199635 absolute error 1.1102230246251565e-16 relative error 1.2271024964728235e-14% Desired digits 8 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 0.38536943944948526 Order of pole (three term test) 32.181424427900716 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.4299999999999995 y[1] (closed_form) -0.9089657496748853 y[1] (numeric) -0.9089657496748853 absolute error 0.0 relative error 0.0% Desired digits 8 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 0.37892128144763915 Order of pole (three term test) 32.173781265917974 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.4199999999999995 y[1] (closed_form) -0.9130889403123085 y[1] (numeric) -0.9130889403123084 absolute error 1.1102230246251565e-16 relative error 1.2158980090651643e-14% Desired digits 8 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 0.3723215599854301 Order of pole (three term test) 32.16626858707935 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.4099999999999995 y[1] (closed_form) -0.9171208228166053 y[1] (numeric) -0.9171208228166051 absolute error 2.220446049250313e-16 relative error 2.421105261170513e-14% Desired digits 8 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 0.3655729148634485 Order of pole (three term test) 32.15888939635619 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.39999999999999947 y[1] (closed_form) -0.9210609940028853 y[1] (numeric) -0.921060994002885 absolute error 3.3306690738754696e-16 relative error 3.616122162985697e-14% Desired digits 8 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 0.358678045449762 Order of pole (three term test) 32.151646645326416 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.38999999999999946 y[1] (closed_form) -0.9249090598573132 y[1] (numeric) -0.924909059857313 absolute error 2.220446049250313e-16 relative error 2.4007182388210836e-14% Desired digits 8 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 0.3516397096002057 Order of pole (three term test) 32.14454323099386 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.37999999999999945 y[1] (closed_form) -0.9286646355765105 y[1] (numeric) -0.9286646355765104 absolute error 1.1102230246251565e-16 relative error 1.1955047948347204e-14% Desired digits 8 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 0.3444607225552761 Order of pole (three term test) 32.13758199462954 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.36999999999999944 y[1] (closed_form) -0.9323273456060346 y[1] (numeric) -0.9323273456060346 absolute error 0.0 relative error 0.0% Desired digits 8 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 0.3371439558140729 Order of pole (three term test) 32.1307657206352 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.35999999999999943 y[1] (closed_form) -0.935896823677935 y[1] (numeric) -0.9358968236779349 absolute error 1.1102230246251565e-16 relative error 1.1862664735436813e-14% Desired digits 8 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 0.32969233598573733 Order of pole (three term test) 32.12409713542956 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3499999999999994 y[1] (closed_form) -0.9393727128473791 y[1] (numeric) -0.9393727128473791 absolute error 0.0 relative error 0.0% Desired digits 8 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 0.32210884361884623 Order of pole (three term test) 32.11757890635776 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3399999999999994 y[1] (closed_form) -0.9427546655283464 y[1] (numeric) -0.9427546655283465 absolute error 1.1102230246251565e-16 relative error 1.1776372636702425e-14% Desired digits 8 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 0.31439651200923513 Order of pole (three term test) 32.11121364062454 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3299999999999994 y[1] (closed_form) -0.9460423435283871 y[1] (numeric) -0.9460423435283872 absolute error 1.1102230246251565e-16 relative error 1.1735447490483739e-14% Desired digits 8 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 0.3065584259867178 Order of pole (three term test) 32.10500388425132 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3199999999999994 y[1] (closed_form) -0.949235418082441 y[1] (numeric) -0.949235418082441 absolute error 0.0 relative error 0.0% Desired digits 8 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 0.298597720681197 Order of pole (three term test) 32.098952121057856 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3099999999999994 y[1] (closed_form) -0.9523335698857136 y[1] (numeric) -0.9523335698857136 absolute error 0.0 relative error 0.0% Desired digits 8 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 0.29051758026865326 Order of pole (three term test) 32.09306077166874 