##############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=false $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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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%