##############ECHO OF PROBLEM################# ##############temp/arctan_tan_m0d5_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(-0.5); 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] = -0.5 y[1] (closed_form) = 0.125 y[1] (numeric) = 0.125 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] = -0.49 y[1] (closed_form) = 0.12005 y[1] (numeric) = 0.1200499981992345 absolute error = 1.800765467296905e-09 relative error = 1.500012884045736e-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] = -0.48 y[1] (closed_form) = 0.1152 y[1] (numeric) = 0.11519999644131 absolute error = 3.558689981586483e-09 relative error = 3.089140609016044e-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] = -0.47 y[1] (closed_form) = 0.11045 y[1] (numeric) = 0.1104499947257767 absolute error = 5.274223252582644e-09 relative error = 4.775213447336029e-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] = -0.46 y[1] (closed_form) = 0.1058 y[1] (numeric) = 0.1057999930522003 absolute error = 6.947799682799349e-09 relative error = 6.566918414744188e-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] = -0.45 y[1] (closed_form) = 0.10125 y[1] (numeric) = 0.1012499914201613 absolute error = 8.579838658984151e-09 relative error = 8.47391472492262e-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] = -0.4399999999999999 y[1] (closed_form) = 0.09679999999999998 y[1] (numeric) = 0.09679998982925479 absolute error = 1.017074519049643e-08 relative error = 1.050696817200045e-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] = -0.4299999999999999 y[1] (closed_form) = 0.09244999999999998 y[1] (numeric) = 0.09244998827908972 absolute error = 1.17209102562521e-08 relative error = 1.267810736208989e-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] = -0.4199999999999999 y[1] (closed_form) = 0.08819999999999997 y[1] (numeric) = 0.08819998676928871 absolute error = 1.32307112626906e-08 relative error = 1.500080642028413e-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] = -0.4099999999999999 y[1] (closed_form) = 0.08404999999999997 y[1] (numeric) = 0.08404998529948755 absolute error = 1.470051241847514e-08 relative error = 1.749019918914354e-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] = -0.3999999999999999 y[1] (closed_form) = 0.07999999999999996 y[1] (numeric) = 0.07999998386933478 absolute error = 1.613066517858197e-08 relative error = 2.016333147322747e-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] = -0.3899999999999999 y[1] (closed_form) = 0.07604999999999996 y[1] (numeric) = 0.07604998247849148 absolute error = 1.752150848022271e-08 relative error = 2.303945888260713e-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] = -0.3799999999999999 y[1] (closed_form) = 0.07219999999999996 y[1] (numeric) = 0.07219998112663076 absolute error = 1.88733692008114e-08 relative error = 2.614040055514045e-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] = -0.3699999999999999 y[1] (closed_form) = 0.06844999999999996 y[1] (numeric) = 0.06844997981343742 absolute error = 2.018656253266471e-08 relative error = 2.94909606028703e-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] = -0.3599999999999999 y[1] (closed_form) = 0.06479999999999995 y[1] (numeric) = 0.06479997853860786 absolute error = 2.146139209402431e-08 relative error = 3.31194322438647e-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] = -0.3499999999999999 y[1] (closed_form) = 0.06124999999999995 y[1] (numeric) = 0.0612499773018495 absolute error = 2.269815044947388e-08 relative error = 3.705820481546758e-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] = -0.3399999999999999 y[1] (closed_form) = 0.05779999999999995 y[1] (numeric) = 0.05779997610288067 absolute error = 2.389711927647253e-08 relative error = 4.134449701811861e-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] = -0.3299999999999998 y[1] (closed_form) = 0.05444999999999995 y[1] (numeric) = 0.05444997494143033 absolute error = 2.505856961515507e-08 relative error = 4.602124814537207e-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] = -0.3199999999999998 y[1] (closed_form) = 0.05119999999999995 y[1] (numeric) = 0.05119997381723773 absolute error = 2.61827622152766e-08 relative error = 5.113820745171216e-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] = -0.3099999999999998 y[1] (closed_form) = 0.04804999999999995 y[1] (numeric) = 0.04804997273005217 absolute error = 2.726994777213498e-08 relative error = 5.675327319903229e-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] = -0.2999999999999998 y[1] (closed_form) = 0.04499999999999995 y[1] (numeric) = 0.04499997167963286 absolute error = 2.832036708616537e-08 relative error = 6.293414908036755e-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] = -0.2899999999999998 y[1] (closed_form) = 0.04204999999999995 y[1] (numeric) = 0.04204997066574861 absolute error = 2.933425133355705e-08 relative error = 6.97604074519788e-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] = -0.2799999999999998 y[1] (closed_form) = 0.03919999999999994 y[1] (numeric) = 