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2999999999999994 y[1] (closed_form) -0.9553364891256062 y[1] (numeric) -0.9553364891256063 absolute error 1.1102230246251565e-16 relative error 1.1621277290908398e-14% Desired digits 8 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 0.28232123669751846 Order of pole (three term test) 32.08733219254516 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.28999999999999937 y[1] (closed_form) -0.9582438755126973 y[1] (numeric) -0.9582438755126973 absolute error 0.0 relative error 0.0% Desired digits 8 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 0.2740119683959375 Order of pole (three term test) 32.081768675042404 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.27999999999999936 y[1] (closed_form) -0.9610554383107711 y[1] (numeric) -0.9610554383107709 absolute error 2.220446049250313e-16 relative error 2.310424519477408e-14% Desired digits 8 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 0.26559309896044253 Order of pole (three term test) 32.076372444493295 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.26999999999999935 y[1] (closed_form) -0.9637708963658906 y[1] (numeric) -0.9637708963658905 absolute error 1.1102230246251565e-16 relative error 1.1519574089770667e-14% Desired digits 8 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 0.2570679958265576 Order of pole (three term test) 32.07114565931809 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.25999999999999934 y[1] (closed_form) -0.9663899781345134 y[1] (numeric) -0.9663899781345132 absolute error 2.220446049250313e-16 relative error 2.2976708156024002e-14% Desired digits 8 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 0.24844006892186937 Order of pole (three term test) 32.06609041016117 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.24999999999999933 y[1] (closed_form) -0.968912421710645 y[1] (numeric) -0.9689124217106446 absolute error 3.3306690738754696e-16 relative error 3.437533670994815e-14% Desired digits 8 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 0.23971276930210264 Order of pole (three term test) 32.06120871905481 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.23999999999999932 y[1] (closed_form) -0.9713379748520298 y[1] (numeric) -0.9713379748520296 absolute error 2.220446049250313e-16 relative error 2.2859664779281055e-14% Desired digits 8 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 0.23088958777074262 Order of pole (three term test) 32.05650253861036 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.22999999999999932 y[1] (closed_form) -0.973666395005375 y[1] (numeric) -0.9736663950053749 absolute error 1.1102230246251565e-16 relative error 1.1402499154949552e-14% Desired digits 8 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 0.221974053482761 Order of pole (three term test) 32.051973751237234 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2199999999999993 y[1] (closed_form) -0.9758974493306056 y[1] (numeric) -0.9758974493306055 absolute error 1.1102230246251565e-16 relative error 1.1376431257061779e-14% Desired digits 8 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 0.21296973253300072 Order of pole (three term test) 32.04762416839002 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2099999999999993 y[1] (closed_form) -0.9780309147241484 y[1] (numeric) -0.978030914724148 absolute error 3.3306690738754696e-16 relative error 3.405484452211695e-14% Desired digits 8 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 0.20388022652978613 Order of pole (three term test) 32.04345552984385 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.1999999999999993 y[1] (closed_form) -0.9800665778412417 y[1] (numeric) -0.9800665778412414 absolute error 3.3306690738754696e-16 relative error 3.3984110357194485e-14% Desired digits 8 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 0.1947091711543264 Order of pole (three term test) 32.03946950299856 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.18999999999999928 y[1] (closed_form) -0.9820042351172704 y[1] (numeric) -0.9820042351172701 absolute error 3.3306690738754696e-16 relative error 3.3917054069300657e-14% Desired digits 8 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 0.18546023470649248 Order of pole (three term test) 32.03566768221175 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.17999999999999927 y[1] (closed_form) -0.9838436927881216 y[1] (numeric) -0.9838436927881212 absolute error 3.3306690738754696e-16 relative error 3.385364055581495e-14% Desired digits 8 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 0.1761371166375462 Order of pole (three term test) 32.03205158816103 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.16999999999999926 y[1] (closed_form) -0.9855847669095609 y[1] (numeric) -0.9855847669095605 absolute error 3.3306690738754696e-16 relative error 3.3793836772855666e-14% Desired digits 8 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 0.1667435460704086 Order of pole (three term test) 32.02862266723583 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.15999999999999925 y[1] (closed_form) -0.987227283375627 y[1] (numeric) -0.9872272833756269 absolute error 1.1102230246251565e-16 relative error 1.1245870564161984e-14% Desired digits 8 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 0.15728328030806016 Order of pole (three term test) 32.02538229095879 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.14999999999999925 y[1] (closed_form) -0.9887710779360424 y[1] (numeric) -0.9887710779360424 absolute error 0.0 relative error 0.0% Desired digits 8 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 0.1477601033306711 Order of pole (three term test) 32.0223317554372 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.13999999999999924 y[1] (closed_form) -0.9902159962126372 y[1] (numeric) -0.9902159962126375 absolute error 2.220446049250313e-16 relative error 2.2423855580429327e-14% Desired digits 8 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 0.13817782428205816 Order of pole (three term test) 32.01947228084462 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.12999999999999923 y[1] (closed_form) -0.9915618937147881 y[1] (numeric) -0.9915618937147883 absolute error 2.220446049250313e-16 relative error 2.239341853821785e-14% Desired digits 8 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 0.12854027594607884 Order of pole (three term test) 32.01680501093274 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.11999999999999922 y[1] (closed_form) -0.9928086358538664 y[1] (numeric) -0.9928086358538665 absolute error 1.1102230246251565e-16 relative error 1.1182648745498751e-14% Desired digits 8 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 0.11885131321356869 Order of pole (three term test) 32.01433101257399 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.10999999999999921 y[1] (closed_form) -0.9939560979566969 y[1] (numeric) -0.9939560979566971 absolute error 2.220446049250313e-16 relative error 2.2339478109897868e-14% Desired digits 8 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 0.10911481154043608 Order of pole (three term test) 32.0120512753347 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.0999999999999992 y[1] (closed_form) -0.9950041652780258 y[1] (numeric) -0.995004165278026 absolute error 2.220446049250313e-16 relative error 2.2315947276762124e-14% Desired digits 8 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 0.099334665397532 Order of pole (three term test) 32.00996671107938 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.08999999999999919 y[1] (closed_form) -0.9959527330119943 y[1] (numeric) -0.9959527330119945 absolute error 2.220446049250313e-16 relative error 2.2294693067764013e-14% Desired digits 8 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 0.0895147867129134 Order of pole (three term test) 32.00807815360594 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.07999999999999918 y[1] (closed_form) -0.9968017063026194 y[1] (numeric) -0.9968017063026196 absolute error 1.1102230246251565e-16 relative error 1.113785236928661e-14% Desired digits 8 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 0.07965910330712436 Order of pole (three term test) 32.006386358312184 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.06999999999999917 y[1] (closed_form) -0.9975510002532796 y[1] (numeric) -0.9975510002532798 absolute error 2.220446049250313e-16 relative error 2.2258972711034713e-14% Desired digits 8 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 0.06977155732211957 Order of pole (three term test) 32.00489200189368 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.059999999999999165 y[1] (closed_form) -0.9982005399352042 y[1] (numeric) -0.9982005399352044 absolute error 2.220446049250313e-16 relative error 2.2244488561331053e-14% Desired digits 8 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 0.05985610364446099 Order of pole (three term test) 32.00359568207307 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.049999999999999156 y[1] (closed_form) -0.9987502603949663 y[1] (numeric) -0.9987502603949665 absolute error 2.220446049250313e-16 relative error 2.223224500960044e-14% Desired digits 8 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 0.04991670832341543 Order of pole (three term test) 32.00249791736099 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.03999999999999915 y[1] (closed_form) -0.999200106660978 y[1] (numeric) -0.9992001066609782 absolute error 2.220446049250313e-16 relative error 