##############ECHO OF PROBLEM################# ##############temp/arctan_tan_0d2_0d5postode.ode################# diff ( y , x , 1 ) = arctan ( tan ( 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) = 0.02205000069217028 absolute error = 6.921702759565829e-10 relative error = 3.139094222025319e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 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) = 0.02420000141918145 absolute error = 1.419181445971862e-09 relative error = 5.864386140379594e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 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) = 0.02645000218118567 absolute error = 2.181185666111363e-09 relative error = 8.246448643143146e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 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) = 0.02880000297834313 absolute error = 2.978343117271409e-09 relative error = 1.034146915719239e-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] = 0.2500000000000001 y[1] (closed_form) = 0.03125000000000001 y[1] (numeric) = 0.03125000381082218 absolute error = 3.810822164773686e-09 relative error = 1.219463092727579e-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] = 0.2600000000000001 y[1] (closed_form) = 0.03380000000000002 y[1] (numeric) = 0.03380000467879954 absolute error = 4.678799521429244e-09 relative error = 1.384260213440604e-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] = 0.2700000000000001 y[1] (closed_form) = 0.03645000000000002 y[1] (numeric) = 0.03645000558246039 absolute error = 5.582460375908038e-09 relative error = 1.531539197779982e-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] = 0.2800000000000001 y[1] (closed_form) = 0.03920000000000002 y[1] (numeric) = 0.03920000652199856 absolute error = 6.521998545394592e-09 relative error = 1.663775139131273e-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] = 0.2900000000000001 y[1] (closed_form) = 0.04205000000000002 y[1] (numeric) = 0.04205000749761671 absolute error = 7.497616680285368e-09 relative error = 1.783024180805081e-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] = 0.3000000000000001 y[1] (closed_form) = 0.04500000000000003 y[1] (numeric) = 0.04500000850952647 absolute error = 8.509526437661119e-09 relative error = 1.891005875035803e-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] = 0.3100000000000001 y[1] (closed_form) = 0.04805000000000004 y[1] (numeric) = 0.04805000955794871 absolute error = 9.557948668637017e-09 relative error = 1.989167256740273e-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] = 0.3200000000000001 y[1] (closed_form) = 0.05120000000000004 y[1] (numeric) = 0.05120001064311362 absolute error = 1.064311358489611e-08 relative error = 2.078733122050021e-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] = 0.3300000000000001 y[1] (closed_form) = 0.05445000000000004 y[1] (numeric) = 0.05445001176526109 absolute error = 1.176526105012288e-08 relative error = 2.160745831060214e-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] = 0.3400000000000001 y[1] (closed_form) = 0.05780000000000005 y[1] (numeric) = 0.05780001292464076 absolute error = 1.292464071878108e-08 relative error = 2.236097010169735e-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] = 0.3500000000000001 y[1] (closed_form) = 0.06125000000000005 y[1] (numeric) = 0.06125001412151238 absolute error = 1.412151233448622e-08 relative error = 2.30555303420183e-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] = 0.3600000000000002 y[1] (closed_form) = 0.06480000000000005 y[1] (numeric) = 0.06480001535614595 absolute error = 1.5356145896539e-08 relative error = 2.369775601317745e-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] = 0.3700000000000002 y[1] (closed_form) = 0.06845000000000007 y[1] (numeric) = 0.06845001662882211 absolute error = 1.662882204156446e-08 relative error = 2.429338501324243e-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] = 0.3800000000000002 y[1] (closed_form) = 0.07220000000000007 y[1] (numeric) = 0.07220001793983225 absolute error = 1.7939832175351e-08 relative error = 2.484741298525067e-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] = 0.3900000000000002 y[1] (closed_form) = 0.07605000000000008 y[1] (numeric) = 0.07605001928947895 absolute error = 1.928947887530619e-08 relative error = 2.536420627916656e-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] = 0.4000000000000002 y[1] (closed_form) = 0.08000000000000007 y[1] (numeric) = 0.08000002067807613 absolute error = 2.067807605699024e-08 relative error = 2.584759507123777e-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] = 0.4100000000000002 y[1] (closed_form) = 0.08405000000000008 y[1] (numeric) = 0.08405002210594953 absolute error = 2.210594944596078e-08 relative error = 2.630095115521804e-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] = 0.4200000000000002 y[1] (closed_form) = 0.08820000000000008 y[1] (numeric) = 0.08820002357343693 absolute error = 2.357343684145086e-08 relative error = 2.672725265470616e-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] = 0.4300000000000002 y[1] (closed_form) = 0.09245000000000009 y[1] (numeric) = 0.09245002508088844 absolute error = 2.508088835229128e-08 relative error = 2.712913829344646e-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] = 0.4400000000000002 y[1] (closed_form) = 0.09680000000000009 y[1] (numeric) = 0.096800026628667 absolute error = 2.662866691038879e-08 relative error = 2.75089534198231e-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] = 0.4500000000000002 y[1] (closed_form) = 0.1012500000000001 y[1] (numeric) = 0.1012500282171487 absolute error = 2.82171485899152e-08 relative error = 2.786878873078041e-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] = 0.4600000000000002 y[1] (closed_form) = 0.1058000000000001 y[1] (numeric) = 0.1058000298467231 absolute error = 2.984672300976321e-08 relative error = 2.821051324174213e-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] = 0.4700000000000003 y[1] (closed_form) = 0.1104500000000001 y[1] (numeric) = 0.1104500315177938 absolute error = 3.15177937082467e-08 relative error = 2.853580236147276e-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] = 0.4800000000000003 y[1] (closed_form) = 0.1152000000000001 y[1] (numeric) = 0.1152000332307788 absolute error = 3.323077871209001e-08 relative error = 2.884616207646699e-05 % Desired digits = 8 Estimated correct digits = 12 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] = 0.4900000000000003 y[1] (closed_form) = 0.1200500000000001 y[1] (numeric) = 0.1200500349861109 absolute error = 3.498611080010594e-08 relative error = 2.914294943782249e-05 % Desired digits = 8 Estimated correct digits = 12 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 Finished! diff ( y , x , 1 ) = arctan ( tan ( 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 %