##############ECHO OF PROBLEM################# ##############temp/sing5postode.ode################# diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(-1.0) x_end=c(-0.7) $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 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(0.0) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(4.0) # 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(x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -1.0 y[1] (closed_form) -1.0 y[1] (numeric) -1.0 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 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0000000000000036 Order of pole (three term test) 2.7784801109712386e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.99 y[1] (closed_form) -1.0306101521283648 y[1] (numeric) -1.0306101521283644 absolute error 4.440892098500626e-16 relative error 4.308993162283058e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.99 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9900000000000022 Order of pole (three term test) 4.028686888608282e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.98 y[1] (closed_form) -1.062482469039261 y[1] (numeric) -1.06248246903926 absolute error 8.881784197001252e-16 relative error 8.359464231944002e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.98 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9800000000000011 Order of pole (three term test) 2.9111977717872984e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.97 y[1] (closed_form) -1.0956826815299676 y[1] (numeric) -1.095682681529967 absolute error 6.661338147750939e-16 relative error 6.079623471322293e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.97 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9700000000000043 Order of pole (three term test) 4.193366102382227e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.96 y[1] (closed_form) -1.1302806712962965 y[1] (numeric) -1.1302806712962954 absolute error 1.1102230246251565e-15 relative error 9.822542779147624e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.96 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.960000000000002 Order of pole (three term test) 3.009863087948006e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.95 y[1] (closed_form) -1.1663507799970843 y[1] (numeric) -1.1663507799970834 absolute error 8.881784197001252e-16 relative error 7.615019725903948e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.95 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9500000000000066 Order of pole (three term test) 8.611576109354578e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.94 y[1] (closed_form) -1.2039721449004557 y[1] (numeric) -1.2039721449004548 absolute error 8.881784197001252e-16 relative error 7.377067845482087e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.94 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9400000000000024 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9299999999999999 y[1] (closed_form) -1.2432290637117602 y[1] (numeric) -1.243229063711759 absolute error 1.3322676295501878e-15 relative error 1.0716187937021002e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.9299999999999999 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9300000000000038 Order of pole (three term test) 8.71789480743141e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9199999999999999 y[1] (closed_form) -1.2842113914687272 y[1] (numeric) -1.2842113914687254 absolute error 1.7763568394002505e-15 relative error 1.3832277545589019e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.9199999999999999 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9200000000000059 Order of pole (three term test) 6.168332069460946e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9099999999999999 y[1] (closed_form) -1.3270149727099374 y[1] (numeric) -1.3270149727099354 absolute error 1.9984014443252818e-15 relative error 1.5059373748016466e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.9099999999999999 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9100000000000041 Order of pole (three term test) 4.347922806223831e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8999999999999999 y[1] (closed_form) -1.3717421124828535 y[1] (numeric) -1.3717421124828508 absolute error 2.6645352591003757e-15 relative error 1.9424462038841735e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.8999999999999999 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8999999999999998 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8899999999999999 y[1] (closed_form) -1.4185020901628302 y[1] (numeric) -1.4185020901628271 absolute error 3.1086244689504383e-15 relative error 2.191483883251521e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.8899999999999999 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8900000000000049 Order of pole (three term test) 8.540778810507257e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8799999999999999 y[1] (closed_form) -1.4674117205108945 y[1] (numeric) -1.467411720510891 absolute error 3.552713678800501e-15 relative error 2.4210748961195344e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.8799999999999999 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8800000000000031 Order of pole (three term test) 2.97462877757965e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8699999999999999 y[1] (closed_form) -1.5185959669128315 y[1] (numeric) -1.5185959669128275 absolute error 3.9968028886505635e-15 relative error 2.6319066925850615e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.8699999999999999 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8700000000000038 Order of pole (three term test) 4.1269893275914613e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8599999999999999 y[1] (closed_form) -1.5721886123234439 y[1] (numeric) -1.5721886123234394 absolute error 4.440892098500626e-15 relative error 2.824656064603913e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.8599999999999999 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8600000000000021 Order of pole (three term test) 5.70161249387475e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8499999999999999 y[1] (closed_form) -1.6283329940972937 y[1] (numeric) -1.6283329940972886 absolute error 5.10702591327572e-15 relative error 3.13635228899045e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.8499999999999999 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8500000000000051 Order of pole (three term test) 7.843011940217178e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8399999999999999 y[1] (closed_form) -1.68718280963179 y[1] (numeric) -1.6871828096317845 absolute error 5.551115123125783e-15 relative error 3.2901681379371424e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.8399999999999999 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8400000000000032 Order of pole (three term test) 5.370496121821806e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8299999999999998 y[1] (closed_form) -1.7489030005928792 y[1] (numeric) -1.7489030005928727 absolute error 6.439293542825908e-15 relative error 3.6819043369717953e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.8299999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8300000000000025 Order of pole (three term test) 3.6608017413383434e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8199999999999998 y[1] (closed_form) -1.813670724452635 y[1] (numeric) -1.8136707244526284 absolute error 6.661338147750939e-15 relative error 3.672848691849138e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.8199999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8200000000000013 Order of pole (three term test) 2.4838223440371285e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8099999999999998 y[1] (closed_form) -1.8816764231589216 y[1] (numeric) -1.8816764231589145 absolute error 7.105427357601002e-15 relative error 3.776115420350832e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.8099999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8100000000000043 Order of pole (three term test) 6.709000878884108e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7999999999999998 y[1] (closed_form) -1.9531250000000013 y[1] (numeric) -1.9531249999999933 absolute error 7.993605777301127e-15 relative error 4.092726157978174e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7999999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8000000000000004 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7899999999999998 y[1] (closed_form) -2.0282371171448927 y[1] (numeric) -2.028237117144884 absolute error 8.881784197001252e-15 relative error 4.3790659987052973e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7899999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7900000000000009 Order of pole (three term test) 3.014422799826905e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7799999999999998 y[1] (closed_form) -2.107250627960689 y[1] (numeric) -2.1072506279606786 absolute error 1.021405182655144e-14 relative error 4.847098722393636e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7799999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7799999999999995 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7699999999999998 y[1] (closed_form) -2.190422160062911 y[1] (numeric) -2.190422160062899 absolute error 1.199040866595169e-14 relative error 5.474017239492919e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7699999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7700000000000031 Order of pole (three term test) 2.6538137860520156e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7599999999999998 y[1] (closed_form) -2.2780288671818067 y[1] (numeric) -2.2780288671817943 absolute error 1.2434497875801753e-14 relative error 5.458446139527946e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7599999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7599999999999993 Order of pole (three term test) 3.493270279658956e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7499999999999998 y[1] (closed_form) -2.3703703703703725 y[1] (numeric) -2.370370370370359 absolute error 1.3322676295501878e-14 relative error 5.62050406216485e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7499999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7500000000000016 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7399999999999998 y[1] (closed_form) -2.46777091189071 y[1] (numeric) -2.4677709118906948 absolute error 1.509903313490213e-14 relative error 6.118490603057574e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7399999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7400000000000049 Order of pole (three term test) 5.952127953339948e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7299999999999998 y[1] (closed_form) -2.570581748355473 y[1] (numeric) -2.570581748355456 absolute error 1.687538997430238e-14 relative error 6.564813581633183e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7299999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7300000000000039 Order of pole (three term test) 7.702270146372195e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7199999999999998 y[1] (closed_form) -2.679183813443075 y[1] (numeric) -2.679183813443057 absolute error 1.8207657603852567e-14 relative error 6.795971785322756e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7199999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7199999999999974 Order of pole (three term test) 2.4768352114390506e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7099999999999997 y[1] (closed_form) -2.79399068483506 y[1] (numeric) -2.793990684835039 absolute error 2.1316282072803006e-14 relative error 7.629331832958987e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7099999999999997 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7100000000000014 Order of pole (three term test) 3.1663169220971253e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; Iterations 300 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.3333333333334%