2.2222235910986504e-14% Desired digits 8 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 0.03995734698458765 Order of pole (three term test) 32.00159914684869 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.02999999999999914 y[1] (closed_form) -0.9995500337489875 y[1] (numeric) -0.9995500337489879 absolute error 3.3306690738754696e-16 relative error 3.3321684372149054e-14% Desired digits 8 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 0.029982003239723647 Order of pole (three term test) 32.000899730032394 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.01999999999999913 y[1] (closed_form) -0.9998000066665778 y[1] (numeric) -0.9998000066665781 absolute error 3.3306690738754696e-16 relative error 3.33133531873061e-14% Desired digits 8 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 0.0199946670933184 Order of pole (three term test) 32.00039994666951 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.00999999999999912 y[1] (closed_form) -0.9999500004166653 y[1] (numeric) -0.9999500004166656 absolute error 3.3306690738754696e-16 relative error 3.33083561426834e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.009999333346667867 Order of pole (three term test) 32.00009999666671 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] 7.79000777999079e-05 y[1] (closed_form) -0.9999999969657889 y[1] (numeric) -0.9999999975166649 absolute error 5.508760114736333e-10 relative error 5.5087601314510743e-08% Desired digits 8 Estimated correct digits 12 Correct digits 10 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.01005576457605521 y[1] (closed_form) -0.9999494412254328 y[1] (numeric) -0.9999494604131096 absolute error 1.9187676780774154e-08 relative error 1.91886469352488e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.0200336290743105 y[1] (closed_form) -0.9997993335645853 y[1] (numeric) -0.9997994559823848 absolute error 1.2241779956401189e-07 relative error 1.2244236963787085e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.030011493572565724 y[1] (closed_form) -0.999549688927508 y[1] (numeric) -0.9995501212955468 absolute error 4.323680388162998e-07 relative error 4.325628266466873e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.03998935807082115 y[1] (closed_form) -0.9992005321680603 y[1] (numeric) -0.9992016589619945 absolute error 1.126793934269621e-06 relative error 0.000112769549053853% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.05011840233420169 y[1] (closed_form) -0.9987443357438808 y[1] (numeric) -0.9987468008623663 absolute error 2.465118485561746e-06 relative error 0.0002468217738352114% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.06009626683245714 y[1] (closed_form) -0.9981947627649345 y[1] (numeric) -0.9981994631968197 absolute error 4.700431885273915e-06 relative error 0.0004708932625787401% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.07007413133071225 y[1] (closed_form) -0.9975458125559394 y[1] (numeric) -0.9975540052583364 absolute error 8.192702396936369e-06 relative error 0.0008212858290633089% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.08005199582896724 y[1] (closed_form) -0.9967975497244019 y[1] (numeric) -0.9968108925336168 absolute error 1.3342809214833551e-05 relative error 0.001338567617719628% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09002986032722224 y[1] (closed_form) -0.9959500487650901 y[1] (numeric) -0.995970655880901 absolute error 2.0607115810866716e-05 relative error 0.002069091299952054% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10000772482547723 y[1] (closed_form) -0.995003394052618 y[1] (numeric) -0.9950338914771168 absolute error 3.0497424498898695e-05 relative error 0.003065057333591962% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10998558932373223 y[1] (closed_form) -0.9939576798330452 y[1] (numeric) -0.9940012607585295 absolute error 4.3580925484287825e-05 relative error 0.004384585618535399% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1201146335871123 y[1] (closed_form) -0.9927949062909743 y[1] (numeric) -0.9928556752561177 absolute error 6.076896514339847e-05 relative error 0.006120998884898381% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1300924980853673 y[1] (closed_form) -0.9915498985629645 y[1] (numeric) -0.9916321338292552 absolute error 8.223526629069777e-05 relative error 0.008293608461851478% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1400703625836223 y[1] (closed_form) -0.9902061751473454 y[1] (numeric) -0.9903151147429337 absolute error 0.00010893959558821997 relative error 0.011001708363615229% Desired digits 8 Estimated correct digits 12 Correct digits 4 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1500482270818773 y[1] (closed_form) -0.9887638698211274 y[1] (numeric) -0.9889055407308915 absolute error 0.00014167090976413554 relative error 0.014328083184285906% Desired digits 8 Estimated correct digits 12 Correct digits 4 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16002609158013228 y[1] (closed_form) -0.9872231261758354 y[1] (numeric) -0.9874043993906806 absolute error 0.000181273214845179 relative error 0.01836192954143704% Desired digits 8 Estimated correct digits 12 Correct digits 4 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17000395607838728 y[1] (closed_form) -0.9855840976032136 y[1] (numeric) -0.9858127430853415 absolute error 0.00022864548212786495 relative error 0.023198982479921804% Desired digits 8 Estimated correct digits 12 Correct digits 4 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18013300034176735 y[1] (closed_form) -0.9838198730920893 y[1] (numeric) -0.9841055368229856 absolute error 0.000285663730896335 relative error 0.02903618220259267% Desired digits 8 Estimated correct digits 12 Correct digits 4 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19011086484002235 y[1] (closed_form) -0.9819832912712215 y[1] (numeric) -0.9823349390164948 absolute error 0.000351647745273298 relative error 0.035809952002143965% Desired digits 8 Estimated correct digits 12 Correct digits 4 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20008872933827734 y[1] (closed_form) -0.9800489461850265 y[1] (numeric) -0.9804773902208176 absolute error 0.0004284440357911201 relative error 0.04371659573319237% Desired digits 8 Estimated correct digits 12 Correct digits 4 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.21006659383653234 y[1] (closed_form) -0.9780170304110086 y[1] (numeric) -0.9785342017223152 absolute error 0.0005171713113065746 relative error 0.05287958135956333% Desired digits 8 Estimated correct digits 12 Correct digits 4 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.22004445833478734 y[1] (closed_form) -0.9758877462405133 y[1] (numeric) -0.9765067489827002 absolute error 0.0006190027421868471 relative error 0.06342970741988292% Desired digits 8 Estimated correct digits 12 Correct digits 4 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.23002232283304233 y[1] (closed_form) -0.9736613056585867 y[1] (numeric) -0.9743964715021034 absolute error 0.0007351658435167385 relative error 0.07550529524427087% Desired digits 8 Estimated correct digits 12 Correct digits 4 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.24000018733129733 y[1] (closed_form) -0.9713379303228712 y[1] (numeric) -0.9722048726757616 absolute error 0.0008669423528904208 relative error 0.08925239361364695% Desired digits 8 Estimated correct digits 12 Correct digits 4 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2501292315946774 y[1] (closed_form) -0.9688804412117411 y[1] (numeric) -0.9698985001948083 absolute error 0.0010180589830671716 relative error 0.10507581119027698% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2601070960929324 y[1] (closed_form) -0.9663624402698491 y[1] (numeric) -0.967547852868443 absolute error 0.001185412598593949 relative error 0.1226674950511251% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2700849605911874 y[1] (closed_form) -0.9637482312269737 y[1] (numeric) -0.9651208023801947 absolute error 0.0013725711532209806 relative error 0.1424200957000485% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2800628250894424 y[1] (closed_form) -0.9610380743458045 y[1] (numeric) -0.9626191071027335 absolute error 0.0015810327569290017 relative error 0.164513019737042% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2900406895876974 y[1] (closed_form) -0.9582322394413051 y[1] (numeric) -0.9600445884894616 absolute error 0.0018123490481565252 relative error 0.18913463496210592% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3000185540859524 y[1] (closed_form) -0.955331005853852 y[1] (numeric) -0.9573991308931784 absolute error 0.0020681250393264072 relative error 0.21648256223799275% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3099964185842074 y[1] (closed_form) -0.9523346624214241 y[1] (numeric) -0.9546846813784784 absolute error 0.002350018957054334 relative error 0.24676398432029467% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.32012546284758747 y[1] (closed_form) -0.9491959441951714 y[1] (numeric) -0.951860602114688 absolute error 0.002664657919516644 relative error 0.28072790826935345% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.33010332734584247 y[1] (closed_form) -0.9460088559721541 y[1] (numeric) -0.9490132925923926 absolute error 0.0030044366202385264 relative error 0.31759074994610437% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.34008119184409746 y[1] (closed_form) -0.9427275859890085 y[1] (numeric) -0.9461032394567941 absolute