##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrt_tzeropostode.ode################# diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.0); x_end=c(0.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=c(0.001); glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-2.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.5); array_given_ord_poles[1][2]=c(0.0); // 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(0.8) * (c(x) + c(2.0)) * sqrt(sqrt(c(0.1) * c(x) + c(0.2)))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 1.069984487962275 y[1] (numeric) = 1.069984487962275 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] = 0.01 y[1] (closed_form) = 1.076676065425809 y[1] (numeric) = 1.07667606542581 absolute error = 4.440892098500626e-16 relative error = 4.124631577785023e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.02000000000000001 y[1] (closed_form) = 1.083375970955018 y[1] (numeric) = 1.083375970955019 absolute error = 4.440892098500626e-16 relative error = 4.099123681491559e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.03000000000000002 y[1] (closed_form) = 1.09008417360947 y[1] (numeric) = 1.090084173609471 absolute error = 4.440892098500626e-16 relative error = 4.073898333736936e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.04000000000000003 y[1] (closed_form) = 1.09680064271563 y[1] (numeric) = 1.09680064271563 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.05000000000000004 y[1] (closed_form) = 1.103525347863256 y[1] (numeric) = 1.103525347863256 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.06000000000000005 y[1] (closed_form) = 1.110258258901869 y[1] (numeric) = 1.110258258901869 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07000000000000005 y[1] (closed_form) = 1.116999345937281 y[1] (numeric) = 1.116999345937281 absolute error = 2.220446049250313e-16 relative error = 1.98786691982091e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.08000000000000006 y[1] (closed_form) = 1.123748579328188 y[1] (numeric) = 1.123748579328188 absolute error = 2.220446049250313e-16 relative error = 1.975927792120338e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000007 y[1] (closed_form) = 1.130505929682826 y[1] (numeric) = 1.130505929682826 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1000000000000001 y[1] (closed_form) = 1.137271367855683 y[1] (numeric) = 1.137271367855683 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1100000000000001 y[1] (closed_form) = 1.144044864944275 y[1] (numeric) = 1.144044864944275 absolute error = 4.440892098500626e-16 relative error = 3.881746454687279e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1200000000000001 y[1] (closed_form) = 1.150826392285975 y[1] (numeric) = 1.150826392285975 absolute error = 2.220446049250313e-16 relative error = 1.929436154865784e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1300000000000001 y[1] (closed_form) = 1.157615921454899 y[1] (numeric) = 1.1576159214549 absolute error = 6.661338147750939e-16 relative error = 5.754359476482431e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1400000000000001 y[1] (closed_form) = 1.164413424258851 y[1] (numeric) = 1.164413424258852 absolute error = 8.881784197001252e-16 relative error = 7.627689626349427e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1500000000000001 y[1] (closed_form) = 1.171218872736315 y[1] (numeric) = 1.171218872736316 absolute error = 8.881784197001252e-16 relative error = 7.583368406838226e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 1.178032239153504 y[1] (numeric) = 1.178032239153504 absolute error = 4.440892098500626e-16 relative error = 3.769754299501777e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 1.184853496001456 y[1] (numeric) = 1.184853496001457 absolute error = 4.440892098500626e-16 relative error = 3.748051648146691e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 1.191682615993191 y[1] (numeric) = 1.191682615993191 absolute error = 4.440892098500626e-16 relative error = 3.726572863362135e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 1.198519572060899 y[1] (numeric) = 1.1985195720609 absolute error = 6.661338147750939e-16 relative error = 5.557971937242975e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 1.205364337353195 y[1] (numeric) = 1.205364337353195 absolute error = 6.661338147750939e-16 relative error = 5.526410514499103e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000002 y[1] (closed_form) = 1.212216885232404 y[1] (numeric) = 1.212216885232404 absolute error = 6.661338147750939e-16 relative error = 5.495170236367266e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000002 y[1] (closed_form) = 1.219077189271908 y[1] (numeric) = 1.219077189271909 absolute error = 2.220446049250313e-16 relative error = 1.821415468020093e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000002 y[1] (closed_form) = 1.225945223253526 y[1] (numeric) = 1.225945223253526 absolute error = 2.220446049250313e-16 relative error = 1.811211469430493e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000002 