0.03919996968817765 absolute error = 3.03118222882981e-08 relative error = 7.732607726606668e-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] = -0.2699999999999998 y[1] (closed_form) = 0.03644999999999995 y[1] (numeric) = 0.03644996874670742 absolute error = 3.125329252340325e-08 relative error = 8.574291501619561e-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] = -0.2599999999999998 y[1] (closed_form) = 0.03379999999999994 y[1] (numeric) = 0.03379996784113438 absolute error = 3.215886556356962e-08 relative error = 9.514457267328306e-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] = -0.2499999999999998 y[1] (closed_form) = 0.03124999999999994 y[1] (numeric) = 0.03124996697126381 absolute error = 3.302873613844626e-08 relative error = 0.0001056919556430282 % 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] = -0.2399999999999998 y[1] (closed_form) = 0.02879999999999994 y[1] (numeric) = 0.02879996613690968 absolute error = 3.386309026243151e-08 relative error = 0.0001175801745223318 % 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] = -0.2299999999999998 y[1] (closed_form) = 0.02644999999999995 y[1] (numeric) = 0.02644996533789445 absolute error = 3.466210549488147e-08 relative error = 0.0001310476578256391 % 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] = -0.2199999999999998 y[1] (closed_form) = 0.02419999999999994 y[1] (numeric) = 0.02419996457404892 absolute error = 3.542595101990731e-08 relative error = 0.0001463882273549892 % 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] = -0.2099999999999997 y[1] (closed_form) = 0.02204999999999994 y[1] (numeric) = 0.02204996384521209 absolute error = 3.615478785107262e-08 relative error = 0.0001639672918415996 % 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] = -0.1999999999999997 y[1] (closed_form) = 0.01999999999999995 y[1] (numeric) = 0.01999996315123101 absolute error = 3.684876893547684e-08 relative error = 0.0001842438446773847 % 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] = -0.1899999999999997 y[1] (closed_form) = 0.01804999999999995 y[1] (numeric) = 0.01804996249196068 absolute error = 3.750803926477753e-08 relative error = 0.0002078007715500146 % 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] = -0.1799999999999997 y[1] (closed_form) = 0.01619999999999995 y[1] (numeric) = 0.01619996186726388 absolute error = 3.813273606600998e-08 relative error = 0.000235387259666729 % 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] = -0.1699999999999997 y[1] (closed_form) = 0.01444999999999995 y[1] (numeric) = 0.0144499612770111 absolute error = 3.87229888536289e-08 relative error = 0.0002679791616168099 % 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] = -0.1599999999999997 y[1] (closed_form) = 0.01279999999999995 y[1] (numeric) = 0.01279996072108037 absolute error = 3.927891958389884e-08 relative error = 0.0003068665592492108 % Desired digits = 8 Estimated correct digits = 11 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] = -0.1499999999999997 y[1] (closed_form) = 0.01124999999999995 y[1] (numeric) = 0.01124996019935723 absolute error = 3.980064272081363e-08 relative error = 0.0003537834908516782 % Desired digits = 8 Estimated correct digits = 11 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] = -0.1399999999999997 y[1] (closed_form) = 0.009799999999999955 y[1] (numeric) = 0.009799959711734597 absolute error = 4.028826535752705e-08 relative error = 0.0004111047485461963 % Desired digits = 8 Estimated correct digits = 11 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] = -0.1299999999999997 y[1] (closed_form) = 0.008449999999999958 y[1] (numeric) = 0.008449959258112667 absolute error = 4.074188729094597e-08 relative error = 0.0004821525123188896 % Desired digits = 8 Estimated correct digits = 11 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] = -0.1199999999999997 y[1] (closed_form) = 0.00719999999999996 y[1] (numeric) = 0.007199958838398851 absolute error = 4.116160110933381e-08 relative error = 0.0005716889042963061 % Desired digits = 8 Estimated correct digits = 11 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] = -0.1099999999999997 y[1] (closed_form) = 0.006049999999999962 y[1] (numeric) = 0.006049958452507693 absolute error = 4.154749226863846e-08 relative error = 0.0006867354093989872 % Desired digits = 8 Estimated correct digits = 11 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] = -0.09999999999999964 y[1] (closed_form) = 0.004999999999999965 y[1] (numeric) = 0.004999958100360802 absolute error = 4.189963916274853e-08 relative error = 0.0008379927832549765 % Desired digits = 8 Estimated correct digits = 11 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] = -0.08999999999999964 y[1] (closed_form) = 0.004049999999999967 y[1] (numeric) = 0.00404995778188678 absolute error = 4.221811318681074e-08 relative error = 0.001042422547822496 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 5 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] = -0.07999999999999963 y[1] (closed_form) = 0.00319999999999997 y[1] (numeric) = 0.003199957497021174 absolute error = 4.250297879577689e-08 relative error = 0.00132821808736804 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 5 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] = -0.06999999999999962 y[1] (closed_form) = 0.002449999999999973 y[1] (numeric) = 0.002449957245706421 absolute error = 4.275429355210872e-08 relative error = 0.001745073206208538 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 5 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] = -0.05999999999999961 y[1] (closed_form) = 0.001799999999999977 y[1] (numeric) = 0.001799957027891798 absolute error = 4.297210817803647e-08 relative error = 0.002387339343224279 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 5 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] = -0.0499999999999996 y[1] (closed_form) = 0.00124999999999998 y[1] (numeric) = 0.001249956843533384 absolute error = 4.315646659654171e-08 relative error = 0.003452517327723392 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 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] = -0.03999999999999959 y[1] (closed_form) = 0.0007999999999999837 y[1] (numeric) = 0.0007999566925940198 absolute error = 4.330740596388341e-08 relative error = 0.005413425745485537 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 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] = -0.02999999999999958 y[1] (closed_form) = 0.0004499999999999875 y[1] (numeric) = 0.0004499565750432876 absolute error = 4.34249566999014e-08 relative error = 0.009649990377756134 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 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] = -0.01999999999999957 y[1] (closed_form) = 0.0001999999999999915 y[1] (numeric) = 0.0001999564908574779 absolute error = 4.350914251357641e-08 relative error = 0.02175457125678914 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 4 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] = -0.009999999999999565 y[1] (closed_form) = 4.999999999999565e-05 y[1] (numeric) = 4.995644001957427e-05 absolute error = 4.355998042137346e-08 relative error = 0.08711996084275452 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 4 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] = 4.371503159461554e-16 y[1] (closed_form) = 9.555019936591174e-32 y[1] (numeric) = -4.357748076092478e-08 absolute error = 4.357748076092478e-08 relative error = -1 % Desired digits = 8 Estimated correct digits = 6 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] = 0.01000000000000044 y[1] (closed_form) = 5.000000000000439e-05 y[1] (numeric) = 4.995643835280501e-05 absolute error = 4.356164719938329e-08 relative error = 0.08712329439875892 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 4 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] = 0.02000000000000045 y[1] (closed_form) = 0.000200000000000009 y[1] (numeric) = 0.0001999564875232725 absolute error = 4.351247673644817e-08 relative error = 0.02175623836822311 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 4 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] = 0.03000000000000046 y[1] (closed_form) = 0.0004500000000000137 y[1] (numeric) = 0.0004499565700403119 absolute error = 4.342995970176618e-08 relative error = 0.009651102155947748 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 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] = 0.04000000000000047 y[1] (closed_form) = 0.0008000000000000186 y[1] (numeric) = 0.0007999566859202713 absolute error = 4.331407974726264e-08 relative error = 0.005414259968407704 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 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] = 0.05000000000000047 y[1] (closed_form) = 0.001250000000000024 y[1] (numeric) = 0.00124995683518619 absolute error = 4.316481383393952e-08 relative error = 0.003453185106715097 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 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] = 0.06000000000000048 y[1] (closed_form) = 0.001800000000000029 y[1] (numeric) = 0.001799957017867815 absolute error = 4.298213221410815e-08 relative error = 0.002387896234117081 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 5 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] = 0.07000000000000049 y[1] (closed_form) = 0.002450000000000035 y[1] (numeric) = 0.002449957234001628 absolute error = 4.276599840707593e-08 relative error = 0.00174555095539083 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 5 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] = 0.0800000000000005 y[1] (closed_form) = 0.00320000000000004 y[1] (numeric) = 0.003199957483630873 absolute error = 4.251636916705395e-08 relative error = 0.001328636536470419 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 5 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] = 0.09000000000000051 y[1] (closed_form) = 0.004050000000000046 y[1] (numeric) = 0.004049957766805591 absolute error = 4.223319445464252e-08 relative error = 0.001042794924805976 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 5 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] = 0.1000000000000005 y[1] (closed_form) = 0.005000000000000052 y[1] (numeric) = 0.00499995808358266 absolute error = 4.19164173917283e-08 relative error = 0.0008383283478345572 % Desired digits = 8 Estimated correct digits = 11 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] = 0.1100000000000005 y[1] (closed_form) = 0.006050000000000058 y[1] (numeric) = 0.006049958434025843 absolute error = 4.156597421464681e-08 relative error = 0.000687040896109858 % Desired digits = 8 Estimated correct digits = 11 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] = 0.1200000000000005 y[1] (closed_form) = 0.007200000000000064 y[1] (numeric) = 0.007199958818205839 absolute error = 4.118179422474277e-08 relative error = 0.0005719693642325334 % Desired digits = 8 Estimated correct digits = 11 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] = 0.1300000000000005 y[1] (closed_form) = 0.008450000000000069 y[1] (numeric) = 0.008449959236200339 absolute error = 4.076379972982325e-08 relative error = 0.0004824118311221647 % Desired digits = 8 Estimated correct digits = 11 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] = 0.1400000000000005 y[1] (closed_form) = 0.009800000000000076 y[1] (numeric) = 0.009799959688094086 absolute error = 4.031190599038115e-08 relative error = 0.000411345979493682 % Desired digits = 8 Estimated correct digits = 11 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] = 0.1500000000000005 y[1] (closed_form) = 0.01125000000000008 y[1] (numeric) = 0.01124996017397895 absolute error = 3.982602113025702e-08 relative error = 0.0003540090767133931 % Desired digits = 8 Estimated correct digits = 11 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] = 0.1600000000000006 y[1] (closed_form) = 0.01280000000000009 y[1] (numeric) = 0.01279996069395402 absolute error = 3.930604607245425e-08 relative error = 0.0003070784849410467 % Desired digits = 8 Estimated correct digits = 11 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] = 0.1700000000000006 y[1] (closed_form) = 0.0144500000000001 y[1] (numeric) = 0.01444996124812563 absolute error = 3.87518744662807e-08 relative error = 0.0002681790620503837 % Desired digits = 8 Estimated correct digits = 11 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] = 0.1800000000000006 y[1] (closed_form) = 0.0162000000000001 y[1] (numeric) = 0.01619996183660753 absolute error = 3.816339257459167e-08 relative error = 0.0002355764973740212 % Desired digits = 8 Estimated correct digits = 11 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] = 0.1900000000000006 y[1] (closed_form) = 0.01805000000000011 y[1] (numeric) = 0.01804996245952089 absolute error = 3.754047921827874e-08 relative error = 0.0002079804942840915 % Desired digits = 8 Estimated correct digits = 11 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] = 0.2000000000000006 y[1] (closed_form) = 0.02000000000000012 y[1] (numeric) = 0.0199999631169945 absolute error = 3.688300562187941e-08 relative error = 0.0001844150281093959 % 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] = 0.2100000000000006 y[1] (closed_form) = 0.02205000000000013 y[1] (numeric) = 0.02204996380916477 absolute error = 3.619083535286172e-08 relative error = 0.0001641307725753356 % 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] = 0.2200000000000006 y[1] (closed_form) = 0.02420000000000013 y[1] (numeric) = 0.02419996453617596 absolute error = 3.546382417937699e-08 relative error = 0.0001465447280139537 % 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] = 0.2300000000000006 y[1] (closed_form) = 0.02645000000000014 y[1] (numeric) = 0.02644996529818019 absolute error = 3.470181995576804e-08 relative error = 0.0001311978070161356 % 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] = 0.2400000000000006 y[1] (closed_form) = 0.02880000000000015 y[1] (numeric) = 0.02879996609533765 absolute error = 3.3904662504608e-08 relative error = 0.0001177245225854438 % 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] = 0.2500000000000006 y[1] (closed_form) = 0.03125000000000015 y[1] (numeric) = 0.03124996692781672 absolute error = 3.307218342935014e-08 relative error = 0.0001058309869739199 % 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] = 0.2600000000000006 y[1] (closed_form) = 0.03380000000000016 y[1] (numeric) = 0.03379996779579409 absolute error = 3.220420607269459e-08 relative error = 9.527871619140365e-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] = 0.2700000000000006 y[1] (closed_form) = 0.03645000000000017 y[1] (numeric) = 0.03644996869945494 absolute error = 3.130054522515469e-08 relative error = 8.587255205803715e-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] = 0.2800000000000006 y[1] (closed_form) = 0.03920000000000018 y[1] (numeric) = 0.03919996963899312 absolute error = 3.036100706260703e-08 relative error = 7.74515486290992e-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] = 0.2900000000000006 y[1] (closed_form) = 0.04205000000000018 y[1] (numeric) = 0.04204997061461126 absolute error = 2.938538892771625e-08 relative error = 6.988201885307044e-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] = 0.3000000000000007 y[1] (closed_form) = 0.0450000000000002 y[1] (numeric) = 0.04499997162652104 absolute error = 2.83734791634016e-08 relative error = 6.305217591866995e-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] = 0.3100000000000007 y[1] (closed_form) = 0.0480500000000002 y[1] (numeric) = 0.04804997267494328 absolute error = 2.732505692548681e-08 relative error = 5.686796446511279e-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] = 0.3200000000000007 y[1] (closed_form) = 0.05120000000000022 y[1] (numeric) = 0.05119997376010821 absolute error = 2.623989200922772e-08 relative error = 5.124978908052267e-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] = 0.3300000000000007 y[1] (closed_form) = 0.05445000000000023 y[1] (numeric) = 0.05444997488225569 absolute error = 2.511774453706206e-08 relative error = 4.612992568790074e-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] = 0.3400000000000007 y[1] (closed_form) = 0.05780000000000023 y[1] (numeric) = 0.05779997604163537 absolute error = 2.395836486146496e-08 relative error = 4.145045823782849e-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] = 0.3500000000000007 y[1] (closed_form) = 0.06125000000000024 y[1] (numeric) = 0.061249977238507 absolute error = 2.276149324575982e-08 relative error = 3.716162162573018e-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] = 0.3600000000000007 y[1] (closed_form) = 0.06480000000000026 y[1] (numeric) = 0.06479997847314056 absolute error = 2.152685969758483e-08 relative error = 3.322046249627276e-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] = 0.3700000000000007 y[1] (closed_form) = 0.06845000000000026 y[1] (numeric) = 0.06844997974581672 absolute error = 2.025418353868158e-08 relative error = 2.958974950866545e-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] = 0.3800000000000007 y[1] (closed_form) = 0.07220000000000028 y[1] (numeric) = 0.07219998105682686 absolute error = 1.894317341877283e-08 relative error = 2.623708229746919e-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] = 0.3900000000000007 y[1] (closed_form) = 0.07605000000000028 y[1] (numeric) = 0.07604998240647357 absolute error = 1.759352671881764e-08 relative error = 2.31341574211934e-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] = 0.4000000000000007 y[1] (closed_form) = 0.08000000000000029 y[1] (numeric) = 0.07999998379507076 absolute error = 1.620492953713359e-08 relative error = 2.025616192141692e-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] = 0.4100000000000008 y[1] (closed_form) = 0.08405000000000031 y[1] (numeric) = 0.08404998522294416 absolute error = 1.477705614816305e-08 relative error = 1.758126846896251e-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] = 0.4200000000000008 y[1] (closed_form) = 0.08820000000000032 y[1] (numeric) = 0.08819998669043155 absolute error = 1.330956876655076e-08 relative error = 1.509021402103255e-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] = 0.4300000000000008 y[1] (closed_form) = 0.09245000000000034 y[1] (numeric) = 0.09244998819788307 absolute error = 1.180211726958813e-08 relative error = 1.276594620831594e-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] = 0.4400000000000008 y[1] (closed_form) = 0.09680000000000034 y[1] (numeric) = 0.09679998974566163 absolute error = 1.025433871149062e-08 relative error = 1.059332511517622e-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] = 0.4500000000000008 y[1] (closed_form) = 0.1012500000000004 y[1] (numeric) = 0.1012499913341433 absolute error = 8.665857004208632e-09 relative error = 8.558871115267755e-06 % Desired digits = 8 Estimated correct digits = 12 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] = 0.4600000000000008 y[1] (closed_form) = 0.1058000000000004 y[1] (numeric) = 0.1057999929637178 absolute error = 7.03628258436062e-09 relative error = 6.650550646843664e-06 % Desired digits = 8 Estimated correct digits = 12 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] = 0.4700000000000008 y[1] (closed_form) = 0.1104500000000004 y[1] (numeric) = 0.1104499946347885 absolute error = 5.36521188587713e-09 relative error = 4.857593377887834e-06 % Desired digits = 8 Estimated correct digits = 12 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] = 0.4800000000000008 y[1] (closed_form) = 0.1152000000000004 y[1] (numeric) = 0.1151999963477735 absolute error = 3.652226882033816e-09 relative error = 3.170335835098788e-06 % Desired digits = 8 Estimated correct digits = 12 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] = 0.4900000000000008 y[1] (closed_form) = 0.1200500000000004 y[1] (numeric) = 0.1200499981031056 absolute error = 1.896894807895677e-09 relative error = 1.580087303536585e-06 % Desired digits = 8 Estimated correct digits = 12 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 Finished! diff ( y , x , 1 ) = arctan ( tan ( x ) ) ; Iterations = 1000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %