##############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; ! /* 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; 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=true; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(x)*c(x)/c(2.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 0.02 y[1] (numeric) = 0.02 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 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] = 0.21 y[1] (closed_form) = 0.02205 y[1] (numeric) = 0.02205000803719315 absolute error = 8.037193143656252e-09 relative error = 3.644985552678572e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 NO INFO (given) for Equation 1 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] = 0.22 y[1] (closed_form) = 0.02420000000000001 y[1] (numeric) = 0.02420001568861933 absolute error = 1.568861932726984e-08 relative error = 6.482900548458609e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 NO INFO (given) for Equation 1 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] = 0.23 y[1] (closed_form) = 0.02645000000000001 y[1] (numeric) = 0.02645002298815831 absolute error = 2.298815829707146e-08 relative error = 8.691175159573328e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 NO INFO (given) for Equation 1 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] = 0.24 y[1] (closed_form) = 0.02880000000000001 y[1] (numeric) = 0.02880002996535194 absolute error = 2.996535193242056e-08 relative error = 0.0001040463608764602 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.2500000000000001 y[1] (closed_form) = 0.03125000000000001 y[1] (numeric) = 0.03125003664611438 absolute error = 3.664611436526855e-08 relative error = 0.0001172675659688593 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.2600000000000001 y[1] (closed_form) = 0.03380000000000002 y[1] (numeric) = 0.03380004305330254 absolute error = 4.305330252030171e-08 relative error = 0.0001273766346754488 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.2700000000000001 y[1] (closed_form) = 0.03645000000000002 y[1] (numeric) = 0.03645004920717879 absolute error = 4.92071787691617e-08 relative error = 0.0001349991187082625 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.2800000000000001 y[1] (closed_form) = 0.03920000000000002 y[1] (numeric) = 0.03920005512578909 absolute error = 5.512578907240773e-08 relative error = 0.0001406270129398156 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.2900000000000001 y[1] (closed_form) = 0.04205000000000002 y[1] (numeric) = 0.04205006082527486 absolute error = 6.082527483075584e-08 relative error = 0.0001446498806914525 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.3000000000000001 y[1] (closed_form) = 0.04500000000000003 y[1] (numeric) = 0.04500006632013166 absolute error = 6.632013162255479e-08 relative error = 0.0001473780702723439 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.3100000000000001 y[1] (closed_form) = 0.04805000000000004 y[1] (numeric) = 0.04805007162342555 absolute error = 7.162342551686462e-08 relative error = 0.0001490601987863987 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.3200000000000001 y[1] (closed_form) = 0.05120000000000004 y[1] (numeric) = 0.05120007674697492 absolute error = 7.674697487941584e-08 relative error = 0.000149896435311359 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.3300000000000001 y[1] (closed_form) = 0.05445000000000004 y[1] (numeric) = 0.05445008170150425 absolute error = 8.170150421482614e-08 relative error = 0.0001500486762439414 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.3400000000000001 y[1] (closed_form) = 0.05780000000000005 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 NO INFO (given) for Equation 1 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] = 0.3500000000000001 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 NO INFO (given) for Equation 1 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] = 0.3600000000000002 y[1] (closed_form) = 0.06480000000000005 y[1] (numeric) = 0.06480009564442718 absolute error = 9.564442712828303e-08 relative error = 0.0001475994245806836 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.3700000000000002 y[1] (closed_form) = 0.06845000000000007 y[1] (numeric) = 0.0684501000124465 absolute error = 1.000124464356489e-07 relative error = 0.0001461102212354255 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.3800000000000002 y[1] (closed_form) = 0.07220000000000007 y[1] (numeric) = 0.07220010425263799 absolute error = 1.042526379252395e-07 relative error = 0.0001443942353535172 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.3900000000000002 y[1] (closed_form) = 0.07605000000000008 y[1] (numeric) = 0.07605010837134606 absolute error = 1.08371345980407e-07 relative error = 0.0001425001262069781 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.4000000000000002 y[1] (closed_form) = 0.08000000000000007 y[1] (numeric) = 0.08000011237443155 absolute error = 1.12374431482376e-07 relative error = 0.0001404680393529699 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.4100000000000002 y[1] (closed_form) = 0.08405000000000008 y[1] (numeric) = 0.08405011626731972 absolute error = 1.16267319633101e-07 relative error = 0.0001383311357919106 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.4200000000000002 y[1] (closed_form) = 0.08820000000000008 y[1] (numeric) = 0.08820012005504207 absolute error = 1.200550419910851e-07 relative error = 0.0001361168276542913 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.4300000000000002 y[1] (closed_form) = 0.09245000000000009 y[1] (numeric) = 0.09245012374227354 absolute error = 1.237422734556848e-07 relative error = 0.0001338477809147482 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.4400000000000002 y[1] (closed_form) = 0.09680000000000009 y[1] (numeric) = 0.09680012733336535 absolute error = 1.273333652546116e-07 relative error = 0.0001315427327010449 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.4500000000000002 y[1] (closed_form) = 0.1012500000000001 y[1] (numeric) = 0.101250130832374 absolute error = 1.308323738791195e-07 relative error = 0.0001292171593867846 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.4600000000000002 y[1] (closed_form) = 0.1058000000000001 y[1] (numeric) = 0.1058001342430873 absolute error = 1.342430871603684e-07 relative error = 0.0001268838252933537 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.4700000000000003 y[1] (closed_form) = 0.1104500000000001 y[1] (numeric) = 0.1104501375690474 absolute error = 1.375690472510405e-07 relative error = 0.0001245532342698418 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.4800000000000003 y[1] (closed_form) = 0.1152000000000001 y[1] (numeric) = 0.1152001408135715 absolute error = 1.408135713587555e-07 relative error = 0.0001222340029155862 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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] = 0.4900000000000003 y[1] (closed_form) = 0.1200500000000001 y[1] (numeric) = 0.1200501439797705 absolute error = 1.439797703284285e-07 relative error = 0.0001199331697862793 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 NO INFO (given) for Equation 1 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 Finished! diff ( y , x , 1 ) = arccos ( cos ( x ) ) ; Iterations = 300 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.3 %