##############ECHO OF PROBLEM################# ##############temp/sing7postode.ode################# diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=64; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(2.0) x_end=c(3.0) $array_y_init[0 + 1] = exact_soln_y(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=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(6.0) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb #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(c(1.0)/ (c( x) - c(6.0) ) / ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 2.0 y[1] (closed_form) -0.0009765625 y[1] (numeric) -0.0009765625 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.000000000000007 Order of pole (three term test) 4.939520197282191e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.009999999999999 y[1] (closed_form) -0.0009888616207243456 y[1] (numeric) -0.0009888616207243467 absolute error 1.0842021724855044e-18 relative error 1.0964144525007669e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.990000000000001 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.990000000000035 Order of pole (three term test) 9.027745722548631e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.019999999999998 y[1] (closed_form) -0.0010013470890107953 y[1] (numeric) -0.0010013470890107975 absolute error 2.168404344971009e-18 relative error 2.165487240905767e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.980000000000002 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9800000000000235 Order of pole (three term test) 4.1239716625438514e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0299999999999967 y[1] (closed_form) -0.0010140222071652644 y[1] (numeric) -0.001014022207165268 absolute error 3.686287386450715e-18 relative error 3.635312284487205e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.9700000000000033 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.970000000000015 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0399999999999956 y[1] (closed_form) -0.0010268903445442815 y[1] (numeric) -0.0010268903445442867 absolute error 5.204170427930421e-18 relative error 5.06789303802438e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.9600000000000044 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.960000000000015 Order of pole (three term test) 6.879894312420594e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0499999999999945 y[1] (closed_form) -0.0010399549390904676 y[1] (numeric) -0.0010399549390904738 absolute error 6.288372600415926e-18 relative error 6.046774109189446e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.9500000000000055 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.950000000000024 Order of pole (three term test) 3.1406570856690234e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0599999999999934 y[1] (closed_form) -0.0010532194989071803 y[1] (numeric) -0.0010532194989071883 absolute error 8.023096076392733e-18 relative error 7.617686612066611e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.9400000000000066 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.940000000000013 Order of pole (three term test) 2.866744998467638e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0699999999999923 y[1] (closed_form) -0.0010666876038734354 y[1] (numeric) -0.001066687603873445 absolute error 9.540979117872439e-18 relative error 8.944492354862404e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.9300000000000077 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.930000000000017 Order of pole (three term test) 2.6161153635335355e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.079999999999991 y[1] (closed_form) -0.001080362907300231 y[1] (numeric) -0.0010803629073002415 absolute error 1.0625181290357943e-17 relative error 9.834826074239909e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.920000000000009 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.920000000000008 Order of pole (three term test) 2.386841006364236e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.08999999999999 y[1] (closed_form) -0.0010942491376294482 y[1] (numeric) -0.0010942491376294608 absolute error 1.2576745200831851e-17 relative error 1.149349336301765e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.91000000000001 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9100000000000192 Order of pole (three term test) 4.354299921512708e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.099999999999989 y[1] (closed_form) -0.0011083501001765456 y[1] (numeric) -0.0011083501001765595 absolute error 1.3877787807814457e-17 relative error 1.252112288852043e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.900000000000011 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9000000000000363 Order of pole (three term test) 7.94165327099197e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.109999999999988 y[1] (closed_form) -0.0011226696789182718 y[1] (numeric) -0.0011226696789182868 absolute error 1.496198998029996e-17 relative error 1.3327152466357083e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.890000000000012 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.8900000000000228 Order of pole (three term test) 7.240535993605118e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.119999999999987 y[1] (closed_form) -0.0011372118383266986 y[1] (numeric) -0.0011372118383267155 absolute error 1.691355389077387e-17 relative error 1.487282608283483e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.880000000000013 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.8800000000000083 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1299999999999857 y[1] (closed_form) -0.0011519806252508894 y[1] (numeric) -0.001151980625250908 absolute error 1.8648277366750676e-17 relative error 