Initializing... Initialized Initializing(2)... PI = 0.314159265358979323846264338327950271e1+/-0.313e-33 E = 0.271828182845904523536028747135266232e1+/-0.256e-32 LOG_E_10 = 0.230258509299404568401799145468436324e1+/-0.5e-32 Initialized(2) ##############ECHO OF PROBLEM################# ##############temp/add_c_sinpostode.ode################# diff ( y , x , 1 ) = 1.0 + sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(-0.5) x_end=c(5.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_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=3 #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(2.0) - c(cos(c(x))) + c(x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -0.5e0+/-0.50e-32 y[1] (closed_form) 0.62241743810962728388371841739617034e0+/-0.835e-32 y[1] (numeric) 0.62241743810962728388371841739617034e0+/-0.897e-32 $glob_prec 0.1e-15+/-0.50e-49% absolute error 0.0e0+/-0.1732e-31 relative error 0.0e0+/-0.278269838528357609118553094822824668e-29% Desired digits 8 Estimated correct digits 14 Correct digits 34 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.420735492403948259952570726310234129e0+/-0.131e-28 Order of pole (three term test) 0.322298488470659301522746696795188645e2+/-0.126e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.49e0+/-0.100e-31 y[1] (closed_form) 0.62766714138987850429453184086334209e0+/-0.157e-31 y[1] (numeric) 0.627667141389878504294531761618406265e0+/-0.146e-31 absolute error 0.79244935825e-25+/-0.303e-31 relative error 0.126253121438735028270262908750067068e-22+/-0.482e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.415248685245985240797407244721891587e0+/-0.129e-28 Order of pole (three term test) 0.322214887266168913602524220434282277e2+/-0.125e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.48e0+/-0.150e-31 y[1] (closed_form) 0.63300507722071580560004516884125847e0+/-0.231e-31 y[1] (numeric) 0.633005077220715805600045011821537028e0+/-0.196e-31 absolute error 0.157019721442e-24+/-0.427e-31 relative error 0.248054442361527005448497526370627818e-22+/-0.674e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.409595784150499142689267710125983079e0+/-0.128e-28 Order of pole (three term test) 0.322132400069637716793391343962435315e2+/-0.125e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.47e0+/-0.200e-31 y[1] (closed_form) 0.63843171180467106354598072346660787e0+/-0.303e-31 y[1] (numeric) 0.638431711804671063545980490150028421e0+/-0.249e-31 absolute error 0.233316579449e-24+/-0.552e-31 relative error 0.36545267901789860199932897415238781e-22+/-0.864e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.403779050202557150413796354719381046e0+/-0.126e-28 Order of pole (three term test) 0.322051059874844508951278314181016985e2+/-0.126e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.46e0+/-0.250e-31 y[1] (closed_form) 0.64394750247447475746361009649959338e0+/-0.374e-31 y[1] (numeric) 0.643947502474474757463609788371713168e0+/-0.306e-31 absolute error 0.308127880212e-24+/-0.680e-31 relative error 0.478498447510034079099452137998255874e-22+/-0.105e-28% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.397800810018183022207205461404099627e0+/-0.124e-28 Order of pole (three term test) 0.321970899216782685889125176826324073e2+/-0.126e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.45e0+/-0.300e-31 y[1] (closed_form) 0.64955289764732307833115938851355356e0+/-0.444e-31 y[1] (numeric) 0.649552897647323078331159007067410881e0+/-0.378e-31 absolute error 0.381446142679e-24+/-0.822e-31 relative error 0.587244155265253640584894029900818033e-22+/-0.126e-28% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.391663454813741701386346842349045078e0+/-0.123e-28 Order of pole (three term test) 0.321891950158646677812684581581678578e2+/-0.126e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.44e0+/-0.350e-31 y[1] (closed_form) 0.65524833678003658283446261100162992e0+/-0.513e-31 y[1] (numeric) 0.655248336780036582834462157737594854e0+/-0.462e-31 absolute error 0.453264035066e-24+/-0.975e-31 relative error 0.691743892542161996218792764494761805e-22+/-0.148e-28% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.38536943944948465283114908374505512e0+/-0.12e-28 Order of pole (three term test) 0.321814244279007099051998461985587733e2+/-0.126e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.43e0+/-0.400e-31 y[1] (closed_form) 0.66103425032511487752408952233655371e0+/-0.582e-31 y[1] (numeric) 0.661034250325114877524088998762178046e0+/-0.522e-31 absolute error 0.523574375664e-24+/-0.11e-30 relative error 0.792053324629535731878523043840824144e-22+/-0.166e-28% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.378921281447638493432268769853120337e0+/-0.118e-28 Order of pole (three term test) 