error 0.0033756534677855665 relative error 0.3580730550325621% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.35005905634235246 y[1] (closed_form) -0.9393524609189793 y[1] (numeric) -0.9431326395552897 absolute error 0.003780178636310416 relative error 0.40242388172510074% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.36003692084060746 y[1] (closed_form) -0.9358838167792378 y[1] (numeric) -0.9401037514124544 absolute error 0.004219934633216571 relative error 0.4509036867139242% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.37001478533886245 y[1] (closed_form) -0.9323219988974288 y[1] (numeric) -0.9370188950051886 absolute error 0.004696896107759807 relative error 0.5037847560514921% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.37999264983711745 y[1] (closed_form) -0.9286673618772914 y[1] (numeric) -0.9338804515317505 absolute error 0.005213089654459102 relative error 0.5613516602888784% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3901216941004975 y[1] (closed_form) -0.9248627863215301 y[1] (numeric) -0.930642155599213 absolute error 0.005779369277682966 relative error 0.6248893742032084% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4000995585987525 y[1] (closed_form) -0.9210222194937214 y[1] (numeric) -0.9274032078444917 absolute error 0.006380988350770278 relative error 0.6928158969148276% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4100774230970075 y[1] (closed_form) -0.9170899584992022 y[1] (numeric) -0.924118220849062 absolute error 0.007028262349859871 relative error 0.7663656421842705% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4200552875952625 y[1] (closed_form) -0.9130663948218991 y[1] (numeric) -0.9207898191760497 absolute error 0.007723424354150632 relative error 0.8458776270763034% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4300331520935175 y[1] (closed_form) -0.9089519290355562 y[1] (numeric) -0.9174206873601405 absolute error 0.008468758324584269 relative error 0.9317058530884079% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4400110165917725 y[1] (closed_form) -0.9047469707638544 y[1] (numeric) -0.9140135696403139 absolute error 0.00926659887645953 relative error 1.0242199394860623% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4499888810900275 y[1] (closed_form) -0.9004519386396306 y[1] (numeric) -0.9105712696866378 absolute error 0.01011933104700724 relative error 1.1238057927106193% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.46011792535340756 y[1] (closed_form) -0.8960001385578108 y[1] (numeric) -0.9070437710378043 absolute error 0.011043632479993515 relative error 1.2325480772546744% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.47009578985166256 y[1] (closed_form) -0.8915249021949192 y[1] (numeric) -0.9035393313017669 absolute error 0.01201442910684769 relative error 1.347626866873642% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.48007365434991756 y[1] (closed_form) -0.8869609083283776 y[1] (numeric) -0.9000085197124288 absolute error 0.013047611384051194 relative error 1.4710469493679879% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.49005151884817255 y[1] (closed_form) -0.8823086113355132 y[1] (numeric) -0.8964543756949189 absolute error 0.014145764359405733 relative error 1.6032671763221134% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5000293833464275 y[1] (closed_form) -0.8775684743848436 y[1] (numeric) -0.8928799966465989 absolute error 0.01531152226175525 relative error 1.7447666716250596% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5100072478446862 y[1] (closed_form) -0.8727409693899634 y[1] (numeric) -0.8892885376286938 absolute error 0.01654756823873038 relative error 1.8960457706364988% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5199851123429449 y[1] (closed_form) -0.8678265769625666 y[1] (numeric) -0.8856832110521851 absolute error 0.01785663408961846 relative error 2.057627014848694% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5301141566063287 y[1] (closed_form) -0.8627493549223337 y[1] (numeric) -0.8820124352254968 absolute error 0.019263080303163038 relative error 2.232755109379031% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5400920211045873 y[1] (closed_form) -0.8576613663705422 y[1] (numeric) -0.8783891542490867 absolute error 0.020727787878544457 relative error 2.416779942678363% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.550069885602846 y[1] (closed_form) -0.852487991665578 y[1] (numeric) -0.8747620355011109 absolute error 0.022274043835532886 relative error 2.612827870104563% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5600477501011046 y[1] (closed_form) -0.8472297458528683 y[1] (numeric) -0.8711345183832016 absolute error 0.023904772530333296 relative error 2.821521865508798% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5700256145993633 y[1] (closed_form) -0.8418871524273495 y[1] (numeric) -0.8675100979859787 absolute error 0.025622945558629207 relative error 3.0435130747336516% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.580003479097622 y[1] (closed_form) -0.8364607432813493 y[1] (numeric) -0.8638923247410869 absolute error 0.027431581459737564 relative error 3.279482232737701% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5901325233610057 y[1] (closed_form) -0.8308669409710169 y[1] (numeric) -0.8602302423495398 absolute error 0.029363301378522944 relative error 3.5340558073241746% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6001103878592644 y[1] (closed_form) -0.8252732802073619 y[1] (numeric) -0.8566368735213301 absolute error 0.03136359331396821 relative error 3.800388800433191% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6100882523575231 y[1] (closed_form) -0.8195974577497375 y[1] (numeric) -0.8530611883173806 absolute error 0.03346373056764318 relative error 4.082947092042014% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6200661168557817 y[1] (closed_form) -0.8138400386657387 y[1] (numeric) -0.8495069557578873 absolute error 0.03566691709214853 relative error 4.3825463724570675% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6300439813540404 y[1] (closed_form) -0.8080015961464723 y[1] (numeric) -0.8459779983766103 absolute error 0.037976402230137984 relative error 4.700040496362303% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.640021845852299 y[1] (closed_form) -0.8020827114494914 y[1] (numeric) -0.8424781918403188 absolute error 0.04039548039082741 relative error 5.036323537983549% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6499997103505577 y[1] (closed_form) -0.7960839738409273 y[1] (numeric) -0.8390114645629361 absolute error 0.04292749072200874 relative error 5.392331981624149% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6601287546139415 y[1] (closed_form) -0.7899132833258593 y[1] (numeric) -0.8355301384376372 absolute error 0.04561685511177793 relative error 5.774919358199958% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6701066191122002 y[1] (closed_form) -0.7837554524512488 y[1] (numeric) -0.8321422178460481 absolute error 0.04838676539479936 relative error 6.173707020916593% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6800844836104588 y[1] (closed_form) -0.7775195932711357 y[1] (numeric) -0.8287995365786215 absolute error 0.051279943307485754 relative error 6.595324896153899% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6900623481087175 y[1] (closed_form) -0.7712063266086653 y[1] (numeric) -0.8255062308468456 absolute error 0.05429990423818032 relative error 7.040904925788274% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7000402126069761 y[1] (closed_form) -0.764816280993436 y[1] (numeric) -0.8222664875958571 absolute error 0.05745020660242106 relative error 7.511634889335486% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7100180771052348 y[1] (closed_form) -0.758350092598925 y[1] (numeric) -0.819084544087602 absolute error 0.060734451488676955 relative error 8.008761663170006% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7199959416034935 y[1] (closed_form) -0.7518084051791528 y[1] (numeric) -0.8159646874789865 absolute error 0.06415628229983372 relative error 8.533594710815391% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7301249858668772 y[1] (closed_form) -0.7450910472453037 y[1] (numeric) -0.8128655236840325 absolute error 0.0677744764387288 relative error 9.096133511374168% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7401028503651359 y[1] (closed_form) -0.7383992040659594 y[1] (numeric) -0.8098840066324351 absolute error 0.07148480256647571 relative error 9.681050869617426% Desired digits 8 Estimated correct digits 12 Correct digits 3 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7500807148633946 y[1] (closed_form) -0.7316338481110449 y[1] (numeric) -0.8069778005854693 absolute error 0.07534395247442438 relative error 10.29804083954696% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7600585793616532 y[1] (closed_form) -0.724795652918792 y[1] (numeric) -0.8041513886889369 absolute error 0.07935573577014488 relative error 10.948704707399246% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7700364438599119 y[1] (closed_form) -0.7178852992790844 y[1] (numeric) -0.8014093017939024 absolute error 0.08352400251481795 relative error 11.634728082424102% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7800143083581705 y[1] (closed_form) -0.7109034751656814 y[1] (numeric) -0.7987561180056163 absolute error 0.08785264283993488 relative error 