1.6188013025556984e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.8700000000000143 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.870000000000025 Order of pole (three term test) 3.00711345674662e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1399999999999846 y[1] (closed_form) -0.0011669801708475648 y[1] (numeric) -0.0011669801708475852 absolute error 2.0383000842727483e-17 relative error 1.746645003224308e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.8600000000000154 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.8600000000000314 Order of pole (three term test) 2.739668659322712e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1499999999999835 y[1] (closed_form) -0.0011822146925621788 y[1] (numeric) -0.0011822146925622012 absolute error 2.233456475320139e-17 relative error 1.889213938358045e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.8500000000000165 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.8500000000000107 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1599999999999824 y[1] (closed_form) -0.0011976884961618533 y[1] (numeric) -0.0011976884961618776 absolute error 2.42861286636753e-17 relative error 2.0277500152588357e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.8400000000000176 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.8400000000000136 Order of pole (three term test) 4.544741084124509e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1699999999999813 y[1] (closed_form) -0.0012134059778216699 y[1] (numeric) -0.0012134059778216954 absolute error 2.5587171270657905e-17 relative error 2.1087065449102614e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.8300000000000187 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.8300000000000343 Order of pole (three term test) 4.137527868056895e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.17999999999998 y[1] (closed_form) -0.0012293716262658607 y[1] (numeric) -0.0012293716262658885 absolute error 2.7755575615628914e-17 relative error 2.2577042631067333e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.82000000000002 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.820000000000028 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.189999999999979 y[1] (closed_form) -0.0012455900249654977 y[1] (numeric) -0.0012455900249655272 absolute error 2.949029909160572e-17 relative error 2.3675766906067337e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.810000000000021 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.810000000000042 Order of pole (three term test) 6.853527962961921e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.199999999999978 y[1] (closed_form) -0.0012620658543943152 y[1] (numeric) -0.0012620658543943464 absolute error 3.122502256758253e-17 relative error 2.4741199089462648e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.800000000000022 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.800000000000039 Order of pole (three term test) 6.2348289452635e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.209999999999977 y[1] (closed_form) -0.0012788038943443707 y[1] (numeric) -0.0012788038943444037 absolute error 3.2959746043559335e-17 relative error 2.5773886198913594e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.790000000000023 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7900000000000373 Order of pole (three term test) 2.8352843972160073e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2199999999999758 y[1] (closed_form) -0.0012958090263032907 y[1] (numeric) -0.0012958090263033256 absolute error 3.491130995403324e-17 relative error 2.6941709191229287e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.7800000000000242 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.780000000000046 Order of pole (three term test) 7.734123771653265e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2299999999999747 y[1] (closed_form) -0.0013130862358949043 y[1] (numeric) -0.0013130862358949414 absolute error 3.707971429900425e-17 relative error 2.823859795753126e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.7700000000000253 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.770000000000035 Order of pole (three term test) 2.3435470471887806e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2399999999999736 y[1] (closed_form) -0.00133064061538514 y[1] (numeric) -0.0013306406153851794 absolute error 3.924811864397526e-17 relative error 2.9495656595913614e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.7600000000000264 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.760000000000041 Order of pole (three term test) 4.259684976018637e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2499999999999725 y[1] (closed_form) -0.0013484773662550947 y[1] (numeric) -0.0013484773662551356 absolute error 4.098284211995207e-17 relative error 3.0391939194179432e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.7500000000000275 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7500000000000386 Order of pole (three term test) 3.8702650038878496e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2599999999999714 y[1] (closed_form) -0.0013666018018432743 y[1] (numeric) -0.0013666018018433173 absolute error 4.2934406030425976e-17 relative error 3.141691015811335e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.7400000000000286 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7400000000000353 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2699999999999703 y[1] (closed_form) -0.0013850193500590518 y[1] (numeric) -0.0013850193500590973 absolute error 4.5536491244391186e-17 relative error 3.287787368634936e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.7300000000000297 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7300000000000346 Order of pole (three term test) 3.1925154660147284e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.279999999999969 y[1] (closed_form) -0.001403735556169459 y[1] (numeric) -0.0014037355561695066 absolute error 4.7704895589362195e-17 relative error 3.3984246804676124e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.720000000000031 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7200000000000437 Order of pole (three term test) 2.898417214964262e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.289999999999968 y[1] (closed_form) -0.0014227560856614981 y[1] (numeric) -0.0014227560856615478 absolute error 4.96564594998361e-17 relative error 3.490159697805739e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.710000000000032 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7100000000000333 Order of pole (three term test) 2.6307271742604493e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.299999999999967 y[1] (closed_form) -0.0014420867271822332 y[1] (numeric) -0.0014420867271822853 absolute error 5.204170427930421e-17 relative error 3.6087777037509492e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.700000000000033 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7000000000000397 Order of pole (three term test) 7.161407485672276e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.309999999999966 y[1] (closed_form) -0.0014617333955589914 y[1] (numeric) -0.0014617333955590456 absolute error 5.421010862427522e-17 relative error 3.7086180550417245e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.690000000000034 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.69000000000005 Order of pole (three term test) 4.331060417896573e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3199999999999648 y[1] (closed_form) -0.0014817021349020777 y[1] (numeric) -0.001481702134902134 absolute error 5.637851296924623e-17 relative error 3.80498290724081e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.6800000000000352 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.6800000000000437 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3299999999999637 y[1] (closed_form) -0.0015019991217924973 y[1] (numeric) -0.0015019991217925556 absolute error 5.833007687972014e-17 relative error 3.883496070897071e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.6700000000000363 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.6700000000000377 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3399999999999626 y[1] (closed_form) -0.0015226306685572487 y[1] (numeric) -0.001522630668557309 absolute error 6.028164079019405e-17 relative error 3.959045488510567e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.6600000000000374 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.6600000000000468 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3499999999999615 y[1] (closed_form) -0.0015436032266348415 y[1] (numeric) -0.0015436032266349044 absolute error 6.288372600415926e-17 relative error 4.073827063788276e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.6500000000000385 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.6500000000000394 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3599999999999604 y[1] (closed_form) -0.0015649233900337852 y[1] (numeric) -0.0015649233900338498 absolute error 6.461844948013606e-17 relative error 4.1291765393538535e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.6400000000000396 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.640000000000048 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3699999999999593 y[1] (closed_form) -0.0015865978988868728 y[1] (numeric) -0.00158659789888694 absolute error 6.722053469410127e-17 relative error 4.236771947149428e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.6300000000000407 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.6300000000000514 Order of pole (three term test) 4.800799376764007e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.379999999999958 y[1] (closed_form) -0.0016086336431041987 y[1] (numeric) -0.0016086336431042686 absolute error 6.982261990806649e-17 relative error 4.3404923307042726e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.620000000000042 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.620000000000059 Order of pole (three term test) 8.69387898958173e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.389999999999957 y[1] (closed_form) -0.0016310376661279235 y[1] (numeric) -0.0016310376661279958 absolute error 7.22078646875346e-17 relative error 4.4271120273363e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.610000000000043 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.610000000000056 Order of pole (three term test) 3.934905661291203e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.399999999999956 y[1] (closed_form) -0.0016538171687919192 y[1] (numeric) -0.0016538171687919938 absolute error 7.45931094670027e-17 relative error 4.510360085419327e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.600000000000044 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.6000000000000574 Order of pole (three term test) 3.560943506071017e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.409999999999955 y[1] (closed_form) -0.0016769795132895258 y[1] (numeric) -0.001676979513289603 absolute error 7.719519468096792e-17 relative error 4.603228248718646e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.590000000000045 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5900000000000616 Order of pole (three term test) 3.221626618136404e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4199999999999537 y[1] (closed_form) -0.0017005322272527575 y[1] (numeric) -0.001700532227252838 absolute error 8.044780119842443e-17 relative error 4.730742523379836e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.5800000000000463 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.580000000000053 Order