##############ECHO OF PROBLEM################# ##############temp/add_lin_fullpostode.ode################# diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=-5.0; 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(0.05 * x * x + 0.2 * x - cos(0.3 * x + 0.1) / 0.3); } // 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 = 10 estimated_steps = 10000000 step_error = 7.905694150420948e-22 est_needed_step_err = 7.905694150420948e-22 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 = 0.3165571430008035 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 10000000 step_error = 7.905694150420948e-22 est_needed_step_err = 7.905694150420948e-22 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.285986968804875e-277 estimated_step_error = 2.285986968804875e-277 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 = 0.3165571430008035 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 5000000 step_error = 1.118033988749895e-21 est_needed_step_err = 1.118033988749895e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.570918320140187e-266 estimated_step_error = 1.570918320140187e-266 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 = 0.3165571430008035 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 2500000 step_error = 1.58113883008419e-21 est_needed_step_err = 1.58113883008419e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.07952690029871e-255 estimated_step_error = 1.07952690029871e-255 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 = 0.3165571430008035 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 1250000 step_error = 2.236067977499789e-21 est_needed_step_err = 2.236067977499789e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.418453068577198e-245 estimated_step_error = 7.418453068577198e-245 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 = 0.3165571430008035 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 625000 step_error = 3.162277660168379e-21 est_needed_step_err = 3.162277660168379e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.097923089242376e-234 estimated_step_error = 5.097923089242376e-234 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 = 0.3165571430008035 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 312500 step_error = 4.472135954999579e-21 est_needed_step_err = 4.472135954999579e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.503267388835152e-223 estimated_step_error = 3.503267388835152e-223 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 = 0.3165571430008035 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 156250 step_error = 6.324555320336758e-21 est_needed_step_err = 6.324555320336758e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.407428829034187e-212 estimated_step_error = 2.407428829034187e-212 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 = 0.3165571430008035 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 78125 step_error = 8.944271909999158e-21 est_needed_step_err = 8.944271909999158e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.654374982798476e-201 estimated_step_error = 1.654374982798476e-201 Double H and LOOP opt_iter = 9 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 = 0.3165571430008035 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 39062.5 step_error = 1.264911064067352e-20 est_needed_step_err = 1.264911064067352e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.13688125186573e-190 estimated_step_error = 1.13688125186573e-190 Double H and LOOP opt_iter = 10 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 = 0.3165571430008035 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 19531.25 step_error = 1.788854381999832e-20 est_needed_step_err = 1.788854381999832e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.812635484011038e-180 estimated_step_error = 7.812635484011038e-180 Double H and LOOP opt_iter = 11 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5583 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (closed_form) = -0.3165571430008035 y[1] (numeric) = -0.3165571430008035 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.000512 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] = -4.899648000000074 y[1] (closed_form) = -0.4447794010600288 y[1] (numeric) = -0.4447794010601226 absolute error = 9.381384558082573e-14 relative error = 2.109221905448907e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -4.799808000000147 y[1] (closed_form) = -0.5707500252851385 y[1] (numeric) = -0.5707500252853249 absolute error = 1.864064458345638e-13 relative error = 3.265991021926592e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -4.69996800000022 y[1] (closed_form) = -0.6950396662696058 y[1] (numeric) = -0.6950396662698838 absolute error = 2.779998453661392e-13 relative error = 3.999769493131391e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -4.599616000000294 y[1] (closed_form) = -0.8181850698145494 y[1] (numeric) = -0.818185069814918 absolute error = 3.68594044175552e-13 relative error = 4.505020413768952e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -4.499776000000367 y[1] (closed_form) = -0.9388431089896553 y[1] (numeric) = -0.9388431089901121 absolute error = 4.568567746332519e-13 relative error = 4.86616741667202e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -4.399936000000441 y[1] (closed_form) = -1.057561282995835 y[1] (numeric) = -1.057561282996379 absolute error = 5.433431482515516e-13 relative error = 5.137698939889153e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -4.299584000000515 y[1] (closed_form) = -1.174848104056725 y[1] (numeric) = -1.174848104057353 absolute error = 6.277200981230635e-13 relative error = 5.342989412465829e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -4.199744000000588 y[1] (closed_form) = -1.289422779080057 y[1] (numeric) = -1.28942277908077 absolute error = 7.129852264142755e-13 relative error = 5.529491474650054e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -4.099904000000661 y[1] (closed_form) = -1.401806342286009 y[1] (numeric) = -1.401806342286804 absolute error = 7.955858194463872e-13 relative error = 5.675433156829482e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -3.999552000000735 y[1] (closed_form) = -1.512475908622912 y[1] (numeric) = -1.512475908623789 absolute error = 8.766321002440236e-13 relative error = 5.796007032219009e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -3.899712000000721 y[1] (closed_form) = -1.620221440385214 y[1] (numeric) = -1.620221440386077 absolute error = 8.628653347386717e-13 relative error = 5.325601261846788e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -3.799872000000708 y[1] (closed_form) = -1.72553428311963 y[1] (numeric) = -1.725534283120479 absolute error = 8.490985692333197e-13 relative error = 4.920786434322339e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -3.700032000000695 y[1] (closed_form) = -1.828336532495225 y[1] (numeric) = -1.828336532496061 absolute error = 8.362199821476679e-13 relative error = 4.573665554920766e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -3.599680000000681 y[1] (closed_form) = -1.929058768035665 y[1] (numeric) = -1.929058768036489 absolute error = 8.233413950620161e-13 relative error = 4.268099078704655e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -3.499840000000668 y[1] (closed_form) = -2.026597774512688 y[1] (numeric) = -2.026597774513499 absolute error = 8.117950756059145e-13 relative error = 4.005703972516783e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -3.400000000000655 y[1] (closed_form) = -2.121400522144263 y[1] (numeric) = -2.121400522145061 absolute error = 7.980283101005625e-13 relative error = 3.761799347979483e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -3.299648000000642 y[1] (closed_form) = -2.213859359939828 y[1] (numeric) = -2.213859359940619 absolute error = 7.904787935331115e-13 relative error = 3.57059173602878e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -3.199808000000628 y[1] (closed_form) = -2.302960100867365 y[1] (numeric) = -2.302960100868142 absolute error = 7.767120280277595e-13 relative error = 3.372668192276653e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -3.099968000000615 y[1] (closed_form) = -2.389113000552717 y[1] (numeric) = -2.389113000553484 absolute error = 7.669420654110581e-13 relative error = 3.210153999553925e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -2.999616000000602 y[1] (closed_form) = -2.472669539778852 y[1] (numeric) = -2.472669539779609 absolute error = 7.571721027943568e-13 relative error = 3.062164557832811e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -2.899776000000589 y[1] (closed_form) = -2.552711651750601 y[1] (numeric) = -2.552711651751349 absolute error = 7.482903185973555e-13 relative error = 2.931354656074031e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -2.799936000000575 y[1] (closed_form) = -2.629610136199352 y[1] (numeric) = -2.629610136200092 absolute error = 7.402967128200544e-13 relative error = 2.815233720881627e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -2.699584000000562 y[1] (closed_form) = -2.703673174477335 y[1] (numeric) = -2.703673174478066 absolute error = 7.30526750203353e-13 relative error = 2.701978763925769e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -2.599744000000549 y[1] (closed_form) = -2.774085382596055 y[1] (numeric) = -2.774085382596778 absolute error = 7.229772336359019e-13 relative error = 2.606182340931852e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -2.499904000000535 y[1] (closed_form) = -2.841175558163472 y[1] (numeric) = -2.841175558164185 absolute error = 7.132072710192006e-13 relative error = 2.510254141001466e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -2.399552000000522 y[1] (closed_form) = -2.905206378088427 y[1] (numeric) = -2.905206378089132 absolute error = 7.052136652418994e-13 relative error = 2.427413317555489e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -2.299712000000509 y[1] (closed_form) = -2.965471121155881 y[1] (numeric) = -2.965471121156579 absolute error = 6.972200594645983e-13 relative error = 2.351127463324734e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -2.199872000000496 y[1] (closed_form) = -3.022254252309684 y[1] (numeric) = -3.022254252310375 absolute error = 6.918909889463976e-13 relative error = 2.289320921354108e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -2.100032000000482 y[1] (closed_form) = -3.075507071131643 y[1] (numeric) = -3.075507071132331 absolute error = 6.87894186057747e-13 relative error = 2.236685431533195e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -1.999680000000469 y[1] (closed_form) = -3.125428603873468 y[1] (numeric) = -3.125428603874148 absolute error = 6.803446694902959e-13 relative error = 2.176804386595547e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -1.899840000000456 y[1] (closed_form) = -3.171465151086239 y[1] (numeric) = -3.171465151086915 absolute error = 6.754596881819452e-13 relative error = 2.129803280198736e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -1.800000000000443 y[1] (closed_form) = -3.213838877399699 y[1] (numeric) = -3.213838877400369 absolute error = 6.701306176637445e-13 relative error = 2.08514067825934e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -1.699648000000429 y[1] (closed_form) = -3.252699136631275 y[1] (numeric) = -3.25269913663194 absolute error = 6.652456363553938e-13 relative error = 2.045211095190222e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -1.599808000000416 y[1] (closed_form) = -3.287612315006641 y[1] (numeric) = -3.287612315007303 absolute error = 6.621370118864434e-13 relative error = 2.014036171065705e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -1.499968000000403 y[1] (closed_form) = -3.318751748692163 y[1] (numeric) = -3.318751748692822 absolute error = 6.590283874174929e-13 relative error = 1.985771872443305e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -1.399616000000389 y[1] (closed_form) = -3.346215785465345 y[1] (numeric) = -3.346215785466 absolute error = 6.545874953189923e-13 relative error = 1.956202281282232e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -1.299776000000376 y[1] (closed_form) = -3.369694615286358 y[1] (numeric) = -3.369694615287014 absolute error = 6.554756737386924e-13 relative error = 1.945207944854047e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -1.199936000000363 y[1] (closed_form) = -3.38931125947175 y[1] (numeric) = -3.389311259472405 absolute error = 6.550315845288424e-13 relative error = 1.932639213050424e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000512 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] = -1.09958400000035 y[1] (closed_form) = -3.405112014739791 y[1] (numeric) = -3.405112014740446 absolute error = 6.550315845288424e-13 relative error = 1.923671179372048e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = -0.9997440000003365 y[1] (closed_form) = -3.416913839241493 y[1] (numeric) = -3.416913839242147 absolute error = 6.536993168992922e-13 relative error = 1.913127891584191e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = -0.8999040000003449 y[1] (closed_form) = -3.424788236047418 y[1] (numeric) = -3.424788236048077 absolute error = 6.590283874174929e-13 relative error = 1.92428945089488e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = -0.7995520000003533 y[1] (closed_form) = -3.428728702844376 y[1] (numeric) = -3.428728702845035 absolute error = 6.585842982076429e-13 relative error = 1.920782760272925e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = -0.6997120000003617 y[1] (closed_form) = -3.428681152825995 y[1] (numeric) = -3.428681152826654 absolute error = 6.590283874174929e-13 relative error = 1.922104617031266e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = -0.5998720000003701 y[1] (closed_form) = -3.424664660153973 y[1] (numeric) = -3.424664660154632 absolute error = 6.590283874174929e-13 relative error = 1.924358887120536e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = -0.5000320000003785 y[1] (closed_form) = -3.416670735111901 y[1] (numeric) = -3.416670735112559 absolute error = 6.581402089977928e-13 relative error = 1.926261732610994e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = -0.3996800000003761 y[1] (closed_form) = -3.40462186798505 y[1] (numeric) = -3.404621867985711 absolute error = 6.616929226765933e-13 relative error = 1.943513695011898e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = -0.2998400000003736 y[1] (closed_form) = -3.388637862962477 y[1] (numeric) = -3.388637862963138 absolute error = 6.612488334667432e-13 relative error = 1.951370610280126e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = -0.2000000000003712 y[1] (closed_form) = -3.368667022203342 y[1] (numeric) = -3.368667022204006 absolute error = 6.643574579356937e-13 relative error = 1.972167191226748e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = -0.09964800000036947 y[1] (closed_form) = -3.34457847622686 y[1] (numeric) = -3.344578476227525 absolute error = 6.648015471455437e-13 relative error = 1.987699053470949e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 0.000191999999630302 y[1] (closed_form) = -3.316622975565703 y[1] (numeric) = -3.316622975566366 absolute error = 6.630251903061435e-13 relative error = 1.999097260046731e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 0.1000319999996301 y[1] (closed_form) = -3.284695443886685 y[1] (numeric) = -3.284695443887347 absolute error = 6.621370118864434e-13 relative error = 2.015824672935144e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 0.2003839999996319 y[1] (closed_form) = -3.248611923852337 y[1] (numeric) = -3.248611923853 absolute error = 6.625811010962934e-13 relative error = 2.039582186568403e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 0.3002239999996343 y[1] (closed_form) = -3.208753616098855 y[1] (numeric) = -3.20875361609952 absolute error = 6.648015471455437e-13 relative error = 2.07183731343573e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 0.4000639999996367 y[1] (closed_form) = -3.164962170268584 y[1] (numeric) = -3.164962170269251 absolute error = 6.67021993194794e-13 relative error = 2.107519639447031e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 0.5004159999996391 y[1] (closed_form) = -3.117001118517997 y[1] (numeric) = -3.117001118518669 absolute error = 6.719069745031447e-13 relative error = 2.155619933888918e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 0.6002559999996308 y[1] (closed_form) = -3.065380807932446 y[1] (numeric) = -3.065380807933114 absolute error = 6.683542608243442e-13 relative error = 2.180330284233558e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 0.7000959999996224 y[1] (closed_form) = -3.009890025546195 y[1] (numeric) = -3.009890025546859 absolute error = 6.639133687258436e-13 relative error = 2.205772845821387e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 0.8004479999996139 y[1] (closed_form) = -2.950240671127167 y[1] (numeric) = -2.950240671127828 absolute error = 6.603606550470431e-13 relative error = 2.23832808458554e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 0.9002879999996055 y[1] (closed_form) = -2.887070137695918 y[1] (numeric) = -2.887070137696573 absolute error = 6.550315845288424e-13 relative error = 2.268845415205613e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 1.000127999999597 y[1] (closed_form) = -2.820115064712625 y[1] (numeric) = -2.820115064713275 absolute error = 6.492584248007915e-13 relative error = 2.302240901177386e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 1.09996799999961 y[1] (closed_form) = -2.749409091924761 y[1] (numeric) = -2.74940909192542 absolute error = 6.590283874174929e-13 relative error = 2.39698191641656e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 1.200319999999624 y[1] (closed_form) = -2.674597176141328 y[1] (numeric) = -2.674597176141996 absolute error = 6.679101716144942e-13 relative error = 2.497236509380063e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 1.300159999999637 y[1] (closed_form) = -2.596481423890459 y[1] (numeric) = -2.59648142389114 absolute error = 6.803446694902959e-13 relative error = 2.620256256141035e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 1.39999999999965 y[1] (closed_form) = -2.514730598925793 y[1] (numeric) = -2.514730598926484 absolute error = 6.910028105266974e-13 relative error = 2.747820425861404e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 1.500351999999664 y[1] (closed_form) = -2.428941198921192 y[1] (numeric) = -2.428941198921892 absolute error = 7.003286839335487e-13 relative error = 2.883267343995804e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 1.600191999999677 y[1] (closed_form) = -2.340034485986607 y[1] (numeric) = -2.340034485987319 absolute error = 7.127631818093505e-13 relative error = 3.045951613438871e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 1.70003199999969 y[1] (closed_form) = -2.247629887549403 y[1] (numeric) = -2.247629887550128 absolute error = 7.251976796851523e-13 relative error = 3.226499539369612e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 1.800383999999703 y[1] (closed_form) = -2.151277258118415 y[1] (numeric) = -2.151277258119157 absolute error = 7.416289804496046e-13 relative error = 3.447389115702641e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 1.900223999999717 y[1] (closed_form) = -2.052012417000638 y[1] (numeric) = -2.052012417001389 absolute error = 7.513989430663059e-13 relative error = 3.661766063602101e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 2.00006399999973 y[1] (closed_form) = -1.949407127008544 y[1] (numeric) = -1.949407127009309 absolute error = 7.644995747568828e-13 relative error = 3.921702984281394e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 2.100415999999743 y[1] (closed_form) = -1.842966668719402 y[1] (numeric) = -1.84296666872018 absolute error = 7.787104294720848e-13 relative error = 4.225309348720763e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 2.200255999999756 y[1] (closed_form) = -1.733836141511285 y[1] (numeric) = -1.733836141512078 absolute error = 7.926992395823618e-13 relative error = 4.571938608289775e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 2.300095999999769 y[1] (closed_form) = -1.621541576826445 y[1] (numeric) = -1.621541576827253 absolute error = 8.077982727172639e-13 relative error = 4.981668581685237e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 2.400447999999783 y[1] (closed_form) = -1.505545987054356 y[1] (numeric) = -1.50554598705518 absolute error = 8.235634396669411e-13 relative error = 5.470197833533245e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 2.500287999999796 y[1] (closed_form) = -1.387097838501995 y[1] (numeric) = -1.387097838502835 absolute error = 8.399947404313934e-13 relative error = 6.055771389122421e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 2.600127999999809 y[1] (closed_form) = -1.265679610367298 y[1] (numeric) = -1.265679610368154 absolute error = 8.562039965909207e-13 relative error = 6.764776722147335e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 2.699967999999823 y[1] (closed_form) = -1.141359468937127 y[1] (numeric) = -1.141359468938 absolute error = 8.72635297355373e-13 relative error = 7.645578111933489e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 2.800319999999836 y[1] (closed_form) = -1.013548050666329 y[1] (numeric) = -1.013548050667219 absolute error = 8.906209103543006e-13 relative error = 8.787160211780653e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 2.900159999999849 y[1] (closed_form) = -0.8836213853698789 y[1] (numeric) = -0.8836213853707876 absolute error = 9.087175456556906e-13 relative error = 1.028401485864114e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000512 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] = 2.999999999999862 y[1] (closed_form) = -0.7510076862273172 y[1] (numeric) = -0.7510076862282434 absolute error = 9.262590694447681e-13 relative error = 1.233354979491389e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000512 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] = 3.100351999999876 y[1] (closed_form) = -0.6150815115596373 y[1] (numeric) = -0.6150815115605816 absolute error = 9.442446824436956e-13 relative error = 1.53515373929776e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000512 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] = 3.200191999999889 y[1] (closed_form) = -0.4773062694029286 y[1] (numeric) = -0.4773062694038913 absolute error = 9.626743846524732e-13 relative error = 2.016890299506647e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000512 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] = 3.300031999999902 y[1] (closed_form) = -0.3370725574009752 y[1] (numeric) = -0.3370725574019566 absolute error = 9.814371537686384e-13 relative error = 2.911649531294056e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000512 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] = 3.400383999999915 y[1] (closed_form) = -0.1937218053440652 y[1] (numeric) = -0.1937218053450663 absolute error = 1.001060345728888e-12 relative error = 5.16751505567959e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000512 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] = 3.500223999999929 y[1] (closed_form) = -0.04879713824159038 y[1] (numeric) = -0.04879713824261073 absolute error = 1.02035047078175e-12 relative error = 2.091004734191755e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 h = 0.000512 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] = 3.600063999999942 y[1] (closed_form) = 0.09834560066727249 y[1] (numeric) = 0.0983456006662326 absolute error = 1.039890396015153e-12 relative error = 1.057383745647514e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000512 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] = 3.700415999999955 y[1] (closed_form) = 0.24839501667442 y[1] (numeric) = 0.2483950166733602 absolute error = 1.059791143731559e-12 relative error = 4.266555577162259e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000512 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] = 3.800255999999969 y[1] (closed_form) = 0.3997363257106632 y[1] (numeric) = 0.3997363257095833 absolute error = 1.07991393605289e-12 relative error = 2.701565673654969e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000512 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] = 3.900095999999982 y[1] (closed_form) = 0.5530454208014119 y[1] (numeric) = 0.5530454208003115 absolute error = 1.100453062008455e-12 relative error = 1.989805937483039e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000512 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] = 4.000447999999995 y[1] (closed_form) = 0.7090377300722147 y[1] (numeric) = 0.7090377300710942 absolute error = 1.12054809875417e-12 relative error = 1.580378661428982e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000512 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] = 4.100287999999922 y[1] (closed_form) = 0.8660351997341827 y[1] (numeric) = 0.8660351997331779 absolute error = 1.004862859588229e-12 relative error = 1.160302560330871e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000512 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] = 4.200127999999848 y[1] (closed_form) = 1.024742308364199 y[1] (numeric) = 1.02474230836331 absolute error = 8.888445535149003e-13 relative error = 8.673834838865654e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 4.299967999999775 y[1] (closed_form) = 1.185071769409051 y[1] (numeric) = 1.18507176940828 absolute error = 7.709388682997087e-13 relative error = 6.505419234517294e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 4.400319999999701 y[1] (closed_form) = 1.347769609618318 y[1] (numeric) = 1.347769609617667 absolute error = 6.514788708500419e-13 relative error = 4.833755459395895e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 4.500159999999628 y[1] (closed_form) = 1.511086937929403 y[1] (numeric) = 1.511086937928872 absolute error = 5.313527395855999e-13 relative error = 3.516361145399724e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 4.599999999999555 y[1] (closed_form) = 1.675761251784898 y[1] (numeric) = 1.675761251784487 absolute error = 4.11004563716233e-13 relative error = 2.452643914987658e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 4.700351999999481 y[1] (closed_form) = 1.842557592928621 y[1] (numeric) = 1.842557592928333 absolute error = 2.875477633779155e-13 relative error = 1.560590368960342e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000512 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] = 4.800191999999408 y[1] (closed_form) = 2.009684274030286 y[1] (numeric) = 2.00968427403012 absolute error = 1.660893644839234e-13 relative error = 8.2644506219299e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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] = 4.900031999999334 y[1] (closed_form) = 2.17789965767094 y[1] (numeric) = 2.177899657670899 absolute error = 4.085620730620576e-14 relative error = 1.875945347725416e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000512 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 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ; Iterations = 19532 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %