##############ECHO OF PROBLEM################# ##############temp/sing6postode.ode################# diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=30; 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) # ELIMINATED in preodein.rb $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 $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(3.0) # 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(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) 0.0625 y[1] (numeric) 0.0625 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 4.000000000000003 Order of pole (three term test) 4.254547669924697e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.009999999999999 y[1] (closed_form) 0.06281367579349373 y[1] (numeric) 0.06281367579349374 absolute error 1.3877787807814457e-17 relative error 2.2093576967918703e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 3.990000000000001 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9900000000000126 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.019999999999998 y[1] (closed_form) 0.06312971894649118 y[1] (numeric) 0.06312971894649123 absolute error 5.551115123125783e-17 relative error 8.793188399636175e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 3.980000000000002 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9800000000000204 Order of pole (three term test) 3.66054555895079e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0299999999999967 y[1] (closed_form) 0.0634481533414969 y[1] (numeric) 0.06344815334149698 absolute error 8.326672684688674e-17 relative error 1.3123585551610994e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.97000000000003 Order of pole (three term test) 6.788891264516986e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0399999999999956 y[1] (closed_form) 0.06376900316294241 y[1] (numeric) 0.06376900316294254 absolute error 1.249000902703301e-16 relative error 1.958633255583213e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.96 Order of pole (three term test) 3.1470905000416404e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0499999999999945 y[1] (closed_form) 0.06409229290177838 y[1] (numeric) 0.06409229290177855 absolute error 1.6653345369377348e-16 relative error 2.598338211257108e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9500000000000153 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0599999999999934 y[1] (closed_form) 0.06441804736014821 y[1] (numeric) 0.06441804736014839 absolute error 1.8041124150158794e-16 relative error 2.8006319485740596e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9400000000000275 Order of pole (three term test) 2.703586747765104e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0699999999999923 y[1] (closed_form) 0.06474629165614514 y[1] (numeric) 0.06474629165614536 absolute error 2.220446049250313e-16 relative error 3.4294567186066297e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.930000000000015 Order of pole (three term test) 2.505129409476993e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.079999999999991 y[1] (closed_form) 0.06507705122865444 y[1] (numeric) 0.06507705122865468 absolute error 2.3592239273284576e-16 relative error 3.625277855690017e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.920000000000029 Order of pole (three term test) 4.641578080018343e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.08999999999999 y[1] (closed_form) 0.06541035184228222 y[1] (numeric) 0.06541035184228249 absolute error 2.636779683484747e-16 relative error 4.0311351479083363e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.91000000000001 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9100000000000166 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.099999999999989 y[1] (closed_form) 0.06574621959237306 y[1] (numeric) 0.06574621959237337 absolute error 3.0531133177191805e-16 relative error 4.6437853562509e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.900000000000011 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.900000000000025 Order of pole (three term test) 3.981272102077787e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.109999999999988 y[1] (closed_form) 0.06608468091011782 y[1] (numeric) 0.06608468091011814 absolute error 3.191891195797325e-16 relative error 4.8300016763925e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.890000000000012 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.8900000000000063 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.119999999999987 y[1] (closed_form) 0.06642576256775383 y[1] (numeric) 0.06642576256775418 absolute error 3.469446951953614e-16 relative error 5.223044219349084e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.880000000000013 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.88000000000002 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) 0.06676949168385932 y[1] (numeric) 0.06676949168385972 absolute error 4.0245584642661925e-16 relative error 6.027540966346878e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.8700000000000143 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.8700000000000263 Order of pole (three term test) 3.158003452373261e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1399999999999846 y[1] (closed_form) 0.06711589572874387 y[1] (numeric) 0.0671158957287443 absolute error 4.3021142204224816e-16 relative error 6.409978103860731e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.8600000000000154 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.8600000000000105 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1499999999999835 y[1] (closed_form) 0.06746500252993701 y[1] (numeric) 0.06746500252993749 absolute error 4.85722573273506e-16 relative error 7.199622842346605e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.8500000000000165 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.850000000000021 Order of pole (three term test) 2.703370280931399e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1599999999999824 y[1] (closed_form) 0.06781684027777715 y[1] (numeric) 0.06781684027777767 absolute error 5.134781488891349e-16 relative error 7.571543392259697e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.8400000000000176 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.840000000000032 Order of pole (three term test) 5.0009254051877527e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1699999999999813 y[1] (closed_form) 0.06817143753110255 y[1] (numeric) 0.0681714375311031 absolute error 5.412337245047638e-16 relative error 7.939303381388008e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.8300000000000187 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.8300000000000347 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.17999999999998 y[1] (closed_form) 0.0685288232230469 y[1] (numeric) 0.0685288232230475 absolute error 5.967448757360216e-16 relative error 8.707939924690412e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.82000000000002 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.8200000000000394 Order of pole (three term test) 8.551543880544887e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.189999999999979 y[1] (closed_form) 0.06888902666694147 y[1] (numeric) 0.06888902666694213 absolute error 6.661338147750939e-16 relative error 9.669665068656848e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 3.810000000000021 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.8100000000000267 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.199999999999978 y[1] (closed_form) 0.06925207756232607 y[1] (numeric) 0.0692520775623268 absolute error 7.355227538141662e-16 relative error 1.0620948565076683e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 3.800000000000022 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.8000000000000385 Order of pole (three term test) 3.6527634120364176e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.209999999999977 y[1] (closed_form) 0.06961800600107126 y[1] (numeric) 0.06961800600107207 absolute error 8.049116928532385e-16 relative error 1.1561832047313344e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7900000000000285 Order of pole (three term test) 3.375125643000593e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2199999999999758 y[1] (closed_form) 0.06998684247361407 y[1] (numeric) 0.0699868424736149 absolute error 8.326672684688674e-16 relative error 1.1897482998790716e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.780000000000039 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2299999999999747 y[1] (closed_form) 0.0703586178753095 y[1] (numeric) 0.07035861787531039 absolute error 8.881784197001252e-16 relative error 1.2623591061356081e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.770000000000037 Order of pole (three term test) 2.8797457878802166e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2399999999999736 y[1] (closed_form) 0.07073336351290077 y[1] (numeric) 0.07073336351290169 absolute error 9.159339953157541e-16 relative error 1.2949108452176188e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.760000000000033 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2499999999999725 y[1] (closed_form) 0.07111111111111007 y[1] (numeric) 0.07111111111111104 absolute error 9.71445146547012e-16 relative error 1.3660947373317556e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7500000000000515 Order of pole (three term test) 7.365003068115202e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2599999999999714 y[1] (closed_form) 0.0714918928193532 y[1] (numeric) 0.07149189281935421 absolute error 1.0130785099704553e-15 relative error 1.4170536966062957e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7400000000000335 Order of pole (three term test) 9.064037693127495e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2699999999999703 y[1] (closed_form) 0.07187574121858016 y[1] (numeric) 0.07187574121858126 absolute error 1.096345236817342e-15 relative error 1.5253341645316244e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.730000000000028 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.279999999999969 y[1] (closed_form) 0.07226268932824484 y[1] (numeric) 0.07226268932824596 absolute error 1.124100812432971e-15 relative error 1.5555756682772683e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7200000000000415 Order of pole (three term test) 3.858618459903657e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.289999999999968 y[1] (closed_form) 0.0726527706134061 y[1] (numeric) 0.07265277061340726 absolute error 1.1657341758564144e-15 relative error 1.6045281769905548e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.71000000000004 Order of pole (three term test) 7.118539927677847e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.299999999999967 y[1] (closed_form) 0.07304601899196363 y[1] (numeric) 0.07304601899196482 absolute error 1.1934897514720433e-15 relative error 1.6338874697652565e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7000000000000344 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.309999999999966 y[1] (closed_form) 0.07344246884203123 y[1] (numeric) 0.07344246884203247 absolute error 1.2351231148954867e-15 relative error 1.6817559844728748e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.690000000000057 Order of pole (three term test) 6.052915646831795e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3199999999999648 y[1] (closed_form) 0.07384215500945038 y[1] (numeric) 0.07384215500945165 absolute error 1.27675647831893e-15 relative error 1.729034693198661e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.6800000000000357 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) 0.07424511281544745 y[1] (numeric) 0.07424511281544877 absolute error 1.3183898417423734e-15 relative error 1.7757260939444207e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.6700000000000443 Order of pole (three term test) 2.5711390759078444e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3399999999999626 y[1] (closed_form) 0.07465137806443754 y[1] (numeric) 0.0746513780644389 absolute error 1.3600232051658168e-15 relative error 1.8218326847119587e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.6600000000000508 Order of pole (three term test) 4.738121560345565e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3499999999999615 y[1] (closed_form) 0.07506098705197814 y[1] (numeric) 0.07506098705197954 absolute error 1.4016565685892601e-15 relative error 1.8673569635030814e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.6500000000000368 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) 0.07547397657287604 y[1] (numeric) 0.07547397657287747 absolute error 1.429412144204889e-15 relative error 1.8939139145857506e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.640000000000034 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) 0.07589038392945059 y[1] (numeric) 0.07589038392945209 absolute error 1.4988010832439613e-15 relative error 1.9749551993797797e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.6300000000000647 Order of pole (three term test) 3.701454267802368e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.379999999999958 y[1] (closed_form) 0.07631024693995733 y[1] (numeric) 0.07631024693995886 absolute error 1.5265566588595902e-15 relative error 2.000460908036008e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.620000000000048 Order of pole (three term test) 3.40745989402625e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.389999999999957 y[1] (closed_form) 0.07673360394717475 y[1] (numeric) 0.07673360394717633 absolute error 1.582067810090848e-15 relative error 2.0617665907885434e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.610000000000053 Order of pole (three term test) 3.136098494942503e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.399999999999956 y[1] (closed_form) 0.07716049382715862 y[1] (numeric) 0.07716049382716023 absolute error 1.609823385706477e-15 relative error 2.086331107875645e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.6000000000000525 Order of pole (three term test) 5.771366517289493e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.409999999999955 y[1] (closed_form) 0.07759095599816691 y[1] (numeric) 0.07759095599816855 absolute error 1.6375789613221059e-15 relative error 2.110528141141596e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5900000000000682 Order of pole (three term test) 5.309297850907104e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4199999999999537 y[1] (closed_form) 0.07802503042975985 y[1] (numeric) 0.07802503042976155 absolute error 1.7069679003611782e-15 relative error 2.187718339818957e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.580000000000073 Order of pole (three term test) 9.766173322021753e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4299999999999526 y[1] (closed_form) 0.07846275765207836 y[1] (numeric) 0.07846275765208009 absolute error 1.734723475976807e-15 relative error 2.2108877228977394e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5700000000000505 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4399999999999515 y[1] (closed_form) 0.07890417876530527 y[1] (numeric) 0.07890417876530705 absolute error 1.7763568394002505e-15 relative error 2.2512836039823626e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5600000000000733 Order of pole (three term test) 8.255313441228783e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4499999999999504 y[1] (closed_form) 0.0793493354493134 y[1] (numeric) 0.07934933544931524 absolute error 1.8457457784393227e-15 relative error 2.3261011172782215e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5500000000000433 Order of pole (three term test) 3.793623476113906e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4599999999999493 y[1] (closed_form) 0.07979826997350468 y[1] (numeric) 0.07979826997350659 absolute error 1.9012569296705806e-15 relative error 2.382579133986053e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5400000000000613 Order of pole (three term test) 3.48579219635657e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4699999999999482 y[1] (closed_form) 0.08025102520684466 y[1] (numeric) 0.0802510252068466 absolute error 1.942890293094024e-15 relative error 2.4210161653216035e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5300000000000673 Order of pole (three term test) 6.404346041925658e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.479999999999947 y[1] (closed_form) 0.08070764462809675 y[1] (numeric) 0.08070764462809873 absolute error 1.9845236565174673e-15 relative error 2.4589041913714766e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5200000000000653 Order of pole (three term test) 5.881844415897357e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.489999999999946 y[1] (closed_form) 0.081168172336261 y[1] (numeric) 0.08116817233626301 absolute error 2.0122792321330962e-15 relative error 2.4791481367803724e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5100000000000695 Order of pole (three term test) 5.4006635461102656e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.499999999999945 y[1] (closed_form) 0.08163265306122192 y[1] (numeric) 0.08163265306122398 absolute error 2.067790383364354e-15 relative error 2.5330432196214137e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.5000000000000715 Order of pole (three term test) 4.9576396748033454e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.509999999999944 y[1] (closed_form) 0.08210113217461004 y[1] (numeric) 0.08210113217461215 absolute error 2.1094237467877974e-15 relative error 2.5692992178250878e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.4900000000000713 Order of pole (three term test) 4.5498432736929914e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5199999999999427 y[1] (closed_form) 0.08257365570088247 y[1] (numeric) 0.08257365570088462 absolute error 2.1510571102112408e-15 relative error 2.605016202750307e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.4800000000000737 Order of pole (three term test) 4.1745622987697043e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5299999999999416 y[1] (closed_form) 0.08305027032862713 y[1] (numeric) 0.08305027032862934 absolute error 2.2065682614424986e-15 relative error 2.6569067779203874e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.4700000000000704 Order of pole (three term test) 7.658573198744716e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5399999999999405 y[1] (closed_form) 0.08353102342209609 y[1] (numeric) 0.08353102342209837 absolute error 2.275957200481571e-15 relative error 2.7246849221286114e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.4600000000000555 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5499999999999394 y[1] (closed_form) 0.08401596303297332 y[1] (numeric) 0.08401596303297561 absolute error 2.2898349882893854e-15 relative error 2.7254760948115367e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.450000000000073 Order of pole (three term test) 3.2196338177548515e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5599999999999383 y[1] (closed_form) 0.08450513791238205 y[1] (numeric) 0.08450513791238441 absolute error 2.3592239273284576e-15 relative error 2.7918112266435036e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.4400000000000763 Order of pole (three term test) 2.951120244473521e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5699999999999372 y[1] (closed_form) 0.08499859752313776 y[1] (numeric) 0.08499859752314018 absolute error 2.4147350785597155e-15 relative error 2.8409116725748236e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.430000000000076 Order of pole (three term test) 5.408629407507353e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.579999999999936 y[1] (closed_form) 0.08549639205225221 y[1] (numeric) 0.0854963920522547 absolute error 2.4980018054066022e-15 relative error 2.921762831675887e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.4200000000000714 Order of pole (three term test) 2.4775179510658243e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.589999999999935 y[1] (closed_form) 0.08599857242369449 y[1] (numeric) 0.08599857242369705 absolute error 2.55351295663786e-15 relative error 2.9692504011081832e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.4100000000000747 Order of pole (three term test) 4.538318731553031e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.599999999999934 y[1] (closed_form) 0.08650519031141532 y[1] (numeric) 0.08650519031141794 absolute error 2.6229018956769323e-15 relative error 3.0320745914026517e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.400000000000089 Order of pole (three term test) 8.311150196169288e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.609999999999933 y[1] (closed_form) 0.08701629815264054 y[1] (numeric) 0.08701629815264322 absolute error 2.67841304690819e-15 relative error 3.078059057637483e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.3900000000000707 Order of pole (three term test) 3.804123168837991e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6199999999999317 y[1] (closed_form) 0.08753194916144039 y[1] (numeric) 0.08753194916144313 absolute error 2.7478019859472624e-15 relative error 3.1391989008257177e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.380000000000074 Order of pole (three term test) 3.4814858324292844e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6299999999999306 y[1] (closed_form) 0.08805219734258105 y[1] (numeric) 0.08805219734258386 absolute error 2.8171909249863347e-15 relative error 3.1994555615978627e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.370000000000071 Order of pole (three term test) 3.1853756070964637e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6399999999999295 y[1] (closed_form) 0.08857709750566523 y[1] (numeric) 0.0885770975056681 absolute error 2.8727020762175925e-15 relative error 3.243165735966749e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.3600000000000847 Order of pole (three term test) 8.741041864949897e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6499999999999284 y[1] (closed_form) 0.08910670527956849 y[1] (numeric) 0.08910670527957142 absolute error 2.9282132274488504e-15 relative error 3.2861872945046125e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.350000000000093 Order of pole (three term test) 7.993354787497087e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6599999999999273 y[1] (closed_form) 0.08964107712717885 y[1] (numeric) 0.08964107712718186 absolute error 3.011479954295737e-15 relative error 3.359486577814299e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.340000000000071 Order of pole (three term test) 2.435889751493088e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.669999999999926 y[1] (closed_form) 0.09018027036044654 y[1] (numeric) 0.09018027036044961 absolute error 3.066991105526995e-15 relative error 3.40095576700798e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.3300000000000822 Order of pole (three term test) 4.452671181016815e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.679999999999925 y[1] (closed_form) 0.09072434315575145 y[1] (numeric) 0.09072434315575457 absolute error 3.1225022567582528e-15 relative error 3.441746887489372e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.3200000000001024 Order of pole (three term test) 4.068516959230799e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.689999999999924 y[1] (closed_form) 0.0912733545695963 y[1] (numeric) 0.09127335456959948 absolute error 3.1780134079895106e-15 relative error 3.4818632699275477e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.310000000000079 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.699999999999923 y[1] (closed_form) 0.09182736455463299 y[1] (numeric) 0.09182736455463625 absolute error 3.2612801348363973e-15 relative error 3.5515340668370027e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.3000000000000833 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) 0.09238643397603057 y[1] (numeric) 0.09238643397603388 absolute error 3.316791286067655e-15 relative error 3.5901280559526613e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2900000000000693 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) 0.09295062462819301 y[1] (numeric) 0.0929506246281964 absolute error 3.3861802251067274e-15 relative error 3.642988133378998e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2800000000000917 Order of pole (three term test) 2.8281922697127065e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7299999999999196 y[1] (closed_form) 0.0935199992518354 y[1] (numeric) 0.09351999925183886 absolute error 3.4555691641457997e-15 relative error 3.695005551529644e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2700000000000817 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7399999999999185 y[1] (closed_form) 0.09409462155142742 y[1] (numeric) 0.09409462155143092 absolute error 3.497202527569243e-15 relative error 3.716686958199674e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2600000000000913 Order of pole (three term test) 2.3540821895507794e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7499999999999174 y[1] (closed_form) 0.09467455621301295 y[1] (numeric) 0.0946745562130165 absolute error 3.552713678800501e-15 relative error 3.75255382323322e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2500000000000853 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) 0.09525986892241545 y[1] (numeric) 0.09525986892241908 absolute error 3.635980405647388e-15 relative error 3.816906790632599e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.240000000000099 Order of pole (three term test) 7.828957167961674e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.769999999999915 y[1] (closed_form) 0.09585062638383839 y[1] (numeric) 0.0958506263838421 absolute error 3.7192471324942744e-15 relative error 3.8802533408601555e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.230000000000089 Order of pole (three term test) 3.567790010100469e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.779999999999914 y[1] (closed_form) 0.09644689633887067 y[1] (numeric) 0.09644689633887445 absolute error 3.774758283725532e-15 relative error 3.91382037889819e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2200000000000983 Order of pole (three term test) 3.250871222785224e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.789999999999913 y[1] (closed_form) 0.09704874758590713 y[1] (numeric) 0.09704874758591099 absolute error 3.858025010572419e-15 relative error 3.9753475511441425e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.210000000000115 Order of pole (three term test) 1.1844986734133097e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.799999999999912 y[1] (closed_form) 0.09765624999999463 y[1] (numeric) 0.09765624999999854 absolute error 3.913536161803677e-15 relative error 4.0074610296871856e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.200000000000102 Order of pole (three term test) 5.3932799074841315e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.809999999999911 y[1] (closed_form) 0.09826947455311408 y[1] (numeric) 0.09826947455311806 absolute error 3.982925100842749e-15 relative error 4.053064411868816e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.190000000000102 Order of pole (three term test) 2.454958228367449e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8199999999999097 y[1] (closed_form) 0.09888849333490993 y[1] (numeric) 0.09888849333491398 absolute error 4.052314039881821e-15 relative error 4.097862049690326e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.1800000000000996 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8299999999999086 y[1] (closed_form) 0.09951337957387796 y[1] (numeric) 0.09951337957388207 absolute error 4.107825191113079e-15 relative error 4.1279124562978605e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.170000000000094 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8399999999999075 y[1] (closed_form) 0.10014420765902314 y[1] (numeric) 0.10014420765902729 absolute error 4.1494585545365226e-15 relative error 4.143483334218232e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.160000000000102 Order of pole (three term test) 3.697993039768497e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8499999999999064 y[1] (closed_form) 0.10078105316199955 y[1] (numeric) 0.1007810531620038 absolute error 4.246603069191224e-15 relative error 4.213691895405242e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.150000000000092 Order of pole (three term test) 3.362561410018675e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8599999999999053 y[1] (closed_form) 0.10142399285974478 y[1] (numeric) 0.10142399285974911 absolute error 4.3298697960381105e-15 relative error 4.269078424101993e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.1400000000000996 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.869999999999904 y[1] (closed_form) 0.10207310475762116 y[1] (numeric) 0.10207310475762557 absolute error 4.413136522884997e-15 relative error 4.323505720105468e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.1300000000000985 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.879999999999903 y[1] (closed_form) 0.1027284681130771 y[1] (numeric) 0.1027284681130816 absolute error 4.496403249731884e-15 relative error 4.376978779419277e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.1200000000001062 Order of pole (three term test) 2.5234309849375423e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.889999999999902 y[1] (closed_form) 0.10339016345984191 y[1] (numeric) 0.10339016345984647 absolute error 4.565792188770956e-15 relative error 4.416079862901435e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.110000000000095 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.899999999999901 y[1] (closed_form) 0.10405827263266763 y[1] (numeric) 0.10405827263267227 absolute error 4.6351811278100286e-15 relative error 4.4544090638257226e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.1000000000001067 Order of pole (three term test) 4.161351694799955e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9099999999998998 y[1] (closed_form) 0.10473287879263257 y[1] (numeric) 0.10473287879263728 absolute error 4.704570066849101e-15 relative error 4.491970545528482e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.090000000000116 Order of pole (three term test) 7.553843535292494e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9199999999998987 y[1] (closed_form) 0.10541406645302057 y[1] (numeric) 0.10541406645302531 absolute error 4.746203430272544e-15 relative error 4.502438422094042e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.080000000000118 Order of pole (three term test) 3.4269289592648016e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9299999999998976 y[1] (closed_form) 0.1061019215057914 y[1] (numeric) 0.10610192150579624 absolute error 4.8433479449272454e-15 relative error 4.564807004614784e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.0700000000001193 Order of pole (three term test) 6.216770949072134e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9399999999998965 y[1] (closed_form) 0.10679653124865782 y[1] (numeric) 0.10679653124866274 absolute error 4.926614671774132e-15 relative error 4.613084914062739e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.0600000000001195 Order of pole (three term test) 5.637108534640929e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9499999999998954 y[1] (closed_form) 0.1074979844127849 y[1] (numeric) 0.10749798441278989 absolute error 4.9960036108132044e-15 relative error 4.647532358959302e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.0500000000001157 Order of pole (three term test) 2.554928712206069e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9599999999998943 y[1] (closed_form) 0.10820637119112819 y[1] (numeric) 0.10820637119113327 absolute error 5.079270337660091e-15 relative error 4.694058475252277e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.040000000000116 Order of pole (three term test) 4.630427731763702e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.969999999999893 y[1] (closed_form) 0.10892178326742796 y[1] (numeric) 0.10892178326743311 absolute error 5.1486592766991635e-15 relative error 4.726932595345069e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.0300000000001113 Order of pole (three term test) 4.1946183968514655e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.979999999999892 y[1] (closed_form) 0.10964431384587611 y[1] (numeric) 0.10964431384588133 absolute error 5.218048215738236e-15 relative error 4.759068694682241e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.020000000000112 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.989999999999891 y[1] (closed_form) 0.11037405768147454 y[1] (numeric) 0.11037405768147984 absolute error 5.3013149425851225e-15 relative error 4.803044351131895e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.0100000000001166 Order of pole (three term test) 3.438812288446462e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.99999999999989 y[1] (closed_form) 0.11111111111110296 y[1] (numeric) 0.11111111111110832 absolute error 5.35682609381638e-15 relative error 4.821143484435096e-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) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.000000000000108 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; Iterations 1001 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.19999999998896%