##############ECHO OF PROBLEM################# ##############temp/arccos_cos_0d2_0d5postode.ode################# diff ( y , x , 1 ) = arccos ( cos ( x ) ) ; ! #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=0.001 # 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=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(x)/c(2.0)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.2 y[1] (closed_form) 0.020000000000000004 y[1] (numeric) 0.020000000000000004 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.21000000000000002 y[1] (closed_form) 0.022050000000000004 y[1] (numeric) 0.022050008037193147 absolute error 8.037193143656252e-09 relative error 3.6449855526785716e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.22000000000000003 y[1] (closed_form) 0.024200000000000006 y[1] (numeric) 0.024200015688619333 absolute error 1.5688619327269837e-08 relative error 6.482900548458609e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.23000000000000004 y[1] (closed_form) 0.026450000000000008 y[1] (numeric) 0.026450022988158305 absolute error 2.298815829707146e-08 relative error 8.691175159573328e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.24000000000000005 y[1] (closed_form) 0.02880000000000001 y[1] (numeric) 0.028800029965351942 absolute error 2.996535193242056e-08 relative error 0.00010404636087646024% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.25000000000000006 y[1] (closed_form) 0.031250000000000014 y[1] (numeric) 0.03125003664611438 absolute error 3.6646114365268545e-08 relative error 0.00011726756596885929% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.26000000000000006 y[1] (closed_form) 0.03380000000000002 y[1] (numeric) 0.03380004305330254 absolute error 4.3053302520301706e-08 relative error 0.00012737663467544876% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2700000000000001 y[1] (closed_form) 0.03645000000000002 y[1] (numeric) 0.036450049207178786 absolute error 4.92071787691617e-08 relative error 0.00013499911870826247% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2800000000000001 y[1] (closed_form) 0.03920000000000002 y[1] (numeric) 0.03920005512578909 absolute error 5.512578907240773e-08 relative error 0.00014062701293981555% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2900000000000001 y[1] (closed_form) 0.042050000000000025 y[1] (numeric) 0.042050060825274856 absolute error 6.082527483075584e-08 relative error 0.00014464988069145255% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3000000000000001 y[1] (closed_form) 0.04500000000000003 y[1] (numeric) 0.045000066320131656 absolute error 6.632013162255479e-08 relative error 0.00014737807027234386% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3100000000000001 y[1] (closed_form) 0.04805000000000004 y[1] (numeric) 0.048050071623425554 absolute error 7.162342551686462e-08 relative error 0.00014906019878639868% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3200000000000001 y[1] (closed_form) 0.05120000000000004 y[1] (numeric) 0.05120007674697492 absolute error 7.674697487941584e-08 relative error 0.00014989643531135896% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3300000000000001 y[1] (closed_form) 0.05445000000000004 y[1] (numeric) 0.054450081701504255 absolute error 8.170150421482614e-08 relative error 0.00015004867624394136% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.34000000000000014 y[1] (closed_form) 0.057800000000000046 y[1] (numeric) 0.05780008649677506 absolute error 8.649677501332276e-08 relative error 0.0001496483996770289% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.35000000000000014 y[1] (closed_form) 0.06125000000000005 y[1] (numeric) 0.06125009114169766 absolute error 9.114169761265112e-08 relative error 0.0001488027716124915% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.36000000000000015 y[1] (closed_form) 0.06480000000000005 y[1] (numeric) 0.06480009564442718 absolute error 9.564442712828303e-08 relative error 0.00014759942458068357% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.37000000000000016 y[1] (closed_form) 0.06845000000000007 y[1] (numeric) 0.0684501000124465 absolute error 1.0001244643564888e-07 relative error 0.00014611022123542554% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.38000000000000017 y[1] (closed_form) 0.07220000000000007 y[1] (numeric) 0.072200104252638 absolute error 1.0425263792523953e-07 relative error 0.00014439423535351722% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3900000000000002 y[1] (closed_form) 0.07605000000000008 y[1] (numeric) 0.07605010837134606 absolute error 1.0837134598040699e-07 relative error 0.00014250012620697813% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4000000000000002 y[1] (closed_form) 0.08000000000000007 y[1] (numeric) 0.08000011237443155 absolute error 1.1237443148237602e-07 relative error 0.0001404680393529699% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4100000000000002 y[1] (closed_form) 0.08405000000000008 y[1] (numeric) 0.08405011626731972 absolute error 1.16267319633101e-07 relative error 0.00013833113579191062% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4200000000000002 y[1] (closed_form) 0.08820000000000008 y[1] (numeric) 0.08820012005504207 absolute error 1.2005504199108508e-07 relative error 0.00013611682765429133% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4300000000000002 y[1] (closed_form) 0.09245000000000009 y[1] (numeric) 0.09245012374227354 absolute error 1.2374227345568478e-07 relative error 0.00013384778091474816% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4400000000000002 y[1] (closed_form) 0.0968000000000001 y[1] (numeric) 0.09680012733336535 absolute error 1.2733336525461159e-07 relative error 0.0001315427327010449% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.45000000000000023 y[1] (closed_form) 0.1012500000000001 y[1] (numeric) 0.10125013083237398 absolute error 1.308323738791195e-07 relative error 0.00012921715938678455% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.46000000000000024 y[1] (closed_form) 0.10580000000000012 y[1] (numeric) 0.10580013424308728 absolute error 1.3424308716036837e-07 relative error 0.0001268838252933537% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.47000000000000025 y[1] (closed_form) 0.11045000000000012 y[1] (numeric) 0.11045013756904737 absolute error 1.3756904725104047e-07 relative error 0.00012455323426984185% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.48000000000000026 y[1] (closed_form) 0.11520000000000012 y[1] (numeric) 0.11520014081357148 absolute error 1.408135713587555e-07 relative error 0.00012223400291558624% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.49000000000000027 y[1] (closed_form) 0.12005000000000013 y[1] (numeric) 0.12005014397977046 absolute error 1.4397977032842846e-07 relative error 0.0001199331697862793% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 Finished! diff ( y , x , 1 ) = arccos ( cos ( x ) ) ; Iterations 300 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.33333333333341%