y[1] (closed_form) = 1.232820961164941 y[1] (numeric) = 1.232820961164941 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000002 y[1] (closed_form) = 1.239704377197174 y[1] (numeric) = 1.239704377197174 absolute error = 2.220446049250313e-16 relative error = 1.791109308067849e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000002 y[1] (closed_form) = 1.246595445742096 y[1] (numeric) = 1.246595445742096 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000002 y[1] (closed_form) = 1.253494141389982 y[1] (numeric) = 1.253494141389982 absolute error = 2.220446049250313e-16 relative error = 1.771405207197931e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000002 y[1] (closed_form) = 1.260400438927108 y[1] (numeric) = 1.260400438927108 absolute error = 2.220446049250313e-16 relative error = 1.761698886062295e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000002 y[1] (closed_form) = 1.267314313333384 y[1] (numeric) = 1.267314313333385 absolute error = 6.661338147750939e-16 relative error = 5.256263641676858e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 1.274235739780028 y[1] (numeric) = 1.274235739780029 absolute error = 6.661338147750939e-16 relative error = 5.227712533711297e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 1.281164693627276 y[1] (numeric) = 1.281164693627277 absolute error = 1.110223024625157e-15 relative error = 8.665732283660237e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 1.288101150422135 y[1] (numeric) = 1.288101150422136 absolute error = 1.110223024625157e-15 relative error = 8.619067099360294e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 1.29504508589616 y[1] (numeric) = 1.295045085896161 absolute error = 1.110223024625157e-15 relative error = 8.572852302334261e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 1.301996475963283 y[1] (numeric) = 1.301996475963284 absolute error = 8.881784197001252e-16 relative error = 6.821665312442612e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000003 y[1] (closed_form) = 1.308955296717664 y[1] (numeric) = 1.308955296717665 absolute error = 8.881784197001252e-16 relative error = 6.785399179997371e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000003 y[1] (closed_form) = 1.315921524431581 y[1] (numeric) = 1.315921524431581 absolute error = 8.881784197001252e-16 relative error = 6.749478621711722e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000003 y[1] (closed_form) = 1.322895135553353 y[1] (numeric) = 1.322895135553354 absolute error = 8.881784197001252e-16 relative error = 6.713898901205117e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000003 y[1] (closed_form) = 1.3298761067053 y[1] (numeric) = 1.329876106705301 absolute error = 1.110223024625157e-15 relative error = 8.348319208288335e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000003 y[1] (closed_form) = 1.336864414681727 y[1] (numeric) = 1.336864414681727 absolute error = 8.881784197001252e-16 relative error = 6.643743448819212e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000003 y[1] (closed_form) = 1.343860036446944 y[1] (numeric) = 1.343860036446945 absolute error = 1.110223024625157e-15 relative error = 8.261448324339604e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 1.350862949133322 y[1] (numeric) = 1.350862949133323 absolute error = 1.332267629550188e-15 relative error = 9.8623448840975e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 1.357873130039369 y[1] (numeric) = 1.35787313003937 absolute error = 8.881784197001252e-16 relative error = 6.540952906803409e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 1.364890556627842 y[1] (numeric) = 1.364890556627842 absolute error = 6.661338147750939e-16 relative error = 4.880492516710448e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 1.37191520652389 y[1] (numeric) = 1.371915206523891 absolute error = 8.881784197001252e-16 relative error = 6.474003753851232e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 1.378947057513221 y[1] (numeric) = 1.378947057513221 absolute error = 6.661338147750939e-16 relative error = 4.830742494033042e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000004 y[1] (closed_form) = 1.385986087540297 y[1] (numeric) = 1.385986087540297 absolute error = 2.220446049250313e-16 relative error = 1.602069507920479e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000004 y[1] (closed_form) = 1.393032274706562 y[1] (numeric) = 1.393032274706562 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000004 y[1] (closed_form) = 1.400085597268692 y[1] (numeric) = 1.400085597268692 absolute error = 2.220446049250313e-16 relative error = 1.585935926761901e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000004 y[1] (closed_form) = 1.40714603363687 y[1] (numeric) = 1.407146033636871 absolute error = 2.220446049250313e-16 relative error = 1.57797840179488e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 Finished! diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 500 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %