##############ECHO OF PROBLEM################# ##############temp/mtest7postode.ode################# diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 4 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=64; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(0.7); array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); array_y2_init[3 + 1] = exact_soln_y2ppp(x_start); array_y2_init[4 + 1] = exact_soln_y2pppp(x_start); glob_look_poles=true; glob_max_h=c(0.1); glob_type_given_pole=3; /* 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_y1 (double x) { return( cos(c(x)) ); } double exact_soln_y2 (double x) { return( sin(c(x)) + c(10.0) * c(x) + c(10.0)); } double exact_soln_y2p (double x) { return( cos(c(x)) + c(10.0)); } double exact_soln_y2pp (double x) { return( neg(sin(c(x)))); } double exact_soln_y2ppp (double x) { return( neg(cos(c(x)))); } double exact_soln_y2pppp (double x) { return( sin(c(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (closed_form) = 11.09983341664683 y2[1] (numeric) = 11.09983341664683 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9950041652780258 y1[1] (numeric) = 0.9950041652780258 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] = 0.11 y2[1] (closed_form) = 11.20977830083718 y2[1] (numeric) = 11.20977830083718 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9939560979566968 y1[1] (numeric) = 0.9939560979566969 absolute error = 1.110223024625157e-16 relative error = 1.116973905494893e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y2[1] (closed_form) = 11.31971220728892 y2[1] (numeric) = 11.31971220728892 absolute error = 1.77635683940025e-15 relative error = 1.569259718684747e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9928086358538663 y1[1] (numeric) = 0.9928086358538663 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] = 0.13 y2[1] (closed_form) = 11.4296341426197 y2[1] (numeric) = 11.42963414261969 absolute error = 1.77635683940025e-15 relative error = 1.554167716336987e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9915618937147881 y1[1] (numeric) = 0.9915618937147881 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] = 0.14 y2[1] (closed_form) = 11.53954311464424 y2[1] (numeric) = 11.53954311464424 absolute error = 1.77635683940025e-15 relative error = 1.539364965971632e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9902159962126371 y1[1] (numeric) = 0.9902159962126372 absolute error = 1.110223024625157e-16 relative error = 1.121192779021467e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y2[1] (closed_form) = 11.6494381324736 y2[1] (numeric) = 11.6494381324736 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9887710779360422 y1[1] (numeric) = 0.9887710779360421 absolute error = 1.110223024625157e-16 relative error = 1.122831208759294e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y2[1] (closed_form) = 11.75931820661425 y2[1] (numeric) = 11.75931820661425 absolute error = 1.77635683940025e-15 relative error = 1.510595094196112e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9872272833756269 y1[1] (numeric) = 0.9872272833756267 absolute error = 2.220446049250313e-16 relative error = 2.249174112832397e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y2[1] (closed_form) = 11.869182349067 y2[1] (numeric) = 11.869182349067 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9855847669095607 y1[1] (numeric) = 0.9855847669095603 absolute error = 3.33066907387547e-16 relative error = 3.379383677285567e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y2[1] (closed_form) = 11.97902957342582 y2[1] (numeric) = 11.97902957342582 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9838436927881214 y1[1] (numeric) = 0.9838436927881212 absolute error = 2.220446049250313e-16 relative error = 2.256909370387664e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y2[1] (closed_form) = 12.0888588949765 y2[1] (numeric) = 12.0888588949765 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9820042351172703 y1[1] (numeric) = 0.9820042351172701 absolute error = 2.220446049250313e-16 relative error = 2.261136937953377e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y2[1] (closed_form) = 12.19866933079506 y2[1] (numeric) = 12.19866933079506 absolute error = 1.77635683940025e-15 relative error = 1.456189024581482e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9800665778412416 y1[1] (numeric) = 0.9800665778412414 absolute error = 2.220446049250313e-16 relative error = 2.265607357146299e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y2[1] (closed_form) = 12.3084598998461 y2[1] (numeric) = 12.3084598998461 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9780309147241483 y1[1] (numeric) = 0.978030914724148 absolute error = 2.220446049250313e-16 relative error = 2.27032296814113e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y2[1] (closed_form) = 12.41822962308087 y2[1] (numeric) = 12.41822962308087 absolute error = 1.77635683940025e-15 relative error = 1.430442899927268e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9758974493306055 y1[1] (numeric) = 0.9758974493306055 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] = 0.2300000000000001 y2[1] (closed_form) = 12.52797752353519 y2[1] (numeric) = 12.52797752353519 absolute error = 1.77635683940025e-15 relative error = 1.417911898439447e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9736663950053748 y1[1] (numeric) = 0.9736663950053749 absolute error = 1.110223024625157e-16 relative error = 1.140249915494956e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y2[1] (closed_form) = 12.63770262642714 y2[1] (numeric) = 12.63770262642713 absolute error = 1.77635683940025e-15 relative error = 1.405601074744115e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9713379748520296 y1[1] (numeric) = 0.9713379748520296 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] = 0.2500000000000001 y2[1] (closed_form) = 12.74740395925452 y2[1] (numeric) = 12.74740395925452 absolute error = 1.77635683940025e-15 relative error = 1.39350478346662e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9689124217106447 y1[1] (numeric) = 0.9689124217106446 absolute error = 1.110223024625157e-16 relative error = 1.145844556998272e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y2[1] (closed_form) = 12.85708055189216 y2[1] (numeric) = 12.85708055189215 absolute error = 5.329070518200751e-15 relative error = 4.14485271107404e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9663899781345132 y1[1] (numeric) = 0.9663899781345132 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] = 0.2700000000000001 y2[1] (closed_form) = 12.96673143668883 y2[1] (numeric) = 12.96673143668883 absolute error = 1.77635683940025e-15 relative error = 1.369934164267583e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9637708963658905 y1[1] (numeric) = 0.9637708963658905 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] = 0.2800000000000001 y2[1] (closed_form) = 13.07635564856412 y2[1] (numeric) = 13.07635564856411 absolute error = 1.77635683940025e-15 relative error = 1.358449469516614e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9610554383107709 y1[1] (numeric) = 0.961055438310771 absolute error = 1.110223024625157e-16 relative error = 1.155212259738704e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y2[1] (closed_form) = 13.18595222510484 y2[1] (numeric) = 13.18595222510483 absolute error = 3.552713678800501e-15 relative error = 2.694317117300381e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9582438755126971 y1[1] (numeric) = 0.9582438755126974 absolute error = 3.33066907387547e-16 relative error = 3.475805229742204e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y2[1] (closed_form) = 13.29552020666134 y2[1] (numeric) = 13.29552020666134 absolute error = 5.329070518200751e-15 relative error = 4.008169996635989e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.955336489125606 y1[1] (numeric) = 0.9553364891256064 absolute error = 4.440892098500626e-16 relative error = 4.64851091636336e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y2[1] (closed_form) = 13.40505863644345 y2[1] (numeric) = 13.40505863644344 absolute error = 3.552713678800501e-15 relative error = 2.650278357710405e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9523335698857134 y1[1] (numeric) = 0.9523335698857137 absolute error = 3.33066907387547e-16 relative error = 3.49737652771725e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y2[1] (closed_form) = 13.51456656061612 y2[1] (numeric) = 13.51456656061612 absolute error = 3.552713678800501e-15 relative error = 2.628803271540907e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9492354180824408 y1[1] (numeric) = 0.9492354180824413 absolute error = 4.440892098500626e-16 relative error = 4.678388536609509e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y2[1] (closed_form) = 13.62404302839487 y2[1] (numeric) = 13.62404302839487 absolute error = 1.77635683940025e-15 relative error = 1.303839716079885e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9460423435283869 y1[1] (numeric) = 0.9460423435283875 absolute error = 5.551115123125783e-16 relative error = 5.86772374524187e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y2[1] (closed_form) = 13.73348709214082 y2[1] (numeric) = 13.73348709214081 absolute error = 1.77635683940025e-15 relative error = 1.293449236513861e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9427546655283462 y1[1] (numeric) = 0.9427546655283467 absolute error = 5.551115123125783e-16 relative error = 5.888186318351214e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y2[1] (closed_form) = 13.84289780745545 y2[1] (numeric) = 13.84289780745545 absolute error = 1.77635683940025e-15 relative error = 1.283226145354874e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9393727128473789 y1[1] (numeric) = 0.9393727128473793 absolute error = 4.440892098500626e-16 relative error = 4.727508088924171e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y2[1] (closed_form) = 13.95227423327509 y2[1] (numeric) = 13.95227423327509 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9358968236779348 y1[1] (numeric) = 0.9358968236779351 absolute error = 3.33066907387547e-16 relative error = 3.558799420631045e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y2[1] (closed_form) = 14.06161543196496 y2[1] (numeric) = 14.06161543196496 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9323273456060344 y1[1] (numeric) = 0.9323273456060348 absolute error = 4.440892098500626e-16 relative error = 4.763232698719078e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y2[1] (closed_form) = 14.17092046941299 y2[1] (numeric) = 14.17092046941299 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9286646355765101 y1[1] (numeric) = 0.9286646355765106 absolute error = 4.440892098500626e-16 relative error = 4.782019179338884e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y2[1] (closed_form) = 14.28018841512316 y2[1] (numeric) = 14.28018841512316 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.924909059857313 y1[1] (numeric) = 0.9249090598573132 absolute error = 2.220446049250313e-16 relative error = 2.400718238821084e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y2[1] (closed_form) = 14.38941834230865 y2[1] (numeric) = 14.38941834230865 absolute error = 1.77635683940025e-15 relative error = 1.234488286560755e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.921060994002885 y1[1] (numeric) = 0.9210609940028852 absolute error = 2.220446049250313e-16 relative error = 2.410748108657132e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y2[1] (closed_form) = 14.49860932798443 y2[1] (numeric) = 14.49860932798442 absolute error = 3.552713678800501e-15 relative error = 2.450382376979595e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.917120822816605 y1[1] (numeric) = 0.9171208228166053 absolute error = 3.33066907387547e-16 relative error = 3.631657891755771e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y2[1] (closed_form) = 14.60776045305957 y2[1] (numeric) = 14.60776045305957 absolute error = 5.329070518200751e-15 relative error = 3.648109191908734e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9130889403123081 y1[1] (numeric) = 0.9130889403123086 absolute error = 4.440892098500626e-16 relative error = 4.863592036260659e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y2[1] (closed_form) = 14.71687080242921 y2[1] (numeric) = 14.71687080242921 absolute error = 5.329070518200751e-15 relative error = 3.621062241927896e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.908965749674885 y1[1] (numeric) = 0.9089657496748855 absolute error = 5.551115123125783e-16 relative error = 6.107067428130578e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y2[1] (closed_form) = 14.825939465066 y2[1] (numeric) = 14.825939465066 absolute error = 5.329070518200751e-15 relative error = 3.594423497247853e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9047516632199633 y1[1] (numeric) = 0.9047516632199637 absolute error = 4.440892098500626e-16 relative error = 4.908409985891296e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y2[1] (closed_form) = 14.93496553411123 y2[1] (numeric) = 14.93496553411123 absolute error = 5.329070518200751e-15 relative error = 3.568184008211626e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9004471023526768 y1[1] (numeric) = 0.9004471023526771 absolute error = 3.33066907387547e-16 relative error = 3.698905871508875e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y2[1] (closed_form) = 15.04394810696552 y2[1] (numeric) = 15.04394810696552 absolute error = 7.105427357601002e-15 relative error = 4.723113445406732e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8960524975255251 y1[1] (numeric) = 0.8960524975255255 absolute error = 4.440892098500626e-16 relative error = 4.956062407910562e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y2[1] (closed_form) = 15.15288628537907 y2[1] (numeric) = 15.15288628537906 absolute error = 7.105427357601002e-15 relative error = 4.689157711463185e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8915682881953289 y1[1] (numeric) = 0.8915682881953292 absolute error = 3.33066907387547e-16 relative error = 3.735741970609178e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y2[1] (closed_form) = 15.26177917554149 y2[1] (numeric) = 15.26177917554148 absolute error = 1.243449787580175e-14 relative error = 8.147475948105229e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.886994922779284 y1[1] (numeric) = 0.8869949227792844 absolute error = 3.33066907387547e-16 relative error = 3.755003538734188e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y2[1] (closed_form) = 15.37062588817116 y2[1] (numeric) = 15.37062588817115 absolute error = 1.06581410364015e-14 relative error = 6.934096967777828e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8823328586101213 y1[1] (numeric) = 0.8823328586101219 absolute error = 5.551115123125783e-16 relative error = 6.2914070001542e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y2[1] (closed_form) = 15.47942553860421 y2[1] (numeric) = 15.4794255386042 absolute error = 8.881784197001252e-15 relative error = 5.737799619792693e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8775825618903725 y1[1] (numeric) = 0.8775825618903731 absolute error = 5.551115123125783e-16 relative error = 6.325461972681297e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y2[1] (closed_form) = 15.58817724688291 y2[1] (numeric) = 15.5881772468829 absolute error = 7.105427357601002e-15 relative error = 4.558215656049098e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8727445076457511 y1[1] (numeric) = 0.8727445076457516 absolute error = 5.551115123125783e-16 relative error = 6.360527135369831e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y2[1] (closed_form) = 15.69688013784374 y2[1] (numeric) = 15.69688013784373 absolute error = 7.105427357601002e-15 relative error = 4.526649433010873e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8678191796776498 y1[1] (numeric) = 0.8678191796776501 absolute error = 3.33066907387547e-16 relative error = 3.837975873168236e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y2[1] (closed_form) = 15.80553334120485 y2[1] (numeric) = 15.80553334120485 absolute error = 3.552713678800501e-15 relative error = 2.247765767915352e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8628070705147608 y1[1] (numeric) = 0.8628070705147614 absolute error = 5.551115123125783e-16 relative error = 6.433784924611156e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y2[1] (closed_form) = 15.91413599165312 y2[1] (numeric) = 15.91413599165312 absolute error = 1.77635683940025e-15 relative error = 1.116213183255403e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8577086813638239 y1[1] (numeric) = 0.8577086813638244 absolute error = 4.440892098500626e-16 relative error = 5.177622886408542e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y2[1] (closed_form) = 16.02268722893066 y2[1] (numeric) = 16.02268722893066 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8525245220595056 y1[1] (numeric) = 0.852524522059506 absolute error = 4.440892098500626e-16 relative error = 5.209107754193908e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y2[1] (closed_form) = 16.13118619792089 y2[1] (numeric) = 16.13118619792089 absolute error = 3.552713678800501e-15 relative error = 2.202388364507504e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8472551110134159 y1[1] (numeric) = 0.8472551110134163 absolute error = 4.440892098500626e-16 relative error = 5.24150523351674e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y2[1] (closed_form) = 16.23963204873397 y2[1] (numeric) = 16.23963204873397 absolute error = 3.552713678800501e-15 relative error = 2.187681142121362e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8419009751622685 y1[1] (numeric) = 0.841900975162269 absolute error = 5.551115123125783e-16 relative error = 6.593548750856189e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y2[1] (closed_form) = 16.34802393679188 y2[1] (numeric) = 16.34802393679188 absolute error = 3.552713678800501e-15 relative error = 2.173176215386483e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8364626499151867 y1[1] (numeric) = 0.8364626499151873 absolute error = 5.551115123125783e-16 relative error = 6.636417207258015e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y2[1] (closed_form) = 16.45636102291279 y2[1] (numeric) = 16.45636102291278 absolute error = 3.552713678800501e-15 relative error = 2.158869554364983e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8309406791001632 y1[1] (numeric) = 0.8309406791001639 absolute error = 6.661338147750939e-16 relative error = 8.016622985607819e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y2[1] (closed_form) = 16.56464247339504 y2[1] (numeric) = 16.56464247339504 absolute error = 3.552713678800501e-15 relative error = 2.144757234879424e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8253356149096781 y1[1] (numeric) = 0.8253356149096787 absolute error = 5.551115123125783e-16 relative error = 6.725888260296725e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y2[1] (closed_form) = 16.67286746010048 y2[1] (numeric) = 16.67286746010048 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8196480178454792 y1[1] (numeric) = 0.8196480178454798 absolute error = 5.551115123125783e-16 relative error = 6.772559686921958e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y2[1] (closed_form) = 16.78103516053731 y2[1] (numeric) = 16.78103516053731 absolute error = 3.552713678800501e-15 relative error = 2.117100432013365e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8138784566625337 y1[1] (numeric) = 0.8138784566625342 absolute error = 5.551115123125783e-16 relative error = 6.820570169517947e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y2[1] (closed_form) = 16.88914475794228 y2[1] (numeric) = 16.88914475794227 absolute error = 1.06581410364015e-14 relative error = 6.310645795956846e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8080275083121516 y1[1] (numeric) = 0.8080275083121521 absolute error = 4.440892098500626e-16 relative error = 5.495966477399989e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y2[1] (closed_form) = 16.9971954413624 y2[1] (numeric) = 16.99719544136238 absolute error = 1.4210854715202e-14 relative error = 8.360705602419633e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8020957578842923 y1[1] (numeric) = 0.8020957578842927 absolute error = 3.33066907387547e-16 relative error = 4.152458158687757e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y2[1] (closed_form) = 17.10518640573605 y2[1] (numeric) = 17.10518640573603 absolute error = 1.77635683940025e-14 relative error = 1.038490196636833e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7960837985490555 y1[1] (numeric) = 0.7960837985490558 absolute error = 2.220446049250313e-16 relative error = 2.789211453991783e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y2[1] (closed_form) = 17.21311685197344 y2[1] (numeric) = 17.21311685197342 absolute error = 1.77635683940025e-14 relative error = 1.031978609496627e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7899922314973647 y1[1] (numeric) = 0.7899922314973651 absolute error = 3.33066907387547e-16 relative error = 4.216078261380448e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y2[1] (closed_form) = 17.32098598703656 y2[1] (numeric) = 17.32098598703655 absolute error = 1.77635683940025e-14 relative error = 1.025551802148976e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.783821665880849 y1[1] (numeric) = 0.7838216658808493 absolute error = 3.33066907387547e-16 relative error = 4.249268958561518e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y2[1] (closed_form) = 17.42879302401847 y2[1] (numeric) = 17.42879302401846 absolute error = 1.77635683940025e-14 relative error = 1.019208178645686e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7775727187509276 y1[1] (numeric) = 0.777572718750928 absolute error = 4.440892098500626e-16 relative error = 5.711224161303343e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y2[1] (closed_form) = 17.53653718222197 y2[1] (numeric) = 17.53653718222195 absolute error = 2.131628207280301e-14 relative error = 1.215535419068528e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7712460149971063 y1[1] (numeric) = 0.7712460149971067 absolute error = 3.33066907387547e-16 relative error = 4.318555958941281e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 Finished! diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 4 ) ) ; Iterations = 600 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 %