##############ECHO OF PROBLEM################# ##############temp/sub_lin_sinpostode.ode################# diff ( y , x , 1 ) = ( 0.1 * x + 1.0 ) - sin ( 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) + (0.05 * x * x) + 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 = 1.095504165278026 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1.095504165278026 desired_abs_gbl_error = 1.095504165278026e-16 range = 4.9 estimated_steps = 4900000.000000001 step_error = 1.237245838742896e-21 est_needed_step_err = 1.237245838742896e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.674790358513323e-258 estimated_step_error = 2.674790358513323e-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 = 1.095504165278026 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1.095504165278026 desired_abs_gbl_error = 1.095504165278026e-16 range = 4.9 estimated_steps = 2450000 step_error = 1.749729845139879e-21 est_needed_step_err = 1.749729845139879e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.838101935663098e-247 estimated_step_error = 1.838101935663098e-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 = 1.095504165278026 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1.095504165278026 desired_abs_gbl_error = 1.095504165278026e-16 range = 4.9 estimated_steps = 1225000 step_error = 2.474491677485791e-21 est_needed_step_err = 2.474491677485791e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.263134028636665e-236 estimated_step_error = 1.263134028636665e-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 = 1.095504165278026 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1.095504165278026 desired_abs_gbl_error = 1.095504165278026e-16 range = 4.9 estimated_steps = 612500.0000000001 step_error = 3.499459690279757e-21 est_needed_step_err = 3.499459690279757e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.68019090245767e-226 estimated_step_error = 8.68019090245767e-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 = 1.095504165278026 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1.095504165278026 desired_abs_gbl_error = 1.095504165278026e-16 range = 4.9 estimated_steps = 306250.0000000001 step_error = 4.948983354971583e-21 est_needed_step_err = 4.948983354971583e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.964981703152477e-215 estimated_step_error = 5.964981703152477e-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 = 1.095504165278026 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1.095504165278026 desired_abs_gbl_error = 1.095504165278026e-16 range = 4.9 estimated_steps = 153125 step_error = 6.998919380559514e-21 est_needed_step_err = 6.998919380559514e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.099104124878063e-204 estimated_step_error = 4.099104124878063e-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 = 1.095504165278026 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1.095504165278026 desired_abs_gbl_error = 1.095504165278026e-16 range = 4.9 estimated_steps = 76562.50000000001 step_error = 9.897966709943166e-21 est_needed_step_err = 9.897966709943166e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.816882783259633e-193 estimated_step_error = 2.816882783259633e-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 = 1.095504165278026 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1.095504165278026 desired_abs_gbl_error = 1.095504165278026e-16 range = 4.9 estimated_steps = 38281.25000000001 step_error = 1.399783876111903e-20 est_needed_step_err = 1.399783876111903e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.935746940941988e-182 estimated_step_error = 1.935746940941988e-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 = 0.09933 Order of pole (three term test) = 32.01 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) = 1.095504165278026 y[1] (numeric) = 1.095504165278026 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) = 1.182145421530163 y[1] (numeric) = 1.182145421530167 absolute error = 3.552713678800501e-15 relative error = 3.005310187812499e-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] = 0.3000639999999968 y[1] (closed_form) = 1.259883494080661 y[1] (numeric) = 1.259883494080666 absolute error = 4.662936703425657e-15 relative error = 3.701085636357359e-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) = 1.329081812195557 y[1] (numeric) = 1.329081812195553 absolute error = 3.774758283725532e-15 relative error = 2.840124850922365e-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] = 0.5000000000000233 y[1] (closed_form) = 1.390082561890386 y[1] (numeric) = 1.390082561890374 absolute error = 1.243449787580175e-14 relative error = 8.945150609537872e-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] = 0.6000960000000366 y[1] (closed_form) = 1.443383165889987 y[1] (numeric) = 1.443383165889968 absolute error = 1.931788062847772e-14 relative error = 1.338375081890771e-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] = 0.7000640000000499 y[1] (closed_form) = 1.489369435990958 y[1] (numeric) = 1.489369435990933 absolute error = 2.442490654175344e-14 relative error = 1.63994949483452e-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] = 0.8000320000000631 y[1] (closed_form) = 1.528718313646769 y[1] (numeric) = 1.528718313646739 absolute error = 3.019806626980426e-14 relative error = 1.975384608153646e-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] = 0.9000000000000764 y[1] (closed_form) = 1.562109968270688 y[1] (numeric) = 1.562109968270651 absolute error = 3.68594044175552e-14 relative error = 2.359590884523955e-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] = 1.00009600000009 y[1] (closed_form) = 1.590327122624832 y[1] (numeric) = 1.590327122624793 absolute error = 3.952393967665557e-14 relative error = 2.485271056147327e-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] = 1.100064000000016 y[1] (closed_form) = 1.614110123430411 y[1] (numeric) = 1.614110123430388 absolute error = 2.309263891220326e-14 relative error = 1.430673073478115e-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] = 1.200031999999943 y[1] (closed_form) = 1.63436376909159 y[1] (numeric) = 1.634363769091581 absolute error = 8.881784197001252e-15 relative error = 5.434398611233235e-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] = 1.299999999999869 y[1] (closed_form) = 1.651998828624566 y[1] (numeric) = 1.651998828624572 absolute error = 5.995204332975845e-15 relative error = 3.62906088617955e-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] = 1.400095999999796 y[1] (closed_form) = 1.667981979403867 y[1] (numeric) = 1.66798197940389 absolute error = 2.309263891220326e-14 relative error = 1.384465731485691e-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] = 1.500063999999722 y[1] (closed_form) = 1.683246962048492 y[1] (numeric) = 1.683246962048528 absolute error = 3.597122599785507e-14 relative error = 2.137014164224513e-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] = 1.600031999999649 y[1] (closed_form) = 1.698805611409513 y[1] (numeric) = 1.698805611409559 absolute error = 4.529709940470639e-14 relative error = 2.666408628537729e-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] = 1.699999999999575 y[1] (closed_form) = 1.7156555057044 y[1] (numeric) = 1.715655505704458 absolute error = 5.795364188543317e-14 relative error = 3.377929991932678e-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] = 1.800095999999502 y[1] (closed_form) = 1.734817697442137 y[1] (numeric) = 1.734817697442213 absolute error = 7.66053886991358e-14 relative error = 4.415760158089516e-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] = 1.900063999999428 y[1] (closed_form) = 1.757226030797684 y[1] (numeric) = 1.757226030797779 absolute error = 9.547918011776346e-14 relative error = 5.433517284877756e-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] = 2.000031999999355 y[1] (closed_form) = 1.783862466199284 y[1] (numeric) = 1.7838624661994 absolute error = 1.159072837708663e-13 relative error = 6.497545969326863e-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] = 2.099999999999455 y[1] (closed_form) = 1.815653895399954 y[1] (numeric) = 1.815653895400037 absolute error = 8.37108160567368e-14 relative error = 4.610505133650316e-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] = 2.200095999999555 y[1] (closed_form) = 1.853538390262437 y[1] (numeric) = 1.853538390262483 absolute error = 4.640732242933154e-14 relative error = 2.50371520078205e-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] = 2.300063999999655 y[1] (closed_form) = 1.898254975155795 y[1] (numeric) = 1.898254975155796 absolute error = 6.661338147750939e-16 relative error = 3.509190406417465e-14 % Desired digits = 16 Estimated correct digits = 11 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] = 2.400031999999755 y[1] (closed_form) = 1.950624350065588 y[1] (numeric) = 1.950624350065535 absolute error = 5.329070518200751e-14 relative error = 2.731981951328335e-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] = 2.499999999999855 y[1] (closed_form) = 2.011356384452972 y[1] (numeric) = 2.011356384452855 absolute error = 1.167954621905665e-13 relative error = 5.806800977357939e-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] = 2.600095999999955 y[1] (closed_form) = 2.081182722908744 y[1] (numeric) = 2.081182722908559 absolute error = 1.84741111297626e-13 relative error = 8.876736735514723e-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] = 2.700064000000055 y[1] (closed_form) = 2.160481787727009 y[1] (numeric) = 2.160481787726744 absolute error = 2.646771690706373e-13 relative error = 1.225084009382453e-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) = 2.249807900244303 y[1] (numeric) = 2.249807900243952 absolute error = 3.512745649913995e-13 relative error = 1.561353593581279e-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) = 2.349541834850678 y[1] (numeric) = 2.349541834850231 absolute error = 4.463096558993129e-13 relative error = 1.899560370788961e-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) = 2.460118760901899 y[1] (numeric) = 2.460118760901348 absolute error = 5.511147094239277e-13 relative error = 2.240195547396601e-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) = 2.581446030815933 y[1] (numeric) = 2.581446030815266 absolute error = 6.674660824046441e-13 relative error = 2.58562865323074e-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) = 2.713749332740929 y[1] (numeric) = 2.713749332740128 absolute error = 8.006928453596629e-13 relative error = 2.95050407087876e-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] = 3.300000000000655 y[1] (closed_form) = 2.85702023009211 y[1] (numeric) = 2.857020230091164 absolute error = 9.463541061904834e-13 relative error = 3.312381537319297e-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] = 3.400096000000755 y[1] (closed_form) = 3.011354984283307 y[1] (numeric) = 3.011354984282208 absolute error = 1.099120794378905e-12 relative error = 3.649921049213307e-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] = 3.500064000000855 y[1] (closed_form) = 3.176152164959879 y[1] (numeric) = 3.176152164958616 absolute error = 1.262989712813578e-12 relative error = 3.976477344968553e-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] = 3.600032000000955 y[1] (closed_form) = 3.351299264832099 y[1] (numeric) = 3.351299264830662 absolute error = 1.436184504655103e-12 relative error = 4.285455852081464e-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] = 3.700000000001055 y[1] (closed_form) = 3.536399968291597 y[1] (numeric) = 3.536399968289976 absolute error = 1.620925615952729e-12 relative error = 4.583547196262936e-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] = 3.800096000001155 y[1] (closed_form) = 3.731223510550905 y[1] (numeric) = 3.731223510549099 absolute error = 1.805666727250355e-12 relative error = 4.839342167909295e-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] = 3.900064000001255 y[1] (closed_form) = 3.934700674528135 y[1] (numeric) = 3.934700674526121 absolute error = 2.014832745089734e-12 relative error = 5.120676035493756e-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] = 4.000032000001355 y[1] (closed_form) = 4.146425397205022 y[1] (numeric) = 4.146425397202797 absolute error = 2.225775119768514e-12 relative error = 5.367937214712317e-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] = 4.100000000001455 y[1] (closed_form) = 4.365676053469974 y[1] (numeric) = 4.365676053467525 absolute error = 2.448707903113245e-12 relative error = 5.609000468935245e-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] = 4.200096000001555 y[1] (closed_form) = 4.59195917265681 y[1] (numeric) = 4.591959172654137 absolute error = 2.672528864877677e-12 relative error = 5.820018785862612e-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] = 4.300064000001655 y[1] (closed_form) = 4.823850983569457 y[1] (numeric) = 4.823850983566551 absolute error = 2.90611978925881e-12 relative error = 6.024480853901497e-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] = 4.400032000001755 y[1] (closed_form) = 5.060743661500692 y[1] (numeric) = 5.060743661497557 absolute error = 3.135269821541442e-12 relative error = 6.195274906715433e-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] = 4.500000000001855 y[1] (closed_form) = 5.301704200573725 y[1] (numeric) = 5.301704200570335 absolute error = 3.389288849575678e-12 relative error = 6.39282902506878e-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] = 4.600096000001956 y[1] (closed_form) = 5.546083028383545 y[1] (numeric) = 5.546083028379908 absolute error = 3.637090628672013e-12 relative error = 6.557944787444113e-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] = 4.700064000002055 y[1] (closed_form) = 5.792269411860799 y[1] (numeric) = 5.792269411856906 absolute error = 3.892886013545649e-12 relative error = 6.720830363266956e-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] = 4.800032000002155 y[1] (closed_form) = 6.039578220718662 y[1] (numeric) = 6.039578220714515 absolute error = 4.146905041579885e-12 relative error = 6.866216298605097e-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] = 4.900000000002255 y[1] (closed_form) = 6.287012369428152 y[1] (numeric) = 6.287012369423769 absolute error = 4.383160501220118e-12 relative error = 6.9717701249231e-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 Finished! diff ( y , x , 1 ) = ( 0.1 * x + 1.0 ) - sin ( 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 %