Initializing... Initialized Initializing(2)... PI = 0.3141592653589793238462643383279486e1+/-0.313e-31 E = 0.2718281828459045235360287471352649e1+/-0.256e-30 LOG_E_10 = 0.2302585092994045684017991454684277e1+/-0.5e-30 Initialized(2) ##############ECHO OF PROBLEM################# ##############temp/sing4postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ! #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(-1.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=c(0.1) $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=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(1.0) # 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) # ELIMINATED in preodein.rb #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=8 $glob_max_minutes=(5.0) $glob_subiter_method=3 $glob_max_iter=1000 $glob_upper_ratio_limit=c(1.1) $glob_lower_ratio_limit=c(0.9) # ELIMINATED in preodein.rb #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(c(1.0) / (c(x) * c( x) + c(1.0))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0e0+/-0.50e-31 min_size 0.1e1+/-0.50e-31 $glob_desired_digits_correct 8 estimated_h 0.1e-2+/-0.5e-31 estimated_answer 0.1e1+/-0.50e-31 desired_abs_gbl_error 0.9999999999999999999999999999751083e-8+/-0.815e-35 range 0.1e1+/-0.100e-29 estimated_steps 0.1e4+/-0.51e-25 step_error 0.1054092553389459777332964514783134e-10+/-0.536e-34 est_needed_step_err 0.1054092553389459777332964514783134e-10+/-0.536e-34 opt_iter 1 SETTING H FOR MIN H SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] -0.2e1+/-0.50e-30 y[1] (closed_form) 0.2e0+/-0.92e-31 y[1] (numeric) 0.2e0+/-0.112e-30 absolute error 0.0e0+/-0.204e-30 relative error 0.0e0+/-0.1020000000000000000000000000000938e-27% Desired digits 8 Estimated correct digits 31 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.223606797749978969640917366873123e1+/-0.474e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.195e1+/-0.5e-30 y[1] (closed_form) 0.2082248828735033836543466944299843e0+/-0.971e-31 y[1] (numeric) 0.2082248828735033836538666946956467e0+/-0.162e-30 absolute error 0.4799997343376e-21+/-0.259e-30 relative error 0.2305198724156324e-18+/-0.124e-27% Desired digits 8 Estimated correct digits 31 Correct digits 21 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2191460700081112565694977042409691e1+/-0.471e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.19e1+/-0.5e-30 y[1] (closed_form) 0.2169197396963123644251626898047722e0+/-0.102e-30 y[1] (numeric) 0.2169197396963123644241690246558114e0+/-0.213e-30 absolute error 0.9936651489608e-21+/-0.315e-30 relative error 0.4580796336709288e-18+/-0.145e-27% Desired digits 8 Estimated correct digits 31 Correct digits 21 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2147091055358388846920969878103863e1+/-0.47e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.185e1+/-0.5e-30 y[1] (closed_form) 0.2261164499717354437535330695308083e0+/-0.108e-30 y[1] (numeric) 0.2261164499717354437519904202592651e0+/-0.266e-30 absolute error 0.15426492715432e-20+/-0.374e-30 relative error 0.6822366403399802000000000000000002e-18+/-0.165e-27% Desired digits 8 Estimated correct digits 31 Correct digits 21 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2102974084481309056343164520015523e1+/-0.466e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.18e1+/-0.5e-30 y[1] (closed_form) 0.2358490566037735849056603773584905e0+/-0.114e-30 y[1] (numeric) 0.2358490566037735849035319497891636e0+/-0.322e-30 absolute error 0.21284275693269e-20+/-0.436e-30 relative error 0.9024532893946056000000000000000002e-18+/-0.184e-27% Desired digits 8 Estimated correct digits 31 Correct digits 21 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2059126028197400063159473892839475e1+/-0.465e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.175e1+/-0.5e-30 y[1] (closed_form) 0.2461538461538461538461538461538461e0+/-0.121e-30 y[1] (numeric) 0.2461538461538461538434016465009623e0+/-0.37e-30 absolute error 0.27521996528838e-20+/-0.491e-30 relative error 0.111808110898404375e-17+/-0.199e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2015564437074637413091653307575905e1+/-0.463e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.17e1+/-0.5e-30 y[1] (closed_form) 0.2570694087403598971722365038560411e0+/-0.128e-30 y[1] (numeric) 0.2570694087403598971688217414751541e0+/-0.409e-30 absolute error 0.3414762380887e-20+/-0.537e-30 relative error 0.1328342566165043e-17+/-0.208e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1972308292331601996806399908324762e1+/-0.459e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.165e1+/-0.5e-30 y[1] (closed_form) 0.2686366689053055742108797850906648e0+/-0.136e-30 y[1] (numeric) 0.2686366689053055742067634375368556e0+/-0.474e-30 absolute error 0.41163475538092e-20+/-0.610e-30 relative error 0.15323103769054747e-17+/-0.227e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.192937813815747378494842310871409e1+/-0.457e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.16e1+/-0.5e-30 y[1] (closed_form) 0.2808988764044943820224719101123595e0+/-0.144e-30 y[1] (numeric) 0.2808988764044943820176154940137788e0+/-0.53e-30 absolute error 0.48564160985807e-20+/-0.674e-30 relative error 0.17288841310947292e-17+/-0.239e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1886796226411320762264132075525196e1+/-0.454e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.155e1+/-0.5e-30 y[1] (closed_form) 0.2939015429831006612784717119764878e0+/-0.152e-30 y[1] (numeric) 0.2939015429831006612728383127132456e0+/-0.576e-30 absolute error 0.56333992632422e-20+/-0.728e-30 relative error 0.191676409931815855e-17+/-0.247e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.184458667456967171922534287275171e1+/-0.45e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.15e1+/-0.5e-30 y[1] (closed_form) 0.3076923076923076923076923076923076e0+/-0.162e-30 y[1] (numeric) 0.3076923076923076923012479317534795e0+/-0.64e-30 absolute error 0.64443759388281e-20+/-0.802e-30 relative error 0.20944221801191325e-17+/-0.26e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.180277563773199464655961063373592e1+/-0.447e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.145e1+/-0.5e-30 y[1] (closed_form) 0.3223207091055600322320709105560032e0+/-0.171e-30 y[1] (numeric) 0.3223207091055600322247862366114467e0+/-0.693e-30 absolute error 0.72846739445565e-20+/-0.864e-30 relative error 0.2260070091298654125e-17+/-0.268e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1761391495380853711018671192915518e1+/-0.443e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.14e1+/-0.5e-30 y[1] (closed_form) 0.3378378378378378378378378378378378e0+/-0.182e-30 y[1] (numeric) 0.337837837837837837829690455656098e0+/-0.779e-30 absolute error 0.81473821817398e-20+/-0.961e-30 relative error 0.24116251257949808e-17+/-0.284e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1720465053408525354345894707010696e1+/-0.438e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.135e1+/-0.5e-30 y[1] (closed_form) 0.3542958370239149689991142604074402e0+/-0.193e-30 y[1] (numeric) 0.3542958370239149689900915000665137e0+/-0.869e-30 absolute error 0.90227603409265e-20+/-0.106e-29 relative error 0.2546674106226504625e-17+/-0.299e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1680029761641144260833404973473896e1+/-0.435e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.1680029761641130445110574450070056e1+/-0.63e-15 Order of pole (six term test) 0.99999999999983832092651291050713e0+/-0.371e-19 TOP MAIN SOLVE Loop x[1] -0.13e1+/-0.5e-30 y[1] (closed_form) 0.3717472118959107806691449814126394e0+/-0.205e-30 y[1] (numeric) 0.3717472118959107806592474475382405e0+/-0.965e-30 absolute error 0.98975338743989e-20+/-0.117e-29 relative error 0.26624366122133041e-17+/-0.314e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1640121946685672516307471322740154e1+/-0.429e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.1640121946685666179147757160685948e1+/-0.675e-15 Order of pole (six term test) 0.99999999999992583300581960467068e0+/-0.396e-19 TOP MAIN SOLVE Loop x[1] -0.125e1+/-0.5e-30 y[1] (closed_form) 0.3902439024390243902439024390243902e0+/-0.217e-30 y[1] (numeric) 0.3902439024390243902331483740233285e0+/-0.103e-29 absolute error 0.107540650010617e-19+/-0.124e-29 relative error 0.2755729156522060625e-17+/-0.317e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1600781059358212171622054418656246e1+/-0.424e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.1600781059358212374238930491219104e1+/-0.15e-16 Order of pole (six term test) 0.100000000000000261739648831464729e1+/-0.968e-21 TOP MAIN SOLVE Loop x[1] -0.12e1+/-0.5e-30 y[1] (closed_form) 0.4098360655737704918032786885245901e0+/-0.23e-30 y[1] (numeric) 0.4098360655737704917917092918459994e0+/-0.108e-29 absolute error 0.115693966785907e-19+/-0.131e-29 relative error 0.28229327895761308e-17+/-0.319e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1562049935181330878825944547152681e1+/-0.418e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.1562049935181333817029591880277654e1+/-0.414e-17 Order of pole (six term test) 0.100000000000003355696660063408799e1+/-0.237e-20 TOP MAIN SOLVE Loop x[1] -0.115e1+/-0.5e-30 y[1] (closed_form) 0.4305705059203444564047362755651237e0+/-0.243e-30 y[1] (numeric) 0.4305705059203444563924220983517601e0+/-0.115e-29 absolute error 0.123141772133636e-19+/-0.139e-29 relative error 0.28599676578036961e-17+/-0.322e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1523975065412817047905433441249134e1+/-0.412e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.1523975065412818025837398631077975e1+/-0.156e-17 Order of pole (six term test) 0.10000000000000062474426068806658e1+/-0.179e-20 TOP MAIN SOLVE Loop x[1] -0.11e1+/-0.5e-30 y[1] (closed_form) 0.4524886877828054298642533936651583e0+/-0.258e-30 y[1] (numeric) 0.4524886877828054298513019033232791e0+/-0.124e-29 absolute error 0.129514903418792e-19+/-0.149e-29 relative error 0.28622793655553032e-17+/-0.329e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1486606874731850552261200821394065e1+/-0.405e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.1486606874731846699535549900103088e1+/-0.9e-18 Order of pole (six term test) 0.99999999999994233025331608789446e0+/-0.789e-21 TOP MAIN SOLVE Loop x[1] -0.105e1+/-0.5e-30 y[1] (closed_form) 0.4756242568370986920332936979785969e0+/-0.272e-30 y[1] (numeric) 0.4756242568370986920198580565372564e0+/-0.13e-29 absolute error 0.134356414413405e-19+/-0.157e-29 relative error 0.2824843613041840125e-17+/-0.33e-27% Desired digits 8 Estimated correct digits 31 Correct digits 20 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1450000000000000000000000000000966e1+/-0.398e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.1449999999999992097954023569645342e1+/-0.205e-17 Order of pole (six term test) 0.99999999999988855887886804801624e0+/-0.15e-20 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; Iterations 20 Total Elapsed Time 1 Minutes 32 Seconds Elapsed Time(since restart) 1 Minutes 29 Seconds Time to Timeout 3 Minutes 28 Seconds Percent Done 0.105e3+/-0.21e-27%