##############ECHO OF PROBLEM################# ##############temp/sub_sin_cospostode.ode################# diff ( y , x , 1 ) = m1 * sin ( x ) - cos ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(cos(x) - sin(x)) ; } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 4900000.000000001 step_error = 1.129384878631564e-21 est_needed_step_err = 1.129384878631564e-21 opt_iter = 1 NO POLE (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 = 0.8951707486311977 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 4900000.000000001 step_error = 1.129384878631564e-21 est_needed_step_err = 1.129384878631564e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.406416108484866e-258 estimated_step_error = 2.406416108484866e-258 Double H and LOOP opt_iter = 2 NO POLE (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 = 0.8951707486311977 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 2450000 step_error = 1.59719141249985e-21 est_needed_step_err = 1.59719141249985e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.653676530510163e-247 estimated_step_error = 1.653676530510163e-247 Double H and LOOP opt_iter = 3 NO POLE (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 = 0.8951707486311977 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 1225000 step_error = 2.258769757263128e-21 est_needed_step_err = 2.258769757263128e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.136397821108563e-236 estimated_step_error = 1.136397821108563e-236 Double H and LOOP opt_iter = 4 NO POLE (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 = 0.8951707486311977 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 612500.0000000001 step_error = 3.194382824999699e-21 est_needed_step_err = 3.194382824999699e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.809265846774536e-226 estimated_step_error = 7.809265846774536e-226 Double H and LOOP opt_iter = 5 NO POLE (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 = 0.8951707486311977 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 306250.0000000001 step_error = 4.517539514526256e-21 est_needed_step_err = 4.517539514526256e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.366485917261428e-215 estimated_step_error = 5.366485917261428e-215 Double H and LOOP opt_iter = 6 NO POLE (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 = 0.8951707486311977 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 153125 step_error = 6.388765649999399e-21 est_needed_step_err = 6.388765649999399e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.687820066233959e-204 estimated_step_error = 3.687820066233959e-204 Double H and LOOP opt_iter = 7 NO POLE (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 = 0.8951707486311977 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 76562.50000000001 step_error = 9.035079029052512e-21 est_needed_step_err = 9.035079029052512e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.534249312149395e-193 estimated_step_error = 2.534249312149395e-193 Double H and LOOP opt_iter = 8 NO POLE (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 = 0.8951707486311977 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 38281.25000000001 step_error = 1.27775312999988e-20 est_needed_step_err = 1.27775312999988e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.741521024354856e-182 estimated_step_error = 1.741521024354856e-182 Double H and LOOP opt_iter = 9 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.49 Order of pole (three term test) = 32.6 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.8951707486311977 y[1] (numeric) = 0.8951707486311977 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.000128 NO POLE (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] = 0.2000959999999943 y[1] (closed_form) = 0.7812840847984535 y[1] (numeric) = 0.7812840847984452 absolute error = 8.215650382226158e-15 relative error = 1.05155737101e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 NO POLE (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] = 0.3000639999999968 y[1] (closed_form) = 0.659736226284491 y[1] (numeric) = 0.6597362262844849 absolute error = 6.106226635438361e-15 relative error = 9.2555575882614e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000128 NO POLE (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] = 0.40003200000001 y[1] (closed_form) = 0.5316007160832656 y[1] (numeric) = 0.5316007160832749 absolute error = 9.214851104388799e-15 relative error = 1.733415856224215e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 NO POLE (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] = 0.5000000000000233 y[1] (closed_form) = 0.3981570232861381 y[1] (numeric) = 0.3981570232861653 absolute error = 2.714495295208508e-14 relative error = 6.817650164261245e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 NO POLE (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] = 0.6000960000000366 y[1] (closed_form) = 0.2605597024170457 y[1] (numeric) = 0.2605597024170916 absolute error = 4.585221091701897e-14 relative error = 1.759758339132158e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 0.7000640000000499 y[1] (closed_form) = 0.1205343199677803 y[1] (numeric) = 0.120534319967845 absolute error = 6.467049118441537e-14 relative error = 5.365317629178334e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 0.8000320000000631 y[1] (closed_form) = -0.02069463155147433 y[1] (numeric) = -0.02069463155139091 absolute error = 8.34193825127727e-14 relative error = 4.030967273095989e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (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] = 0.9000000000000764 y[1] (closed_form) = -0.1617169413569264 y[1] (numeric) = -0.161716941356824 absolute error = 1.023348072948238e-13 relative error = 6.328020208405999e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 1.00009600000009 y[1] (closed_form) = -0.3013013277877965 y[1] (numeric) = -0.3013013277876758 absolute error = 1.206812427767545e-13 relative error = 4.005333918134908e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 1.100064000000016 y[1] (closed_form) = -0.4376973051624083 y[1] (numeric) = -0.4376973051623879 absolute error = 2.042810365310288e-14 relative error = 4.667176016887515e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 NO POLE (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] = 1.200031999999943 y[1] (closed_form) = -0.5697227518976888 y[1] (numeric) = -0.5697227518977664 absolute error = 7.760458942129844e-14 relative error = 1.362146573272796e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 1.299999999999869 y[1] (closed_form) = -0.6960593567924447 y[1] (numeric) = -0.6960593567926142 absolute error = 1.695310558602614e-13 relative error = 2.435583319237144e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 1.400095999999796 y[1] (closed_form) = -0.8155935033498665 y[1] (numeric) = -0.8155935033501241 absolute error = 2.576827640154988e-13 relative error = 3.159450914666742e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 1.500063999999722 y[1] (closed_form) = -0.9268261498980577 y[1] (numeric) = -0.9268261498983978 absolute error = 3.40172334745148e-13 relative error = 3.670292802836474e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 1.600031999999649 y[1] (closed_form) = -1.0288041767863 y[1] (numeric) = -1.028804176786714 absolute error = 4.141131881851834e-13 relative error = 4.025189608762658e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 1.699999999999575 y[1] (closed_form) = -1.120509304747627 y[1] (numeric) = -1.120509304748109 absolute error = 4.82058837292243e-13 relative error = 4.302140421768451e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 1.800095999999502 y[1] (closed_form) = -1.201121398007837 y[1] (numeric) = -1.201121398008377 absolute error = 5.397904345727511e-13 relative error = 4.49405393549761e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 1.900063999999428 y[1] (closed_form) = -1.269629524623748 y[1] (numeric) = -1.269629524624342 absolute error = 5.939693181744587e-13 relative error = 4.678288482228549e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.000031999999355 y[1] (closed_form) = -1.325460043512765 y[1] (numeric) = -1.325460043513402 absolute error = 6.372680161348399e-13 relative error = 4.807900617252387e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.099999999999455 y[1] (closed_form) = -1.368055471248536 y[1] (numeric) = -1.368055471249131 absolute error = 5.950795411990839e-13 relative error = 4.349820264641705e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.200095999999555 y[1] (closed_form) = -1.397018634184951 y[1] (numeric) = -1.397018634185518 absolute error = 5.662137425588298e-13 relative error = 4.053014961315604e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.300063999999655 y[1] (closed_form) = -1.411986314032994 y[1] (numeric) = -1.411986314033544 absolute error = 5.500044863993026e-13 relative error = 3.895253664522776e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.400031999999755 y[1] (closed_form) = -1.41285491359191 y[1] (numeric) = -1.412854913592459 absolute error = 5.493383525845275e-13 relative error = 3.888144120813801e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.499999999999855 y[1] (closed_form) = -1.39961575965092 y[1] (numeric) = -1.399615759651481 absolute error = 5.617728504603292e-13 relative error = 4.013764825000555e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.600095999999955 y[1] (closed_form) = -1.372357345677875 y[1] (numeric) = -1.372357345678466 absolute error = 5.915268275202834e-13 relative error = 4.310297382698813e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.700064000000055 y[1] (closed_form) = -1.331421511219318 y[1] (numeric) = -1.331421511219948 absolute error = 6.301625887772389e-13 relative error = 4.733005914859638e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.800032000000155 y[1] (closed_form) = -1.277191058676444 y[1] (numeric) = -1.277191058677129 absolute error = 6.854516954035716e-13 relative error = 5.366868885802465e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.900000000000255 y[1] (closed_form) = -1.210207494363386 y[1] (numeric) = -1.210207494364138 absolute error = 7.51620987671231e-13 relative error = 6.210678674293051e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 3.000096000000355 y[1] (closed_form) = -1.13103100768907 y[1] (numeric) = -1.131031007689903 absolute error = 8.335554468885675e-13 relative error = 7.36987263144707e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 3.100064000000455 y[1] (closed_form) = -1.040654527087568 y[1] (numeric) = -1.04065452708849 absolute error = 9.223732888585801e-13 relative error = 8.863395726917979e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 3.200032000000555 y[1] (closed_form) = -0.9398868184799377 y[1] (numeric) = -0.9398868184809592 absolute error = 1.021516204957607e-12 relative error = 1.086850230126311e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 3.300000000000655 y[1] (closed_form) = -0.829734075764866 y[1] (numeric) = -0.8297340757659983 absolute error = 1.132316462815197e-12 relative error = 1.36467393094758e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 3.400096000000755 y[1] (closed_form) = -0.7111397427021316 y[1] (numeric) = -0.7111397427033816 absolute error = 1.250000103425464e-12 relative error = 1.757741873173638e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 3.500064000000855 y[1] (closed_form) = -0.5855910750461137 y[1] (numeric) = -0.5855910750474905 absolute error = 1.376787572837657e-12 relative error = 2.351107507451746e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 3.600032000000955 y[1] (closed_form) = -0.4541951158819445 y[1] (numeric) = -0.4541951158834514 absolute error = 1.506905711323725e-12 relative error = 3.317749704106029e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 3.700000000001055 y[1] (closed_form) = -0.3182638908004608 y[1] (numeric) = -0.3182638908021032 absolute error = 1.642352920327994e-12 relative error = 5.160349533204463e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 3.800096000001155 y[1] (closed_form) = -0.1789751488870712 y[1] (numeric) = -0.178975148888852 absolute error = 1.780797731498751e-12 relative error = 9.949972063565032e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (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] = 3.900064000001255 y[1] (closed_form) = -0.03807566823463249 y[1] (numeric) = -0.03807566823655394 absolute error = 1.921449110930951e-12 relative error = 5.046396294584945e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (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] = 4.000032000001355 y[1] (closed_form) = 0.1032040086691205 y[1] (numeric) = 0.1032040086670576 absolute error = 2.062877646480388e-12 relative error = 1.998834806014292e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (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] = 4.100000000001455 y[1] (closed_form) = 0.243453164533169 y[1] (numeric) = 0.2434531645309662 absolute error = 2.202765747583157e-12 relative error = 9.048006222498882e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 4.200096000001555 y[1] (closed_form) = 0.3814456856307071 y[1] (numeric) = 0.381445685628366 absolute error = 2.341071780875836e-12 relative error = 6.137365997481283e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 4.300064000001655 y[1] (closed_form) = 0.5154510493830963 y[1] (numeric) = 0.5154510493806216 absolute error = 2.474687121889474e-12 relative error = 4.80101286989567e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 4.400032000001755 y[1] (closed_form) = 0.6443094895016372 y[1] (numeric) = 0.6443094894990327 absolute error = 2.604583215770617e-12 relative error = 4.042441184259477e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 4.500000000001855 y[1] (closed_form) = 0.7667343182365222 y[1] (numeric) = 0.7667343182337955 absolute error = 2.726707748479384e-12 relative error = 3.556261515397893e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 4.600096000001956 y[1] (closed_form) = 0.8816446336172146 y[1] (numeric) = 0.8816446336143724 absolute error = 2.842170943040401e-12 relative error = 3.223714901297059e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 4.700064000002055 y[1] (closed_form) = 0.9875993800437214 y[1] (numeric) = 0.9875993800407715 absolute error = 2.949862576429041e-12 relative error = 2.986902013140642e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 4.800032000002155 y[1] (closed_form) = 1.083692669022418 y[1] (numeric) = 1.083692669019375 absolute error = 3.042677221287704e-12 relative error = 2.807693830791026e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 4.900000000002255 y[1] (closed_form) = 1.168964982048703 y[1] (numeric) = 1.168964982045578 absolute error = 3.124833725109966e-12 relative error = 2.673162817617897e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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 ) = m1 * sin ( x ) - cos ( x ) ; Iterations = 38282 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %