##############ECHO OF PROBLEM################# ##############temp/arcsin_sin_0d2_0d5postode.ode################# diff ( y , x , 1 ) = arcsin ( sin ( 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=false; 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 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (closed_form) = 0.02205 y[1] (numeric) = 0.02204999965391495 absolute error = 3.460850495073942e-10 relative error = 1.5695467097841e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (closed_form) = 0.02420000000000001 y[1] (numeric) = 0.02419999929040946 absolute error = 7.095905495135835e-10 relative error = 2.932192353361914e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (closed_form) = 0.02645000000000001 y[1] (numeric) = 0.02644999890940744 absolute error = 1.090592564173543e-09 relative error = 4.12322330500394e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (closed_form) = 0.02880000000000001 y[1] (numeric) = 0.02879999851082882 absolute error = 1.489171185670157e-09 relative error = 5.170733283576934e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = 0.03125000000000001 y[1] (numeric) = 0.0312499980945894 absolute error = 1.905410610542058e-09 relative error = 6.097313953734582e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 0.03380000000000002 y[1] (numeric) = 0.03379999766060084 absolute error = 2.339399181316981e-09 relative error = 6.921299353008817e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 0.03645000000000002 y[1] (numeric) = 0.03644999720877053 absolute error = 2.791229490595182e-09 relative error = 7.657694075706942e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 0.03920000000000002 y[1] (numeric) = 0.03919999673900156 absolute error = 3.260998457377262e-09 relative error = 8.318873615758318e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 0.04205000000000002 y[1] (numeric) = 0.04204999625119261 absolute error = 3.748807410330901e-09 relative error = 8.915118692820211e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000001 y[1] (closed_form) = 0.04500000000000003 y[1] (numeric) = 0.04499999574523787 absolute error = 4.254762167588133e-09 relative error = 9.455027039084733e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000001 y[1] (closed_form) = 0.04805000000000004 y[1] (numeric) = 0.0480499952210269 absolute error = 4.778973140828757e-09 relative error = 9.945833799851724e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000001 y[1] (closed_form) = 0.05120000000000004 y[1] (numeric) = 0.05119999467844458 absolute error = 5.321555453241533e-09 relative error = 1.039366299461236e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000001 y[1] (closed_form) = 0.05445000000000004 y[1] (numeric) = 0.05444999411737101 absolute error = 5.882629029729802e-09 relative error = 1.080372640905381e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000001 y[1] (closed_form) = 0.05780000000000005 y[1] (numeric) = 0.05779999353768132 absolute error = 6.462318721811577e-09 relative error = 1.118048221766708e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000001 y[1] (closed_form) = 0.06125000000000005 y[1] (numeric) = 0.06124999293924569 absolute error = 7.060754356191801e-09 relative error = 1.152776221419069e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (closed_form) = 0.06480000000000005 y[1] (numeric) = 0.06479999232192907 absolute error = 7.678070984562524e-09 relative error = 1.184887497617672e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (closed_form) = 0.06845000000000007 y[1] (numeric) = 0.06844999168559117 absolute error = 8.314408897480696e-09 relative error = 1.214668940464673e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (closed_form) = 0.07220000000000007 y[1] (numeric) = 0.0721999910300863 absolute error = 8.969913770084936e-09 relative error = 1.242370328266611e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = 0.07605000000000008 y[1] (numeric) = 0.07604999035526314 absolute error = 9.644736939651288e-09 relative error = 1.268209985489977e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (closed_form) = 0.08000000000000007 y[1] (numeric) = 0.07999998966096473 absolute error = 1.033903533620428e-08 relative error = 1.292379417025534e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000002 y[1] (closed_form) = 0.08405000000000008 y[1] (numeric) = 0.08404998894702821 absolute error = 1.1052971871095e-08 relative error = 1.315047218452705e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000002 y[1] (closed_form) = 0.08820000000000008 y[1] (numeric) = 0.08819998821328472 absolute error = 1.178671536761211e-08 relative error = 1.336362286577336e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000002 y[1] (closed_form) = 0.09245000000000009 y[1] (numeric) = 0.09244998745955915 absolute error = 1.254044093568218e-08 relative error = 1.356456564162485e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000002 y[1] (closed_form) = 0.09680000000000009 y[1] (numeric) = 0.09679998668567008 absolute error = 1.331433001350302e-08 relative error = 1.375447315444525e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000002 y[1] (closed_form) = 0.1012500000000001 y[1] (numeric) = 0.1012499858914294 absolute error = 1.410857065897719e-08 relative error = 1.393439077429845e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000002 y[1] (closed_form) = 0.1058000000000001 y[1] (numeric) = 0.1057999850766425 absolute error = 1.492335764685659e-08 relative error = 1.410525297434459e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = 0.1104500000000001 y[1] (numeric) = 0.1104499842411073 absolute error = 1.575889277405373e-08 relative error = 1.426789748669418e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (closed_form) = 0.1152000000000001 y[1] (numeric) = 0.1151999833846151 absolute error = 1.661538501229742e-08 relative error = 1.442307726761928e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = 0.1200500000000001 y[1] (numeric) = 0.1200499825069493 absolute error = 1.749305079956631e-08 relative error = 1.457147088676909e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 Finished! diff ( y , x , 1 ) = arcsin ( sin ( 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 %