of pole (three term test) 2.9138286909511787e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4299999999999526 y[1] (closed_form) -0.0017244830079464143 y[1] (numeric) -0.0017244830079464972 absolute error 8.283304597789254e-17 relative error 4.8033553010495334e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.5700000000000474 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5700000000000593 Order of pole (three term test) 7.904093897145025e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4399999999999515 y[1] (closed_form) -0.0017488397265806644 y[1] (numeric) -0.0017488397265807499 absolute error 8.543513119185775e-17 relative error 4.885246480470839e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.5600000000000485 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5600000000000462 Order of pole (three term test) 2.3816337886968945e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4499999999999504 y[1] (closed_form) -0.0017736104327457961 y[1] (numeric) -0.0017736104327458844 absolute error 8.825405684032006e-17 relative error 4.97595499050434e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.5500000000000496 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.550000000000059 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4599999999999493 y[1] (closed_form) -0.0017988033589729517 y[1] (numeric) -0.001798803358973043 absolute error 9.128982292327947e-17 relative error 5.075030712384398e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.5400000000000507 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.540000000000053 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4699999999999482 y[1] (closed_form) -0.001824426925424794 y[1] (numeric) -0.0018244269254248878 absolute error 9.389190813724468e-17 relative error 5.146378121742704e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.5300000000000518 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5300000000000726 Order of pole (three term test) 7.02464596885969e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.479999999999947 y[1] (closed_form) -0.0018504897447201864 y[1] (numeric) -0.0018504897447202831 absolute error 9.6710833785707e-17 relative error 5.2262291137598655e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.520000000000053 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5200000000000684 Order of pole (three term test) 3.171326356689711e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.489999999999946 y[1] (closed_form) -0.0018770006268971125 y[1] (numeric) -0.0018770006268972123 absolute error 9.974659986866641e-17 relative error 5.3141484578808294e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.510000000000054 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.510000000000058 Order of pole (three term test) 2.862603806981763e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.499999999999945 y[1] (closed_form) -0.0019039685845182053 y[1] (numeric) -0.0019039685845183086 absolute error 1.0321604682062002e-16 relative error 5.4211003091071795e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.500000000000055 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5000000000000617 Order of pole (three term test) 5.166359747918374e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.509999999999944 y[1] (closed_form) -0.001931402837923404 y[1] (numeric) -0.0019314028379235097 absolute error 1.0560129160008813e-16 relative error 5.4675953419240075e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.490000000000056 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.490000000000061 Order of pole (three term test) 4.6606921527768294e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5199999999999427 y[1] (closed_form) -0.0019593128206344163 y[1] (numeric) -0.001959312820634525 absolute error 1.0885389811754465e-16 relative error 5.55571815644519e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.4800000000000573 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.480000000000064 Order of pole (three term test) 4.2032752395983324e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5299999999999416 y[1] (closed_form) -0.0019877081849158295 y[1] (numeric) -0.0019877081849159414 absolute error 1.1188966420050406e-16 relative error 5.629079009162609e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.4700000000000584 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.4700000000000606 Order of pole (three term test) 3.789624154680235e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5399999999999405 y[1] (closed_form) -0.0020165988074978746 y[1] (numeric) -0.0020165988074979896 absolute error 1.1492543028346347e-16 relative error 5.6989734327007226e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.4600000000000595 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.460000000000078 Order of pole (three term test) 6.831319529873468e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5499999999999394 y[1] (closed_form) -0.002045994795466033 y[1] (numeric) -0.0020459947954661515 absolute error 1.1839487723541708e-16 relative error 5.78666561116297e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.4500000000000606 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.4500000000000584 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5599999999999383 y[1] (closed_form) -0.0020759064923228437 y[1] (numeric) -0.0020759064923229647 absolute error 1.209969624493823e-16 relative error 5.828632594813665e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.4400000000000617 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.4400000000000723 Order of pole (three term test) 5.5445841054390524e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5699999999999372 y[1] (closed_form) -0.002106344484227472 y[1] (numeric) -0.002106344484227597 absolute error 1.249000902703301e-16 relative error 5.929708611558796e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.4300000000000628 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.430000000000074 Order of pole (three term test) 4.9929057104559355e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.579999999999936 y[1] (closed_form) -0.0021373196064187945 y[1] (numeric) -0.0021373196064189233 absolute error 1.2880321809127793e-16 relative error 6.026390143264317e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.420000000000064 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.4200000000000643 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.589999999999935 y[1] (closed_form) -0.002168842949827943 y[1] (numeric) -0.002168842949828075 absolute error 1.3183898417423734e-16 relative error 6.07877044230871e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.410000000000065 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.410000000000072 Order of pole (three term test) 4.045038754180251e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.599999999999934 y[1] (closed_form) -0.0022009258678864817 y[1] (numeric) -0.0022009258678866183 absolute error 1.3660947373317356e-16 relative error 6.206909361484207e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.400000000000066 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.400000000000073 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.609999999999933 y[1] (closed_form) -0.0022335799835366027 y[1] (numeric) -0.0022335799835367432 absolute error 1.4051260155412137e-16 relative error 6.290914253790757e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.390000000000067 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.3900000000000743 Order of pole (three term test) 3.273061595810211e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6199999999999317 y[1] (closed_form) -0.0022668171964499496 y[1] (numeric) -0.002266817196450094 absolute error 1.444157293750692e-16 relative error 6.370859088295161e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.3800000000000683 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.3800000000000665 Order of pole (three term test) 2.942837307089659e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6299999999999306 y[1] (closed_form) -0.002300649690461922 y[1] (numeric) -0.002300649690462071 absolute error 1.487525380650112e-16 relative error 6.4656752691082155e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.3700000000000694 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.3700000000000845 Order of pole (three term test) 5.290192434625696e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6399999999999295 y[1] (closed_form) -0.0023350899412285593 y[1] (numeric) -0.002335089941228711 absolute error 1.5178830414797062e-16 relative error 6.500319386760338e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.3600000000000705 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.3600000000000723 Order of pole (three term test) 4.753451036530088e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6499999999999284 y[1] (closed_form) -0.002370150724113346 y[1] (numeric) -0.0023701507241135006 absolute error 1.5482407023093003e-16 relative error 6.532245762085382e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.3500000000000716 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.350000000000076 Order of pole (three term test) 4.269805497566529e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6599999999999273 y[1] (closed_form) -0.002405845122311573 y[1] (numeric) -0.002405845122311733 absolute error 1.6002824065886045e-16 relative error 6.651643498360479e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.3400000000000727 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.340000000000077 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.669999999999926 y[1] (closed_form) -0.0024421865352201363 y[1] (numeric) -0.0024421865352203 absolute error 1.6393136847980827e-16 relative error 6.712483510807321e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.330000000000074 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.330000000000078 Order of pole (three term test) 3.441814381683627e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.679999999999925 y[1] (closed_form) -0.0024791886870609518 y[1] (numeric) -0.0024791886870611205 absolute error 1.687018580387445e-16 relative error 6.804720387730492e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.320000000000075 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.3200000000000807 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.689999999999924 y[1] (closed_form) -0.0025168656357664816 y[1] (numeric) -0.0025168656357666547 absolute error 1.730386667286865e-16 relative error 6.875165057271308e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.310000000000076 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.3100000000000898 Order of pole (three term test) 2.7707849157711986e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.699999999999923 y[1] (closed_form) -0.0025552317821361426 y[1] (numeric) -0.0025552317821363195 absolute error 1.7694179454963432e-16 relative error 6.924686667826006e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.300000000000077 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.3000000000000766 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.709999999999922 y[1] (closed_form) -0.002594301879272721 y[1] (numeric) -0.0025943018792729026 absolute error 1.8171228410857054e-16 relative error 7.004284488261298e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.290000000000078 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.290000000000086 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7199999999999207 y[1] (closed_form) -0.002634091042308241 y[1] (numeric) -0.002634091042308427 absolute error 1.8604909279851256e-16 relative error 7.063123096743029e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.2800000000000793 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.280000000000098 Order of pole (three term test) 7.985707589080043e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7299999999999196 y[1] (closed_form) -0.0026746147584290766 y[1] (numeric) -0.002674614758429267 absolute error 1.9038590148845458e-16 relative error 7.118255101541312e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.2700000000000804 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.270000000000096 Order of pole (three term test) 7.154414959513878e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7399999999999185 y[1] (closed_form) -0.0027158888972104687 y[1] (numeric) -0.002715888897210664 absolute error 1.951563910473908e-16 relative error 7.1857280777515945e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.2600000000000815 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2600000000000895 Order of pole (three term test) 3.203750130216061e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7499999999999174 y[1] (closed_form) -0.0027579297212709905 y[1] (numeric) -0.0027579297212711905 absolute error 1.9992688060632702e-16 relative error 7.249165164157657e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.2500000000000826 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.250000000000087 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7599999999999163 y[1] (closed_form) -0.0028007538972578817 y[1] (numeric) -0.0028007538972580864 absolute error 2.0469737016526324e-16 relative error 7.308652515512882e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.2400000000000837 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2400000000000837 Order of pole (three term test) 2.5671154579764288e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.769999999999915 y[1] (closed_form) -0.0028443785071745925 y[1] (numeric) -0.002844378507174802 absolute error 2.0946785972419946e-16 relative error 7.364275155217308e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.230000000000085 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2300000000000857 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.779999999999914 y[1] (closed_form) -0.0028888210600623034 y[1] (numeric) -0.0028888210600625176 absolute error 2.1423834928313568e-16 relative error 7.416116984362998e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.220000000000086 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.220000000000092 Order of pole (three term test) 4.1083403135521406e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.789999999999913 y[1] (closed_form) -0.0029340995040476204 y[1] (numeric) -0.00293409950404784 absolute error 2.194425197110661e-16 relative error 7.479041505182182e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.210000000000087 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2100000000001017 Order of pole (three term test) 7.346258264501909e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.799999999999912 y[1] (closed_form) -0.0029802322387691214 y[1] (numeric) -0.0029802322387693456 absolute error 2.242130092700023e-16 relative error 7.523340173066697e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.200000000000088 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2000000000000997 Order of pole (three term test) 3.282874265989521e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.809999999999911 y[1] (closed_form) -0.003027238128195882 y[1] (numeric) -0.0030272381281961115 absolute error 2.2941717969793274e-16 relative error 7.57843189014855e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.190000000000089 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.190000000000097 Order of pole (three term test) 5.866102074911825e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8199999999999097 y[1] (closed_form) -0.00307513651385165 y[1] (numeric) -0.0030751365138518855 absolute error 2.3548871186385156e-16 relative error 7.65782952409156e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.1800000000000903 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.1800000000001085 Order of pole (three term test) 5.239156181737076e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8299999999999086 y[1] (closed_form) -0.0031239472284588098 y[1] (numeric) -0.003123947228459051 absolute error 2.411265631607762e-16 relative error 7.718650333275164e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.1700000000000914 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.1700000000000994 Order of pole (three term test) 4.677550291232883e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8399999999999075 y[1] (closed_form) -0.0031736906100168524 y[1] (numeric) -0.0031736906100170987 absolute error 2.463307335887066e-16 relative error 7.761649255010355e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.1600000000000925 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.1600000000001085 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8499999999999064 y[1] (closed_form) -0.0032243875163306284 y[1] (numeric) -0.0032243875163308804 absolute error 2.5196858488563123e-16 relative error 7.81446347901672e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.1500000000000936 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.1500000000000985 Order of pole (three term test) 3.724474131009756e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8599999999999053 y[1] (closed_form) -0.00327605934000422 y[1] (numeric) -0.003276059340004478 absolute error 2.5804011705155006e-16 relative error 7.876539777549257e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.1400000000000947 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.1400000000001245 Order of pole (three term test) 9.964915287497603e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.869999999999904 y[1] (closed_form) -0.003328728023916928 y[1] (numeric) -0.003328728023917192 absolute error 2.641116492174689e-16 relative error 7.934311464313856e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.130000000000096 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.1300000000001047 Order of pole (three term test) 5.922583236669145e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.879999999999903 y[1] (closed_form) -0.003382416077198453 y[1] (numeric) -0.003382416077198723 absolute error 2.701831813833877e-16 relative error 7.987875388978514e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.120000000000097 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.1200000000000987 Order of pole (three term test) 5.278133930315026e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.889999999999902 y[1] (closed_form) -0.003437146591721059 y[1] (numeric) -0.0034371465917213346 absolute error 2.7538735181131813e-16 relative error 8.012092136967173e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.110000000000098 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.1100000000001136 Order of pole (three term test) 7.053103963073645e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.899999999999901 y[1] (closed_form) -0.0034929432591271742 y[1] (numeric) -0.003492943259127457 absolute error 2.8275992658421956e-16 relative error 8.095176634929831e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.100000000000099 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.100000000000111 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9099999999998998 y[1] (closed_form) -0.003549830388411622 y[1] (numeric) -0.00354983038841191 absolute error 2.883977778811442e-16 relative error 8.12426922769649e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.0900000000001002 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.0900000000001073 Order of pole (three term test) 3.7275225606939604e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9199999999998987 y[1] (closed_form) -0.003607832924078399 y[1] (numeric) -0.003607832924078693 absolute error 2.940356291780688e-16 relative error 8.149923662365229e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.0800000000001013 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.080000000000108 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9299999999998976 y[1] (closed_form) -0.0036669764648927503 y[1] (numeric) -0.003666976464893051 absolute error 3.0054084221298183e-16 relative error 8.195875950945649e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.0700000000001024 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.0700000000001113 Order of pole (three term test) 2.9505062475242674e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9399999999998965 y[1] (closed_form) -0.0037272872832500516 y[1] (numeric) -0.0037272872832503595 absolute error 3.0791341698588326e-16 relative error 8.26105941362788e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.0600000000001035 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.0600000000001075 Order of pole (three term test) 2.6235320540159417e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9499999999998954 y[1] (closed_form) -0.003788792345183917 y[1] (numeric) -0.0037887923451842306 absolute error 3.135512682828079e-16 relative error 8.275757542673861e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.0500000000001046 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.05000000000009 Order of pole (three term test) 6.995688973137243e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9599999999998943 y[1] (closed_form) -0.00385151933103678 y[1] (numeric) -0.0038515193310371012 absolute error 3.213575239247035e-16 relative error 8.343656004400689e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.0400000000001057 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.0400000000001213 Order of pole (three term test) 8.287509182983034e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.969999999999893 y[1] (closed_form) -0.003915496656817206 y[1] (numeric) -0.003915496656817534 absolute error 3.2786273695961654e-16 relative error 8.373464867829225e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.030000000000107 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.030000000000128 Order of pole (three term test) 7.360539349787284e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.979999999999892 y[1] (closed_form) -0.003980753496269057 y[1] (numeric) -0.003980753496269392 absolute error 3.3480163086352377e-16 relative error 8.41050899477486e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.020000000000108 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.0200000000001195 Order of pole (three term test) 6.534689538404568e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.989999999999891 y[1] (closed_form) -0.004047319803678747 y[1] (numeric) -0.004047319803679091 absolute error 3.434752482434078e-16 relative error 8.486486487457981e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.010000000000109 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.010000000000113 Order of pole (three term test) 2.8996051232923426e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.99999999999989 y[1] (closed_form) -0.0041152263374478045 y[1] (numeric) -0.004115226337448157 absolute error 3.5214886562329184e-16 relative error 8.557217434647562e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.00000000000011 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.000000000000122 Order of pole (three term test) 5.144464594279791e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; Iterations 1001 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.19999999998896%