##############ECHO OF PROBLEM################# ##############temp/sing1postode.ode################# diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(-2.0) x_end=c(-1.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=c(0.001) $glob_min_h=c(0.001) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=2 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(0.0) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.001) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(1.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=c(0.0) #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=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(x) + c(0.000001))) 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) 0.24999993750001562 y[1] (numeric) 0.24999993750001562 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 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0000083335095917 Order of pole (three term test) 2.000050001534285 Radius of convergence (six term test) for eq 1 1.999999363725047 Order of pole (six term test) 1.000000000262487 TOP MAIN SOLVE Loop x[1] -1.990000000000001 y[1] (closed_form) 0.2525188120201982 y[1] (numeric) 0.2525188120201985 absolute error 2.7755575615628914e-16 relative error 1.0991488275102779e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9900002512562667 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.990008375388292 Order of pole (three term test) 2.0000505053403224 Radius of convergence (six term test) for eq 1 1.9899999675715794 Order of pole (six term test) 1.0000000000907523 TOP MAIN SOLVE Loop x[1] -1.9800000000000022 y[1] (closed_form) 0.255075947588014 y[1] (numeric) 0.2550759475880146 absolute error 6.106226635438361e-16 relative error 2.393885700779924e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9800002525252387 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.980008417690061 Order of pole (three term test) 2.000051016799527 Radius of convergence (six term test) for eq 1 1.9799996874383983 Order of pole (six term test) 1.0000000001762714 TOP MAIN SOLVE Loop x[1] -1.9700000000000033 y[1] (closed_form) 0.25767212304565273 y[1] (numeric) 0.2576721230456535 absolute error 7.771561172376096e-16 relative error 3.016065952543566e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9700002538070935 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9700084604212915 Order of pole (three term test) 2.0000515360674056 Radius of convergence (six term test) for eq 1 1.9699990734217119 Order of pole (six term test) 1.0000000003683915 TOP MAIN SOLVE Loop x[1] -1.9600000000000044 y[1] (closed_form) 0.2603081371542738 y[1] (numeric) 0.26030813715427487 absolute error 1.0547118733938987e-15 relative error 4.0517821875418935e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9600002551020288 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9600085035886339 Order of pole (three term test) 2.000052063304321 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.9500000000000055 y[1] (closed_form) 0.2629848092084642 y[1] (numeric) 0.26298480920846556 absolute error 1.3877787807814457e-15 relative error 5.277030201700259e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9500002564102452 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9500085471987056 Order of pole (three term test) 2.000052598673255 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.9400000000000066 y[1] (closed_form) 0.2657029796729231 y[1] (numeric) 0.2657029796729248 absolute error 1.6653345369377348e-15 relative error 6.267654728553439e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9400002577319482 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9400085912584066 Order of pole (three term test) 2.000053142343074 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.9300000000000077 y[1] (closed_form) 0.2684635108422994 y[1] (numeric) 0.26846351084230136 absolute error 1.942890293094024e-15 relative error 7.237073995636282e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9300002590673477 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9300086357747097 Order of pole (three term test) 2.000053694485524 Radius of convergence (six term test) for eq 1 1.9299994523939343 Order of pole (six term test) 1.0000000002635456 TOP MAIN SOLVE Loop x[1] -1.9200000000000088 y[1] (closed_form) 0.2712672875251474 y[1] (numeric) 0.2712672875251496 absolute error 2.220446049250313e-15 relative error 8.185454536402478e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9200002604166577 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9200086807547792 Order of pole (three term test) 2.0000542552785685 Radius of convergence (six term test) for eq 1 1.9199995867151778 Order of pole (six term test) 1.0000000002135057 TOP MAIN SOLVE Loop x[1] -1.91000000000001 y[1] (closed_form) 0.2741152177530144 y[1] (numeric) 0.2741152177530169 absolute error 2.4980018054066022e-15 relative error 9.112962884305726e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.9100002617800966 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.910008726205841 Order of pole (three term test) 2.0000548249029015 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.900000000000011 y[1] (closed_form) 0.27700823351572157 y[1] (numeric) 0.27700823351572434 absolute error 2.7755575615628914e-15 relative error 1.0019765572799715e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.9000002631578876 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9000087721354193 Order of pole (three term test) 2.0000554035456894 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8900000000000121 y[1] (closed_form) 0.27994729152394826 y[1] (numeric) 0.27994729152395137 absolute error 3.1086244689504383e-15 relative error 1.1104320574162472e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.890000264550258 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8900088185510144 Order of pole (three term test) 2.0000559913977627 Radius of convergence (six term test) for eq 1 1.8899990064534127 Order of pole (six term test) 1.000000000443901 TOP MAIN SOLVE Loop x[1] -1.8800000000000132 y[1] (closed_form) 0.28293337400028634 y[1] (numeric) 0.2829333740002898 absolute error 3.4416913763379853e-15 relative error 1.216431744222052e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8800002659574413 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.880008865460418 Order of pole (three term test) 2.000056588655403 Radius of convergence (six term test) for eq 1 1.879999683931361 Order of pole (six term test) 1.0000000002070504 TOP MAIN SOLVE Loop x[1] -1.8700000000000143 y[1] (closed_form) 0.28596748949998435 y[1] (numeric) 0.2859674894999882 absolute error 3.83026943495679e-15 relative error 1.3394073017370039e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8700002673796743 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8700089128715984 Order of pole (three term test) 2.0000571955214506 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8600000000000154 y[1] (closed_form) 0.2890506737626632 y[1] (numeric) 0.2890506737626674 absolute error 4.218847493575595e-15 relative error 1.4595529007621864e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8600002688172004 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8600089607926145 Order of pole (three term test) 2.0000578122024613 Radius of convergence (six term test) for eq 1 1.8600010308837291 Order of pole (six term test) 0.9999999997044 TOP MAIN SOLVE Loop x[1] -1.8500000000000165 y[1] (closed_form) 0.2921839905963452 y[1] (numeric) 0.2921839905963498 absolute error 4.6074255521944e-15 relative error 1.5768918559811168e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8500002702702671 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.850009009231698 Order of pole (three term test) 2.0000584389106306 Radius of convergence (six term test) for eq 1 1.850000873146526 Order of pole (six term test) 0.999999999763844 TOP MAIN SOLVE Loop x[1] -1.8400000000000176 y[1] (closed_form) 0.2953685327952056 y[1] (numeric) 0.2953685327952104 absolute error 4.829470157119431e-15 relative error 1.6350658993414015e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8400002717391282 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8400090581973598 Order of pole (three term test) 2.000059075865215 Radius of convergence (six term test) for eq 1 1.8399999904067432 Order of pole (six term test) 1.0000000001041371 TOP MAIN SOLVE Loop x[1] -1.8300000000000187 y[1] (closed_form) 0.29860542309252486 y[1] (numeric) 0.2986054230925301 absolute error 5.218048215738236e-15 relative error 1.747472688773435e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8300002732240421 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.830009107698208 Order of pole (three term test) 2.000059723291032 Radius of convergence (six term test) for eq 1 1.8300003628416615 Order of pole (six term test) 0.9999999999607745 TOP MAIN SOLVE Loop x[1] -1.8200000000000198 y[1] (closed_form) 0.3018958151503934 y[1] (numeric) 0.3018958151503989 absolute error 5.551115123125783e-15 relative error 1.8387519284957367e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.820000274725274 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.820009157743057 Order of pole (three term test) 2.0000603814184106 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.810000000000021 y[1] (closed_form) 0.30524089458779713 y[1] (numeric) 0.305240894587803 absolute error 5.88418203051333e-15 relative error 1.9277174634347197e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8100002762430938 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8100092083409247 Order of pole (three term test) 2.000061050484337 Radius of convergence (six term test) for eq 1 1.8099999028330889 Order of pole (six term test) 1.0000000001418563 TOP MAIN SOLVE Loop x[1] -1.800000000000022 y[1] (closed_form) 0.3086418800487949 y[1] (numeric) 0.3086418800488011 absolute error 6.217248937900877e-15 relative error 2.014389277604827e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.8000002777777784 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8000092595010309 Order of pole (three term test) 2.0000617307331763 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.7900000000000231 y[1] (closed_form) 0.3121000243125838 y[1] (numeric) 0.31210002431259043 absolute error 6.6058269965196814e-15 relative error 2.1165736885376256e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7900002793296104 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7900093112328488 Order of pole (three term test) 2.000062422415651 Radius of convergence (six term test) for eq 1 1.7899999856728883 Order of pole (six term test) 1.0000000001209042 TOP MAIN SOLVE Loop x[1] -1.7800000000000242 y[1] (closed_form) 0.31561661544734165 y[1] (numeric) 0.31561661544734865 absolute error 6.994405055138486e-15 relative error 2.216107997110644e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7800002808988784 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.780009363545918 Order of pole (three term test) 2.0000631257881705 Radius of convergence (six term test) for eq 1 1.7800006719085237 Order of pole (six term test) 0.9999999998192308 TOP MAIN SOLVE Loop x[1] -1.7700000000000253 y[1] (closed_form) 0.31919297800982904 y[1] (numeric) 0.3191929780098363 absolute error 7.271960811294775e-15 relative error 2.2782333297666864e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7700002824858785 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7700094164501485 Order of pole (three term test) 2.000063841116882 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.7600000000000264 y[1] (closed_form) 0.3228304742928382 y[1] (numeric) 0.32283047429284595 absolute error 7.771561172376096e-15 relative error 2.4073195659114092e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7600002840909126 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.760009469955611 Order of pole (three term test) 2.000064568673652 Radius of convergence (six term test) for eq 1 1.7599995166557583 Order of pole (six term test) 1.0000000003316032 TOP MAIN SOLVE Loop x[1] -1.7500000000000275 y[1] (closed_form) 0.32653050562268177 y[1] (numeric) 0.32653050562269 absolute error 8.215650382226158e-15 relative error 2.5160437511218782e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.75000028571429 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7500095240726432 Order of pole (three term test) 2.0000653087396554 Radius of convergence (six term test) for eq 1 1.7499995381046483 Order of pole (six term test) 1.0000000003268337 TOP MAIN SOLVE Loop x[1] -1.7400000000000286 y[1] (closed_form) 0.33029451370902807 y[1] (numeric) 0.3302945137090367 absolute error 8.604228440844963e-15 relative error 2.605017063173151e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7400002873563267 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7400095788117245 Order of pole (three term test) 2.000066061602178 Radius of convergence (six term test) for eq 1 1.7399994339539837 Order of pole (six term test) 1.000000000396863 TOP MAIN SOLVE Loop x[1] -1.7300000000000297 y[1] (closed_form) 0.3341239820495117 y[1] (numeric) 0.33412398204952065 absolute error 8.93729534823251e-15 relative error 2.6748440185021346e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7300002890173467 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7300096341837303 Order of pole (three term test) 2.000066827559184 Radius of convergence (six term test) for eq 1 1.729999388081778 Order of pole (six term test) 1.000000000407617 TOP MAIN SOLVE Loop x[1] -1.7200000000000308 y[1] (closed_form) 0.3380204373916734 y[1] (numeric) 0.33802043739168286 absolute error 9.43689570931383e-15 relative error 2.791812170333075e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7200002906976808 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.720009690199616 Order of pole (three term test) 2.000067606915052 Radius of convergence (six term test) for eq 1 1.7200003076760884 Order of pole (six term test) 0.9999999999776712 TOP MAIN SOLVE Loop x[1] -1.710000000000032 y[1] (closed_form) 0.3419854512549199 y[1] (numeric) 0.34198545125492974 absolute error 9.825473767932635e-15 relative error 2.8730677670286663e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7100002923976678 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7100097468707116 Order of pole (three term test) 2.0000683999844644 Radius of convergence (six term test) for eq 1 1.7099997114324785 Order of pole (six term test) 1.0000000002902318 TOP MAIN SOLVE Loop x[1] -1.700000000000033 y[1] (closed_form) 0.34602064151533546 y[1] (numeric) 0.3460206415153458 absolute error 1.0325074129013956e-14 relative error 2.9839474557925626e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.7000002941176546 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7000098042086 Order of pole (three term test) 2.0000692070912396 Radius of convergence (six term test) for eq 1 1.7000007729241886 Order of pole (six term test) 0.9999999997733386 TOP MAIN SOLVE Loop x[1] -1.6900000000000341 y[1] (closed_form) 0.35012767405633044 y[1] (numeric) 0.35012767405634126 absolute error 1.0824674490095276e-14 relative error 3.0916363635836864e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.6900002958579965 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6900098622250814 Order of pole (three term test) 2.0000700285683353 Radius of convergence (six term test) for eq 1 1.689999781644429 Order of pole (six term test) 1.0000000002497984 TOP MAIN SOLVE Loop x[1] -1.6800000000000352 y[1] (closed_form) 0.3543082644882701 y[1] (numeric) 0.3543082644882813 absolute error 1.1213252548714081e-14 relative error 3.16482952067445e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.6800002976190567 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6800099209323218 Order of pole (three term test) 2.0000708647594965 Radius of convergence (six term test) for eq 1 1.6800000272845907 Order of pole (six term test) 1.0000000001464588 TOP MAIN SOLVE Loop x[1] -1.6700000000000363 y[1] (closed_form) 0.3585641799403982 y[1] (numeric) 0.3585641799404099 absolute error 1.1712852909795402e-14 relative error 3.2665987192982726e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.670000299401207 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6700099803426953 Order of pole (three term test) 2.0000717160176333 Radius of convergence (six term test) for eq 1 1.6699997713375105 Order of pole (six term test) 1.0000000002634444 TOP MAIN SOLVE Loop x[1] -1.6600000000000374 y[1] (closed_form) 0.3628972409285506 y[1] (numeric) 0.3628972409285628 absolute error 1.2212453270876722e-14 relative error 3.3652648445682685e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.6600003012048294 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6600100404689209 Order of pole (three term test) 2.0000725827070887 Radius of convergence (six term test) for eq 1 1.6600005931510007 Order of pole (six term test) 0.9999999998298126 TOP MAIN SOLVE Loop x[1] -1.6500000000000385 y[1] (closed_form) 0.3673093233023434 y[1] (numeric) 0.3673093233023562 absolute error 1.2823075934420558e-14 relative error 3.491083705453754e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.6500003030303139 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6500101013240225 Order of pole (three term test) 2.000073465203423 Radius of convergence (six term test) for eq 1 1.6499999687707576 Order of pole (six term test) 1.000000000173527 TOP MAIN SOLVE Loop x[1] -1.6400000000000396 y[1] (closed_form) 0.3718023602757255 y[1] (numeric) 0.3718023602757388 absolute error 1.3322676295501878e-14 relative error 3.5832683487059884e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.6400003048780603 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.640010162921328 Order of pole (three term test) 2.0000743638928373 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.6300000000000407 y[1] (closed_form) 0.3763783445449981 y[1] (numeric) 0.376378344545012 absolute error 1.3933298959045715e-14 relative error 3.701939593758937e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.6300003067484783 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6300102252744912 Order of pole (three term test) 2.0000752791745793 Radius of convergence (six term test) for eq 1 1.6300004427714363 Order of pole (six term test) 0.9999999999143228 TOP MAIN SOLVE Loop x[1] -1.6200000000000419 y[1] (closed_form) 0.38103933049863503 y[1] (numeric) 0.38103933049864946 absolute error 1.4432899320127035e-14 relative error 3.787771540864267e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.6200003086419879 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6200102883975211 Order of pole (three term test) 2.000076211459028 Radius of convergence (six term test) for eq 1 1.6200005711299024 Order of pole (six term test) 0.9999999998288622 TOP MAIN SOLVE Loop x[1] -1.610000000000043 y[1] (closed_form) 0.385787436523479 y[1] (numeric) 0.38578743652349395 absolute error 1.4932499681208355e-14 relative error 3.870654735616193e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.6100003105590193 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.610010352304775 Order of pole (three term test) 2.000077161170349 Radius of convergence (six term test) for eq 1 1.6100008271560022 Order of pole (six term test) 0.9999999996782556 TOP MAIN SOLVE Loop x[1] -1.600000000000044 y[1] (closed_form) 0.3906248474121475 y[1] (numeric) 0.3906248474121629 absolute error 1.5432100042289676e-14 relative error 3.950619154036378e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.6000003125000135 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6000104170109437 Order of pole (three term test) 2.0000781287456086 Radius of convergence (six term test) for eq 1 1.6000010888013896 Order of pole (six term test) 0.9999999995308055 TOP MAIN SOLVE Loop x[1] -1.5900000000000452 y[1] (closed_form) 0.3955538168767558 y[1] (numeric) 0.3955538168767718 absolute error 1.6042722705833512e-14 relative error 4.055762331534271e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.590000314465423 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5900104825311208 Order of pole (three term test) 2.0000791146354415 Radius of convergence (six term test) for eq 1 1.5900007566042589 Order of pole (six term test) 0.9999999997146141 TOP MAIN SOLVE Loop x[1] -1.5800000000000463 y[1] (closed_form) 0.4005766701743596 y[1] (numeric) 0.4005766701743761 absolute error 1.6486811915683575e-14 relative error 4.11576937531268e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5800003164557108 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5800105488807346 Order of pole (three term test) 2.000080119304949 Radius of convergence (six term test) for eq 1 1.5799995241135179 Order of pole (six term test) 1.0000000004712533 TOP MAIN SOLVE Loop x[1] -1.5700000000000474 y[1] (closed_form) 0.4056958068498246 y[1] (numeric) 0.4056958068498417 absolute error 1.709743457922741e-14 relative error 4.214348359177477e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5700003184713527 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.570010616075654 Order of pole (three term test) 2.000081143234283 Radius of convergence (six term test) for eq 1 1.5700004552654092 Order of pole (six term test) 0.999999999897021 TOP MAIN SOLVE Loop x[1] -1.5600000000000485 y[1] (closed_form) 0.4109137036021672 y[1] (numeric) 0.41091370360218493 absolute error 1.7708057242771247e-14 relative error 4.309434581406803e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.560000320512836 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5600106841321375 Order of pole (three term test) 2.0000821869191516 Radius of convergence (six term test) for eq 1 1.560000199533054 Order of pole (six term test) 1.0000000000783569 TOP MAIN SOLVE Loop x[1] -1.5500000000000496 y[1] (closed_form) 0.416232917280757 y[1] (numeric) 0.41623291728077527 absolute error 1.8263168755083825e-14 relative error 4.387728119726045e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5500003225806611 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.550010753066857 Order of pole (three term test) 2.0000832508706625 Radius of convergence (six term test) for eq 1 1.5499997684415345 Order of pole (six term test) 1.0000000003473417 TOP MAIN SOLVE Loop x[1] -1.5400000000000507 y[1] (closed_form) 0.42165608801815063 y[1] (numeric) 0.42165608801816945 absolute error 1.8818280267396403e-14 relative error 4.462945230044052e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5400003246753413 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5400108228969325 Order of pole (three term test) 2.000084335617255 Radius of convergence (six term test) for eq 1 1.539999864209944 Order of pole (six term test) 1.0000000002995844 TOP MAIN SOLVE Loop x[1] -1.5300000000000518 y[1] (closed_form) 0.4271859425067238 y[1] (numeric) 0.4271859425067432 absolute error 1.9373391779708982e-14 relative error 4.5351192190515606e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5300003267974025 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5300108936399195 Order of pole (three term test) 2.0000854417044533 Radius of convergence (six term test) for eq 1 1.5300005625483628 Order of pole (six term test) 0.9999999998418314 TOP MAIN SOLVE Loop x[1] -1.5200000000000529 y[1] (closed_form) 0.4328252974266936 y[1] (numeric) 0.4328252974267136 absolute error 1.9984014443252818e-14 relative error 4.617108695370897e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5200003289473858 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5200109653138374 Order of pole (three term test) 2.0000865696955437 Radius of convergence (six term test) for eq 1 1.5200006362879477 Order of pole (six term test) 0.999999999786608 TOP MAIN SOLVE Loop x[1] -1.510000000000054 y[1] (closed_form) 0.43857706303357985 y[1] (numeric) 0.4385770630336005 absolute error 2.0650148258027912e-14 relative error 4.708442369328107e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5100003311258454 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5100110379371798 Order of pole (three term test) 2.000087720172505 Radius of convergence (six term test) for eq 1 1.51000052431817 Order of pole (six term test) 0.9999999998511022 TOP MAIN SOLVE Loop x[1] -1.500000000000055 y[1] (closed_form) 0.4444442469136354 y[1] (numeric) 0.4444442469136567 absolute error 2.1316282072803006e-14 relative error 4.796165598009236e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 1.5000003333333514 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.500011111528948 Order of pole (three term test) 2.0000888937376744 Radius of convergence (six term test) for eq 1 1.500000795076373 Order of pole (six term test) 0.9999999996548308 Finished! diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; Iterations 501 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.39999999998895%