12.357886254453906% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7899921728564292 y[1] (closed_form) -0.703850875667725 y[1] (numeric) -0.796196462227733 absolute error 0.09234558656000802 relative error 13.120049964049866% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.800121217119813 y[1] (closed_form) -0.6966197483895978 y[1] (numeric) -0.7936984904214829 absolute error 0.09707874203188505 relative error 13.93568618407756% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8100990816180716 y[1] (closed_form) -0.6894266660222187 y[1] (numeric) -0.7913415461133658 absolute error 0.10191488009114713 relative error 14.782555580445543% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8200769461163303 y[1] (closed_form) -0.6821649464359852 y[1] (numeric) -0.7890923531956973 absolute error 0.10692740675971202 relative error 15.674714351471906% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.830054810614589 y[1] (closed_form) -0.6748353125855803 y[1] (numeric) -0.7869557197925091 absolute error 0.11212040720692884 relative error 16.614484321715175% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8400326751128476 y[1] (closed_form) -0.6674384941870235 y[1] (numeric) -0.7849364984710747 absolute error 0.11749800428405122 relative error 17.604319395327984% Desired digits 8 Estimated correct digits 12 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8500105396111063 y[1] (closed_form) -0.6599752276450238 y[1] (numeric) -0.783039585758806 absolute error 0.12306435811378214 relative error 18.646814752867343% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.859988404109365 y[1] (closed_form) -0.6524462559796647 y[1] (numeric) -0.7812699216557685 absolute error 0.12882366567610382 relative error 19.744716824632828% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8701174483727487 y[1] (closed_form) -0.6447367736029017 y[1] (numeric) -0.7796087223991544 absolute error 0.13487194879625264 relative error 20.91891672977867% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8800953128710074 y[1] (closed_form) -0.6370776799692329 y[1] (numeric) -0.7781106654604951 absolute error 0.1410329854912622 relative error 22.137486514685815% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.890073177369266 y[1] (closed_form) -0.6293551608223048 y[1] (numeric) -0.776755010127556 absolute error 0.14739984930525118 relative error 23.42077390970482% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9000510418675247 y[1] (closed_form) -0.6215699849926005 y[1] (numeric) -0.7755468659549428 absolute error 0.1539768809623423 relative error 24.772251665944797% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9100289063657834 y[1] (closed_form) -0.6137229275485117 y[1] (numeric) -0.7744913834608267 absolute error 0.16076845591231503 relative error 26.1956085874936% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.920006770864042 y[1] (closed_form) -0.6058147697191753 y[1] (numeric) -0.7735937536141727 absolute error 0.16777898389499746 relative error 27.694766169661268% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9301358151274258 y[1] (closed_form) -0.597725104659467 y[1] (numeric) -0.7728493592055004 absolute error 0.1751242545460333 relative error 29.29846064367737% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9401136796256845 y[1] (closed_form) -0.5896962183177912 y[1] (numeric) -0.7722857583251959 absolute error 0.18258954000740468 relative error 30.9633221878669% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9500915441239431 y[1] (closed_form) -0.5816086236168526 y[1] (numeric) -0.7718959012550644 absolute error 0.19028727763821174 relative error 32.71740994053204% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9600694086222018 y[1] (closed_form) -0.5734631257329447 y[1] (numeric) -0.7716851361369088 absolute error 0.19822201040396414 relative error 34.56578139189265% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9700472731204605 y[1] (closed_form) -0.565260535607025 y[1] (numeric) -0.7716588489320086 absolute error 0.2063983133249836 relative error 36.51383748262833% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9800251376187191 y[1] (closed_form) -0.5570016698639816 y[1] (numeric) -0.7718224628849104 absolute error 0.21482079302092882 relative error 38.5673517053167% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9900030021169778 y[1] (closed_form) -0.5486873507313308 y[1] (numeric) -0.7721814379835068 absolute error 0.223494087252176 relative error 40.73250220809477% Desired digits 8 Estimated correct digits 11 Correct digits 2 h 0.0001511797651250803 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ; Iterations 7654 Total Elapsed Time 3 Seconds Elapsed Time(since restart) 3 Seconds Time to Timeout 2 Minutes 57.0 Seconds Percent Done 100.01416130727434%