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/lin_arcsin_0d2_0d5postode.ode################# diff ( y , x , 1 ) = arcsin ( x + 0.0001 ) ; ! #BEGIN FIRST INPUT BLOCK max_terms=30 # Digits:=32; ELIMINATED in preodein.rb ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.2) x_end=c(0.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_display_interval=0.0001 # 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=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(x) + c(0.0001)) * arcsin(c(x) + c(0.0001)) + sqrt(c(1.0) - (c(x) + c(0.0001)) * (c(x) +c(0.0001)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.2e0+/-0.50e-33 y[1] (closed_form) 0.102008762216655550465070759077868515e1+/-0.507e-32 y[1] (numeric) 0.102008762216655550465070759077868515e1+/-0.609e-32 $glob_prec 0.1e-15+/-0.50e-49% absolute error 0.0e0+/-0.1116e-31 relative error 0.0e0+/-0.109402366595698613056665148787849636e-29% Desired digits 8 Estimated correct digits 14 Correct digits 34 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.21e0+/-0.550e-32 y[1] (closed_form) 0.102215329006396403013398645993082927e1+/-0.167e-31 y[1] (numeric) 0.10221532896998563912775305504543775e1+/-0.191e-31 absolute error 0.36410763885645590947645177e-9+/-0.358e-31 relative error 0.356216276360731452364740218876252734e-7+/-0.35e-29% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.22e0+/-0.105e-31 y[1] (closed_form) 0.102432124194253715469645218636115956e1+/-0.299e-31 y[1] (numeric) 0.10243212411940240818527941687512652e1+/-0.346e-31 absolute error 0.74851307284365801760989436e-9+/-0.645e-31 relative error 0.730740555008082561153557020316782754e-7+/-0.629e-29% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.23e0+/-0.155e-31 y[1] (closed_form) 0.102659170877264023260633181146606995e1+/-0.441e-31 y[1] (numeric) 0.102659170761903183787485926057842465e1+/-0.436e-31 absolute error 0.11536083947314725508876453e-8+/-0.877e-31 relative error 0.112372658465232429204070158337340943e-6+/-0.854e-29% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.24e0+/-0.205e-31 y[1] (closed_form) 0.102896493394596183097078072052969538e1+/-0.591e-31 y[1] (numeric) 0.10289649323661500056066901238089743e1+/-0.551e-31 absolute error 0.157981182536409059672072108e-8+/-0.114e-30 relative error 0.153534078105625473274378126001220637e-6+/-0.11e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.25e0+/-0.255e-31 y[1] (closed_form) 0.103144117352691179500813354558226946e1+/-0.765e-31 y[1] (numeric) 0.103144117149934280530882677638783446e1+/-0.686e-31 absolute error 0.2027568989699306769194435e-8+/-0.145e-30 relative error 0.196576309123498893933631015470686083e-6+/-0.14e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.26e0+/-0.305e-31 y[1] (closed_form) 0.103402069652048715030731790687116756e1+/-0.943e-31 y[1] (numeric) 0.103402069402313284953135204309301457e1+/-0.801e-31 absolute error 0.249735430077596586377815299e-8+/-0.174e-30 relative error 0.241518792532842261705303332743165588e-6+/-0.168e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.27e0+/-0.355e-31 y[1] (closed_form) 0.103670378515743835560498605963994838e1+/-0.112e-30 y[1] (numeric) 0.103670378216776589508008223246600628e1+/-0.931e-31 absolute error 0.29896724605249038271739421e-8+/-0.205e-30 relative error 0.288382516137035145088769054772226138e-6+/-0.197e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.28e0+/-0.405e-31 y[1] (closed_form) 0.103949073519763871523612122325860302e1+/-0.131e-30 y[1] (numeric) 0.103949073169257862792959325415760945e1+/-0.1e-30 absolute error 0.350506008730652796910099357e-8+/-0.231e-30 relative error 0.337190122876863326958278508894008897e-6+/-0.222e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.29e0+/-0.455e-31 y[1] (closed_form) 0.104238185625263600694696085570973092e1+/-0.153e-30 y[1] (numeric) 0.104238185220854852580809276659741182e1+/-0.1e-30 absolute error 0.40440874811388680891123191e-8+/-0.253e-30 relative error 0.387966027697121217776412626150641514e-6+/-0.242e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.3e0+/-0.505e-31 y[1] (closed_form) 0.104537747212844822919686176520150664e1+/-0.177e-30 y[1] (numeric) 0.104537746752108769040789445240215757e1+/-0.1e-30 absolute error 0.460736053878896731279934907e-8+/-0.277e-30 relative error 0.44073654365328135051424329289097341e-6+/-0.264e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.31e0+/-0.555e-31 y[1] (closed_form) 0.104847792118975555079177124212778631e1+/-0.201e-30 y[1] (numeric) 0.104847791599423271853608734244595469e1+/-0.1e-30 absolute error 0.519552283225568389968183162e-8+/-0.301e-30 relative error 0.495530018062763592002074313748483857e-6+/-0.287e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.32e0+/-0.605e-31 y[1] (closed_form) 0.105168355674673887118325948554163616e1+/-0.228e-30 y[1] (numeric) 0.10516835509374810054893738787655097e1+/-0.1e-30 absolute error 0.580925786569388560677612646e-8+/-0.328e-30 relative error 0.552376979598706588947042672599439648e-6+/-0.311e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.33e0+/-0.655e-31 y[1] (closed_form) 0.105499474746592278904738874350170765e1+/-0.253e-30 y[1] (numeric) 0.10549947410166312615050142606217666e1+/-0.1e-30 absolute error 0.644929152754237448287994105e-8+/-0.353e-30 relative error 0.611310297329294711249344860341437303e-6+/-0.334e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.34e0+/-0.705e-31 y[1] (closed_form) 0.10584118778064982616804092191992795e1+/-0.282e-30 y[1] (numeric) 0.105841187069010350513223695877750152e1+/-0.1e-30 absolute error 0.711639475654817226042177798e-8+/-0.382e-30 relative error 0.672365352824319957792035178381966145e-6+/-0.36e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.35e0+/-0.755e-31 y[1] (closed_form) 0.106193534848372898159475829454465295e1+/-0.313e-30 y[1] (numeric) 0.106193534067234253903482872495532344e1+/-0.1e-30 absolute error 0.781138644255992956958932951e-8+/-0.413e-30 relative error 0.735580226584727531898543743331322375e-6+/-0.388e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.36e0+/-0.805e-31 y[1] (closed_form) 0.106556557696118681343310442795359327e1+/-0.344e-30 y[1] (numeric) 0.106556556842605022800279717511887196e1+/-0.1e-30 absolute error 0.853513658543030725283472131e-8+/-0.444e-30 relative error 0.800995900202695763882918515522985527e-6+/-0.416e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.37e0+/-0.855e-31 y[1] (closed_form) 0.106930299797371701098622007091676065e1+/-0.376e-30 y[1] (numeric) 0.106930298868514727282173909031760267e1+/-0.1e-30 absolute error 0.928856973816448098059915798e-8+/-0.476e-30 relative error 0.868656475832006398873817814419137942e-6+/-0.445e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.38e0+/-0.905e-31 y[1] (closed_form) 0.107314806408320505694759936697175466e1+/-0.409e-30 y[1] (numeric) 0.107314805401053629331759910411045177e1+/-0.1e-30 absolute error 0.1007266876363000026286130289e-7+/-0.509e-30 relative error 0.938609414744192257593996702478139466e-6+/-0.474e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.39e0+/-0.955e-31 y[1] (closed_form) 0.107710124626940575303226438844501424e1+/-0.446e-30 y[1] (numeric) 0.107710123538092681527095126327325769e1+/-0.1e-30 absolute error 0.1088847893776131312517175655e-7+/-0.546e-30 relative error 0.101090579696886496317366363414842964e-5+/-0.506e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.4e0+/-0.1e-30 y[1] (closed_form) 0.10811630345583038166795583641015114e1+/-0.479e-30 y[1] (numeric) 0.108116302282119138035966719669189105e1+/-0.1e-30 absolute error 0.1173711243631989116740962035e-7+/-0.579e-30 relative error 0.10856006042710244530861514951746482e-5+/-0.535e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.41e0+/-0.1e-30 y[1] (closed_form) 0.108533393869070620167829712966049081e1+/-0.492e-30 y[1] (numeric) 0.108533392607095295468837316650437042e1+/-0.1e-30 absolute error 0.1261975324698992396315612039e-7+/-0.592e-30 relative error 0.116275302900909716891097871201069045e-5+/-0.545e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.42e0+/-0.1e-30 y[1] (closed_form) 0.108961448883402249954913903268914753e1+/-0.505e-30 y[1] (numeric) 0.108961447529635994555251501684998076e1+/-0.1e-30 absolute error 0.1353766255399662401583916677e-7+/-0.605e-30 relative error 0.124242681175091945596500476157066733e-5+/-0.555e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.43e0+/-0.1e-30 y[1] (closed_form) 0.109400523634047435753669578249630341e1+/-0.522e-30 y[1] (numeric) 0.109400522184828970889304799020545449e1+/-0.1e-30 absolute error 0.1449218464864364779229084892e-7+/-0.622e-30 relative error 0.132469061090795510099853473536382843e-5+/-0.568e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.44e0+/-0.1e-30 y[1] (closed_form) 0.109850675455529161312427627060175613e1+/-0.534e-30 y[1] (numeric) 0.109850673907053818681057405322474729e1+/-0.1e-30 absolute error 0.1548475342631370221737700884e-7+/-0.634e-30 relative error 0.140961840808911489134114318746915717e-5+/-0.577e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.45e0+/-0.1e-30 y[1] (closed_form) 0.110311963967880610598738521866611027e1+/-0.551e-30 y[1] (numeric) 0.110311962316190656726380726359418337e1+/-0.1e-30 absolute error 0.165168995387235779550719269e-7+/-0.651e-30 relative error 0.149728995338463757757116072983179351e-5+/-0.59e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.46e0+/-0.1e-30 y[1] (closed_form) 0.110784451168674886213347766446459917e1+/-0.566e-30 y[1] (numeric) 0.11078444940964905823690646069216857e1+/-0.1e-30 absolute error 0.1759025827976441305754291347e-7+/-0.666e-30 relative error 0.158779125537954438429031779044014062e-5+/-0.601e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.47e0+/-0.1e-30 y[1] (closed_form) 0.111268201531349830803203373559414187e1+/-0.582e-30 y[1] (numeric) 0.111268199660692001371127674874084038e1+/-0.1e-30 absolute error 0.1870657829432075698685330149e-7+/-0.682e-30 relative error 0.168121512137950535912543260831092009e-5+/-0.612e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.48e0+/-0.1e-30 y[1] (closed_form) 0.111763282110352304126932073671148354e1+/-0.597e-30 y[1] (numeric) 0.111763280123579182894412438226437899e1+/-0.1e-30 absolute error 0.1986773121232519635444710455e-7+/-0.697e-30 relative error 0.177766175412675240709430953005117772e-5+/-0.623e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.49e0+/-0.1e-30 y[1] (closed_form) 0.112269762653682022279313384733009056e1+/-0.612e-30 y[1] (numeric) 0.112269760546109789749016735197568827e1+/-0.1e-30 absolute error 0.2107572232530296649535440229e-7+/-0.712e-30 relative error 0.187723941221067173614603848771889211e-5+/-0.634e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 Finished! diff ( y , x , 1 ) = arcsin ( x + 0.0001 ) ; Iterations 300 Total Elapsed Time 2 Minutes 37 Seconds Elapsed Time(since restart) 2 Minutes 37 Seconds Time to Timeout 23 Seconds Percent Done 0.100333333333333333333333333333333333e3+/-0.336e-28%