##############ECHO OF PROBLEM################# ##############temp/expt_c_sin_newpostode.ode################# diff ( y , x , 1 ) = expt ( 2.0 , sin ( x ) ) * cos ( x ) * ln ( 2.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=1.4; x_end=1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(expt(2.0,sin(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.3999999999999999 estimated_steps = 399999.9999999999 step_error = 5.2704627669473e-15 est_needed_step_err = 5.2704627669473e-15 opt_iter = 1 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 min_size = 1.979930418515512 glob_desired_digits_correct = 10 estimated_h = -1e-06 estimated_answer = 1.979930418515512 desired_abs_gbl_error = 1.979930418515512e-10 range = -0.3999999999999999 estimated_steps = 399999.9999999999 step_error = 1.043514955193239e-14 est_needed_step_err = 1.043514955193239e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.305604892242639e-167 estimated_step_error = 1.305604892242639e-167 Double H and LOOP opt_iter = 2 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 min_size = 1.979930418515512 glob_desired_digits_correct = 10 estimated_h = -2e-06 estimated_answer = 1.979930418515512 desired_abs_gbl_error = 1.979930418515512e-10 range = -0.3999999999999999 estimated_steps = 200000 step_error = 1.475753002173431e-14 est_needed_step_err = 1.475753002173431e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.761763705560705e-160 estimated_step_error = 8.761763705560705e-160 Double H and LOOP opt_iter = 3 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 min_size = 1.979930418515512 glob_desired_digits_correct = 10 estimated_h = -4e-06 estimated_answer = 1.979930418515512 desired_abs_gbl_error = 1.979930418515512e-10 range = -0.3999999999999999 estimated_steps = 99999.99999999999 step_error = 2.087029910386477e-14 est_needed_step_err = 2.087029910386477e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.879916855103474e-152 estimated_step_error = 5.879916855103474e-152 Double H and LOOP opt_iter = 4 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 min_size = 1.979930418515512 glob_desired_digits_correct = 10 estimated_h = -8e-06 estimated_answer = 1.979930418515512 desired_abs_gbl_error = 1.979930418515512e-10 range = -0.3999999999999999 estimated_steps = 49999.99999999999 step_error = 2.951506004346862e-14 est_needed_step_err = 2.951506004346862e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.945941064917173e-144 estimated_step_error = 3.945941064917173e-144 Double H and LOOP opt_iter = 5 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 min_size = 1.979930418515512 glob_desired_digits_correct = 10 estimated_h = -1.6e-05 estimated_answer = 1.979930418515512 desired_abs_gbl_error = 1.979930418515512e-10 range = -0.3999999999999999 estimated_steps = 25000 step_error = 4.174059820772955e-14 est_needed_step_err = 4.174059820772955e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.648070396798384e-136 estimated_step_error = 2.648070396798384e-136 Double H and LOOP opt_iter = 6 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 min_size = 1.979930418515512 glob_desired_digits_correct = 10 estimated_h = -3.2e-05 estimated_answer = 1.979930418515512 desired_abs_gbl_error = 1.979930418515512e-10 range = -0.3999999999999999 estimated_steps = 12500 step_error = 5.903012008693724e-14 est_needed_step_err = 5.903012008693724e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.777082141703814e-128 estimated_step_error = 1.777082141703814e-128 Double H and LOOP opt_iter = 7 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 min_size = 1.979930418515512 glob_desired_digits_correct = 10 estimated_h = -6.4e-05 estimated_answer = 1.979930418515512 desired_abs_gbl_error = 1.979930418515512e-10 range = -0.3999999999999999 estimated_steps = 6249.999999999999 step_error = 8.34811964154591e-14 est_needed_step_err = 8.34811964154591e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.192569142441269e-120 estimated_step_error = 1.192569142441269e-120 Double H and LOOP opt_iter = 8 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 min_size = 1.979930418515512 glob_desired_digits_correct = 10 estimated_h = -0.000128 estimated_answer = 1.979930418515512 desired_abs_gbl_error = 1.979930418515512e-10 range = -0.3999999999999999 estimated_steps = 3125 step_error = 1.180602401738745e-13 est_needed_step_err = 1.180602401738745e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.003055173839079e-113 estimated_step_error = 8.003055173839079e-113 Double H and LOOP opt_iter = 9 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 min_size = 1.979930418515512 glob_desired_digits_correct = 10 estimated_h = -0.000256 estimated_answer = 1.979930418515512 desired_abs_gbl_error = 1.979930418515512e-10 range = -0.3999999999999999 estimated_steps = 1562.5 step_error = 1.669623928309182e-13 est_needed_step_err = 1.669623928309182e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.370570343663976e-105 estimated_step_error = 5.370570343663976e-105 Double H and LOOP opt_iter = 10 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 min_size = 1.979930418515512 glob_desired_digits_correct = 10 estimated_h = -0.000512 estimated_answer = 1.979930418515512 desired_abs_gbl_error = 1.979930418515512e-10 range = -0.3999999999999999 estimated_steps = 781.2499999999999 step_error = 2.361204803477489e-13 est_needed_step_err = 2.361204803477489e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.60387497691804e-97 estimated_step_error = 3.60387497691804e-97 Double H and LOOP opt_iter = 11 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 min_size = 1.979930418515512 glob_desired_digits_correct = 10 estimated_h = -0.001024 estimated_answer = 1.979930418515512 desired_abs_gbl_error = 1.979930418515512e-10 range = -0.3999999999999999 estimated_steps = 390.6249999999999 step_error = 3.339247856618364e-13 est_needed_step_err = 3.339247856618364e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.418178931955352e-89 estimated_step_error = 2.418178931955352e-89 Double H and LOOP opt_iter = 12 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 min_size = 1.979930418515512 glob_desired_digits_correct = 10 estimated_h = -0.002048 estimated_answer = 1.979930418515512 desired_abs_gbl_error = 1.979930418515512e-10 range = -0.3999999999999999 estimated_steps = 195.3125 step_error = 4.722409606954979e-13 est_needed_step_err = 4.722409606954979e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.622355179718919e-81 estimated_step_error = 1.622355179718919e-81 Double H and LOOP opt_iter = 13 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 min_size = 1.979930418515512 glob_desired_digits_correct = 10 estimated_h = -0.004096 estimated_answer = 1.979930418515512 desired_abs_gbl_error = 1.979930418515512e-10 range = -0.3999999999999999 estimated_steps = 97.65624999999999 step_error = 6.678495713236728e-13 est_needed_step_err = 6.678495713236728e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.08813030714462e-73 estimated_step_error = 1.08813030714462e-73 Double H and LOOP opt_iter = 14 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 min_size = 1.979930418515512 glob_desired_digits_correct = 10 estimated_h = -0.008192 estimated_answer = 1.979930418515512 desired_abs_gbl_error = 1.979930418515512e-10 range = -0.3999999999999999 estimated_steps = 48.82812499999999 step_error = 9.444819213909958e-13 est_needed_step_err = 9.444819213909958e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.294076552130112e-66 estimated_step_error = 7.294076552130112e-66 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL 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 START of Soultion TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 1.979930418515512 y[1] (numeric) = 1.979930418515512 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = -0.01 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] = 1.39 y[1] (analytic) = 1.977531690959575 y[1] (numeric) = 1.977530264427014 absolute error = 1.42653256074432e-06 relative error = 7.213702653999498e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = -0.01 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] = 1.38 y[1] (analytic) = 1.97500120069637 y[1] (numeric) = 1.974998182891798 absolute error = 3.01780457245826e-06 relative error = 0.0001528001386224072 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = -0.01 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] = 1.37 y[1] (analytic) = 1.972339713723575 y[1] (numeric) = 1.972334931587576 absolute error = 4.782135999636949e-06 relative error = 0.0002424600572793196 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = -0.01 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] = 1.36 y[1] (analytic) = 1.969548034167002 y[1] (numeric) = 1.969541306458994 absolute error = 6.727708007803201e-06 relative error = 0.0003415863889122465 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = -0.01 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] = 1.35 y[1] (analytic) = 1.966627003806209 y[1] (numeric) = 1.966618141249537 absolute error = 8.862556672539768e-06 relative error = 0.0004506475633349475 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = -0.01 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] = 1.34 y[1] (analytic) = 1.963577501579146 y[1] (numeric) = 1.963566307012301 absolute error = 1.119456684506304e-05 relative error = 0.0005701107715921655 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = -0.01 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] = 1.33 y[1] (analytic) = 1.960400443066292 y[1] (numeric) = 1.960386711600113 absolute error = 1.373146617855703e-05 relative error = 0.0007004419034449633 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = -0.01 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] = 1.32 y[1] (analytic) = 1.957096779954772 y[1] (numeric) = 1.957080299135451 absolute error = 1.648081932126289e-05 relative error = 0.0008421054845148613 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = -0.01 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] = 1.31 y[1] (analytic) = 1.953667499482965 y[1] (numeric) = 1.953648049460683 absolute error = 1.945002228231907e-05 relative error = 0.0009955646130913518 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = -0.01 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] = 1.3 y[1] (analytic) = 1.950113623866097 y[1] (numeric) = 1.95009097756912 absolute error = 2.264629697723564e-05 relative error = 0.001161280896665877 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.29 y[1] (analytic) = 1.946436209703382 y[1] (numeric) = 1.946410133017427 absolute error = 2.607668595455692e-05 relative error = 0.001339714387995832 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.28 y[1] (analytic) = 1.942636347367233 y[1] (numeric) = 1.94260659931992 absolute error = 2.974804731259439e-05 relative error = 0.001531323520890082 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.27 y[1] (analytic) = 1.938715160375128 y[1] (numeric) = 1.93868149332532 absolute error = 3.366704980778401e-05 relative error = 0.001736565045546437 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.26 y[1] (analytic) = 1.934673804744692 y[1] (numeric) = 1.93463596457653 absolute error = 3.784016816177349e-05 relative error = 0.001955893963570104 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.25 y[1] (analytic) = 1.930513468332593 y[1] (numeric) = 1.930471194654026 absolute error = 4.227367856701747e-05 relative error = 0.002189763462439334 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.24 y[1] (analytic) = 1.926235370157852 y[1] (numeric) = 1.926188396503451 absolute error = 4.697365440109458e-05 relative error = 0.002438624849737089 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.23 y[1] (analytic) = 1.921840759710179 y[1] (numeric) = 1.921788813748033 absolute error = 5.194596214597169e-05 relative error = 0.002702927486760419 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.22 y[1] (analytic) = 1.91733091624396 y[1] (numeric) = 1.917273719986438 absolute error = 5.719625752176327e-05 relative error = 0.002983118721822439 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.21 y[1] (analytic) = 1.912707148058531 y[1] (numeric) = 1.912644418076697 absolute error = 6.272998183409761e-05 relative error = 0.003279643823037462 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.2 y[1] (analytic) = 1.907970791765374 y[1] (numeric) = 1.907902239406836 absolute error = 6.855235853819863e-05 relative error = 0.003592945910601163 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.19 y[1] (analytic) = 1.903123211542896 y[1] (numeric) = 1.903048543152872 absolute error = 7.466839002412407e-05 relative error = 0.003923465888663565 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.18 y[1] (analytic) = 1.89816579837944 y[1] (numeric) = 1.898084715524817 absolute error = 8.108285462293807e-05 relative error = 0.00427164237666502 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.17 y[1] (analytic) = 1.8930999693052 y[1] (numeric) = 1.893012169001364 absolute error = 8.780030383648274e-05 relative error = 0.004637911640171171 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.16 y[1] (analytic) = 1.887927166613703 y[1] (numeric) = 1.887832341553912 absolute error = 9.48250597911926e-05 relative error = 0.005022707521142164 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.15 y[1] (analytic) = 1.882648857073539 y[1] (numeric) = 1.882546695860619 absolute error = 0.000102161212920393 relative error = 0.005426461367798365 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.14 y[1] (analytic) = 1.877266531131019 y[1] (numeric) = 1.877156718511148 absolute error = 0.0001098126198713079 relative error = 0.00584960196382704 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.13 y[1] (analytic) = 1.871781702104438 y[1] (numeric) = 1.871663919202797 absolute error = 0.0001177829016407728 relative error = 0.006292555457100037 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.12 y[1] (analytic) = 1.86619590537063 y[1] (numeric) = 1.866069829928692 absolute error = 0.0001260754419385446 relative error = 0.006755745287818845 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.11 y[1] (analytic) = 1.860510697544508 y[1] (numeric) = 1.86037600415873 absolute error = 0.0001346933857779842 relative error = 0.007239592116065326 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.1 y[1] (analytic) = 1.854727655652263 y[1] (numeric) = 1.854584016013968 absolute error = 0.0001436396382954452 relative error = 0.007744513748835573 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.09 y[1] (analytic) = 1.848848376298931 y[1] (numeric) = 1.848695459435136 absolute error = 0.0001529168637954825 relative error = 0.008270925066424059 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.08 y[1] (analytic) = 1.842874474830987 y[1] (numeric) = 1.842711947345963 absolute error = 0.0001625274850232117 relative error = 0.008819237948266518 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.07 y[1] (analytic) = 1.836807584494672 y[1] (numeric) = 1.836635110812011 absolute error = 0.0001724736826607121 relative error = 0.00938986119812662 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.06 y[1] (analytic) = 1.830649355590736 y[1] (numeric) = 1.830466598195688 absolute error = 0.0001827573950474726 relative error = 0.009983200468693701 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = -0.01 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] = 1.05 y[1] (analytic) = 1.824401454626258 y[1] (numeric) = 1.824208074308135 absolute error = 0.0001933803181226601 relative error = 0.01059965818555409 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = -0.01 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] = 1.04 y[1] (analytic) = 1.818065563464242 y[1] (numeric) = 1.817861219558653 absolute error = 0.0002043439055881002 relative error = 0.01123963347057364 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = -0.01 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] = 1.03 y[1] (analytic) = 1.811643378471641 y[1] (numeric) = 1.811427729102354 absolute error = 0.0002156493692870853 relative error = 0.01190352206453645 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = -0.01 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] = 1.02 y[1] (analytic) = 1.805136609666497 y[1] (numeric) = 1.804909311986695 absolute error = 0.0002272976798016746 relative error = 0.01259171624931303 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = -0.01 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] = 1.01 y[1] (analytic) = 1.798546979864822 y[1] (numeric) = 1.798307690297563 absolute error = 0.0002392895672587159 relative error = 0.01330460476916209 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = -0.01 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 ) = expt ( 2.0 , sin ( x ) ) * cos ( x ) * ln ( 2.0 ) ; Iterations = 40 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 0 %