0.321737812659179740857660275949911379e2+/-0.125e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.42e0+/-0.450e-31 y[1] (closed_form) 0.66691105968769172756391121033433272e0+/-0.649e-31 y[1] (numeric) 0.666911059687691727563910617964199249e0+/-0.582e-31 absolute error 0.592370133471e-24+/-0.123e-30 relative error 0.888229584539205943104413786165145618e-22+/-0.184e-28% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.37232155998542966795979959236448149e0+/-0.116e-28 Order of pole (three term test) 0.321662685870793459496333118114235713e2+/-0.124e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.41e0+/-0.500e-31 y[1] (closed_form) 0.67287917718339489452435794172298226e0+/-0.715e-31 y[1] (numeric) 0.672879177183394894524357282078553268e0+/-0.642e-31 absolute error 0.659644428992e-24+/-0.135e-30 relative error 0.980331166961066873728259844264879228e-22+/-0.2e-28% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.365572914863447947056533222704009568e0+/-0.114e-28 Order of pole (three term test) 0.321588893963561932324526214878505135e2+/-0.126e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.4e0+/-0.550e-31 y[1] (closed_form) 0.67893900599711491720147326794819839e0+/-0.780e-31 y[1] (numeric) 0.678939005997114917201472542557663544e0+/-0.702e-31 absolute error 0.725390534846e-24+/-0.148e-30 relative error 0.106841782316021842156943170544272318e-21+/-0.217e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.358678045449761388201604683412596103e0+/-0.112e-28 Order of pole (three term test) 0.321516466453264172975159213070138245e2+/-0.125e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.39e0+/-0.600e-31 y[1] (closed_form) 0.68509094014268695854932324711889807e0+/-0.844e-31 y[1] (numeric) 0.685090940142686958549322457517021601e0+/-0.774e-31 absolute error 0.789601876469e-24+/-0.161e-30 relative error 0.115255045746853122980897125617450724e-21+/-0.235e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.351639709600205099581857284740994447e0+/-0.111e-28 Order of pole (three term test) 0.321445432309938613290581975809161462e2+/-0.126e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.38e0+/-0.650e-31 y[1] (closed_form) 0.69133536442348975050746919227544221e0+/-0.906e-31 y[1] (numeric) 0.691335364423489750507468340003409418e0+/-0.84e-31 absolute error 0.852272032792e-24+/-0.174e-30 relative error 0.123279102538420938673722186005063338e-21+/-0.251e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.344460722555275676969420712640354998e0+/-0.108e-28 Order of pole (three term test) 0.321375819946295474211866535584312575e2+/-0.125e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.37e0+/-0.700e-31 y[1] (closed_form) 0.69767265439396557679618709550912212e0+/-0.968e-31 y[1] (numeric) 0.69767265439396557679618618211438527e0+/-0.909e-31 absolute error 0.91339473685e-24+/-0.187e-30 relative error 0.130920243340112239540659292282369911e-21+/-0.268e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.337143955814072541122873168156723514e0+/-0.105e-28 Order of pole (three term test) 0.321307657206352060521515826300521834e2+/-0.124e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.36e0+/-0.750e-31 y[1] (closed_form) 0.70410317632206514164908763187525944e0+/-0.102e-30 y[1] (numeric) 0.704103176322065141649086658911383028e0+/-0.984e-31 absolute error 0.972963876412e-24+/-0.2e-30 relative error 0.138184844086963014374153550621598729e-21+/-0.284e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.329692335985736584163111778823917768e0+/-0.103e-28 Order of pole (three term test) 0.321240971354295525170164727761533967e2+/-0.125e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.35e0+/-0.800e-31 y[1] (closed_form) 0.71062728715262107996496764269633442e0+/-0.108e-30 y[1] (numeric) 0.710627287152621079964966611722839788e0+/-0.1e-30 absolute error 0.1030973494632e-23+/-0.208e-30 relative error 0.145079356403967966325790645504559479e-21+/-0.292e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.322108843618845534151433739491080765e0+/-0.1e-28 Order of pole (three term test) 0.321175789063577557933048246474271992e2+/-0.124e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.34e0+/-0.850e-31 y[1] (closed_form) 0.71724533447165377149735593997342286e0+/-0.114e-30 y[1] (numeric) 0.71724533447165377149735485255563228e0+/-0.1e-30 absolute error 0.108741779058e-23+/-0.214e-30 relative error 0.151610298222577814699987011659905398e-21+/-0.298e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.314396512009234264116143250574588943e0+/-0.977e-29 Order of pole (three term test) 0.321112136406245360375372032973193398e2+/-0.124e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.33e0+/-0.900e-31 y[1] (closed_form) 0.72395765647161302847058942163379473e0+/-0.12e-30 y[1] (numeric) 0.723957656471613028470588279342674848e0+/-0.1e-30 absolute error 0.1142291119882e-23+/-0.22e-30 relative error 0.157784244654478651626493625906479728e-21+/-0.303e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.306558425986716901508556339627987727e0+/-0.966e-29 Order of pole (three term test) 0.321050038842513174594347317040789861e2+/-0.124e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.32e0+/-0.950e-31 y[1] (closed_form) 0.73076458191755913242469272623390826e0+/-0.126e-30 y[1] (numeric) 0.730764581917559132424691530645913008e0+/-0.1e-30 absolute error 0.1195587995252e-23+/-0.226e-30 relative error 0.163607819102935082517381635803437134e-21+/-0.309e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.298597720681196033067798316164260511e0+/-0.936e-29 Order of pole (three term test) 0.320989521210578536987349017357221808e2+/-0.124e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.31e0+/-0.1e-30 y[1] (closed_form) 0.73766643011428660215719456379779225e0+/-0.131e-30 y[1] (numeric) 0.737666430114286602157193316494705205e0+/-0.1e-30 absolute error 0.1247303087045e-23+/-0.231e-30 relative error 0.169087684639757217982516689313460529e-21+/-0.313e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.290517580268652544960790029256381962e0+/-0.907e-29 Order of pole (three term test) 0.320930607716687330408908289684191359e2+/-0.124e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3e0+/-0.1e-30 y[1] (closed_form) 0.7446635108743939803576897724319501e0+/-0.13e-30 y[1] (numeric) 0.744663510874393980357688475000726312e0+/-0.1e-30 absolute error 0.1297431223788e-23+/-0.23e-30 relative error 0.174230535650194365550386885863935415e-21+/-0.308e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.282321236697517685541454402377815359e0+/-0.879e-29 Order of pole (three term test) 0.320873321925451608563212511533280902e2+/-0.124e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.29e0+/-0.1e-30 y[1] (closed_form) 0.75175612448730283192987522206813788e0+/-0.129e-30 y[1] (numeric) 0.75175612448730283192987387610074515e0+/-0.1e-30 absolute error 0.134596739273e-23+/-0.229e-30 relative error 0.179043089758390575243603115405049507e-21+/-0.304e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.274011968395936784922560154373488125e0+/-0.854e-29 Order of pole (three term test) 0.32081768675042406537326174983076372e2+/-0.124e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.28e0+/-0.1e-30 y[1] (closed_form) 0.75894456168922905207540994640352295e0+/-0.128e-30 y[1] (numeric) 0.758944561689229052075408553496782686e0+/-0.1e-30 absolute error 0.1392906740264e-23+/-0.228e-30 relative error 0.183532080019616028927113898456351649e-21+/-0.3e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.265593098960441708636120048463488014e0+/-0.833e-29 Order of pole (three term test) 0.320763724444932919413261982894223203e2+/-0.124e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.27e0+/-0.1e-30 y[1] (closed_form) 0.76622910363410948698376729050779696e0+/-0.127e-30 y[1] (numeric) 0.766229103634109486983765852263224446e0+/-0.1e-30 absolute error 0.1438244572514e-23+/-0.227e-30 relative error 0.187704247423208298526080994402476338e-21+/-0.296e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.257067995826556558916745349010908121e0+/-0.811e-29 Order of pole (three term test) 0.320711456593180879328282207881946158e2+/-0.125e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.26e0+/-0.1e-30 y[1] (closed_form) 0.77361002186548677444178235354993509e0+/-0.126e-30 y[1] (numeric) 0.773610021865486774441780871573579357e0+/-0.1e-30 absolute error 0.1481976355733e-23+/-0.226e-30 relative error 0.191566333662451189714936344050832713e-21+/-0.292e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.248440068921868363602422163487880133e0+/-0.774e-29 Order of pole (three term test) 0.320660904101611750536328692204517105e2+/-0.124e-26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.25e0+/-0.1e-30 y[1] (closed_form) 0.7810875782893552158554045505058108e0+/-0.125e-30 y[1] (numeric) 0.78108757828935521585540302640809403e0+/-0.1e-30 absolute error 0.152409771677e-23+/-0.225e-30 relative error 0.195125074208438560053012940433534415e-21+/-0.288e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.239712769302101506418331330566882007e0+/-0.751e-29 Order of pole (three term test) 0.320612087190548136455045163382200024e2+/-0.124e-26 NO COMPLEX POLE (six term test) for Equation 1 Finished! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = 1.0 + sin ( x ) ; Iterations 253 Total Elapsed Time 3 Minutes 1 Seconds Elapsed Time(since restart) 3 Minutes 1 Seconds Expected Time Remaining 1 Hours 2 Minutes 18 Seconds Optimized Time Remaining 1 Hours 2 Minutes 18 Seconds Expected Total Time 1 Hours 5 Minutes 19 Seconds Time to Timeout 0.0 Seconds Percent Done 0.461818181818181818181818181818181818e1+/-0.191e-29%