##############ECHO OF PROBLEM################# ##############temp/cospostode.ode################# diff ( y , x , 1 ) = cos ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.0; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=false; 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(1.0 + sin(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 estimated_steps = 5000000 step_error = 1.118033988749895e-21 est_needed_step_err = 1.118033988749895e-21 opt_iter = 1 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 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 = 3.63273008957653e-266 estimated_step_error = 3.63273008957653e-266 Double H and LOOP opt_iter = 2 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 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 = 4.992786217576429e-255 estimated_step_error = 4.992786217576429e-255 Double H and LOOP opt_iter = 3 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 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 = 6.862033126531284e-244 estimated_step_error = 6.862033126531284e-244 Double H and LOOP opt_iter = 4 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 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 = 9.431106516006481e-233 estimated_step_error = 9.431106516006481e-233 Double H and LOOP opt_iter = 5 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 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 = 1.296201409642849e-221 estimated_step_error = 1.296201409642849e-221 Double H and LOOP opt_iter = 6 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 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 = 1.781485652302212e-210 estimated_step_error = 1.781485652302212e-210 Double H and LOOP opt_iter = 7 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 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 = 2.448455236776724e-199 estimated_step_error = 2.448455236776724e-199 Double H and LOOP opt_iter = 8 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 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 = 3.365131253649334e-188 estimated_step_error = 3.365131253649334e-188 Double H and LOOP opt_iter = 9 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 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 = 4.625001177936491e-177 estimated_step_error = 4.625001177936491e-177 Double H and LOOP opt_iter = 10 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 estimated_steps = 9765.625 step_error = 2.529822128134703e-20 est_needed_step_err = 2.529822128134703e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.356553216812763e-166 estimated_step_error = 6.356553216812763e-166 Double H and LOOP opt_iter = 11 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 estimated_steps = 4882.8125 step_error = 3.577708763999663e-20 est_needed_step_err = 3.577708763999663e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.736380216919211e-155 estimated_step_error = 8.736380216919211e-155 Double H and LOOP opt_iter = 12 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 estimated_steps = 2441.40625 step_error = 5.059644256269407e-20 est_needed_step_err = 5.059644256269407e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.200718953509692e-143 estimated_step_error = 1.200718953509692e-143 Double H and LOOP opt_iter = 13 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 estimated_steps = 1220.703125 step_error = 7.155417527999326e-20 est_needed_step_err = 7.155417527999326e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.6502555603408e-132 estimated_step_error = 1.6502555603408e-132 Double H and LOOP opt_iter = 14 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 estimated_steps = 610.3515625 step_error = 1.011928851253881e-19 est_needed_step_err = 1.011928851253881e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.268093952488647e-121 estimated_step_error = 2.268093952488647e-121 Double H and LOOP opt_iter = 15 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 estimated_steps = 305.17578125 step_error = 1.431083505599865e-19 est_needed_step_err = 1.431083505599865e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.117244486194331e-110 estimated_step_error = 3.117244486194331e-110 Double H and LOOP opt_iter = 16 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 estimated_steps = 152.587890625 step_error = 2.023857702507763e-19 est_needed_step_err = 2.023857702507763e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.284307616974801e-99 estimated_step_error = 4.284307616974801e-99 Double H and LOOP opt_iter = 17 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 5 estimated_steps = 76.2939453125 step_error = 2.862167011199731e-19 est_needed_step_err = 2.862167011199731e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.88830435263384e-88 estimated_step_error = 5.88830435263384e-88 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 1.099833416646828 y[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 SETTING H FOR POLE 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) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1993346653975308 y[1] (closed_form) = 1.198017214663721 y[1] (numeric) = 1.198017214663721 absolute error = 2.220446049250313e-16 relative error = 1.853434176130419e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1941 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3086027973348146 y[1] (closed_form) = 1.303727736110465 y[1] (numeric) = 1.303727736110465 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2894 Order of pole (three term test) = 32.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4079374627323454 y[1] (closed_form) = 1.396716885595887 y[1] (numeric) = 1.396716885595888 absolute error = 2.220446049250313e-16 relative error = 1.589761011805191e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3642 Order of pole (three term test) = 32.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5072721281298761 y[1] (closed_form) = 1.485794698311445 y[1] (numeric) = 1.485794698311445 absolute error = 2.220446049250313e-16 relative error = 1.49445010927403e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4246 Order of pole (three term test) = 32.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6066067935274063 y[1] (closed_form) = 1.570082932526311 y[1] (numeric) = 1.570082932526311 absolute error = 4.440892098500626e-16 relative error = 2.828444285649992e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4684 Order of pole (three term test) = 32.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7059414589249365 y[1] (closed_form) = 1.648750568231705 y[1] (numeric) = 1.648750568231706 absolute error = 1.110223024625157e-15 relative error = 6.733723378278362e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4937 Order of pole (three term test) = 32.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8052761243224668 y[1] (closed_form) = 1.721022000387094 y[1] (numeric) = 1.721022000387096 absolute error = 1.332267629550188e-15 relative error = 7.741142351756879e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4996 Order of pole (three term test) = 32.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.904610789719997 y[1] (closed_form) = 1.786184685815558 y[1] (numeric) = 1.786184685815559 absolute error = 1.332267629550188e-15 relative error = 7.458733915535083e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4859 Order of pole (three term test) = 32.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.003945455117527 y[1] (closed_form) = 1.843596168355554 y[1] (numeric) = 1.843596168355555 absolute error = 1.332267629550188e-15 relative error = 7.226461263143873e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.453 Order of pole (three term test) = 32.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.103280120515058 y[1] (closed_form) = 1.892690413006241 y[1] (numeric) = 1.892690413006243 absolute error = 1.77635683940025e-15 relative error = 9.385353395322517e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4023 Order of pole (three term test) = 32.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.202614785912588 y[1] (closed_form) = 1.932983386616366 y[1] (numeric) = 1.932983386616368 absolute error = 2.220446049250313e-15 relative error = 1.148714502475441e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3358 Order of pole (three term test) = 32.13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.301949451310118 y[1] (closed_form) = 1.9640778300952 y[1] (numeric) = 1.964077830095203 absolute error = 2.442490654175344e-15 relative error = 1.243581398226441e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2561 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.401284116707648 y[1] (closed_form) = 1.985667175095054 y[1] (numeric) = 1.985667175095057 absolute error = 2.886579864025407e-15 relative error = 1.4537078017051e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.009933466539753071 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1663 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.505055086899326 y[1] (closed_form) = 1.997839822864359 y[1] (numeric) = 1.997839822864361 absolute error = 2.664535259100376e-15 relative error = 1.333708152478489e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.007275776712777524 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06555 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.600101216846044 y[1] (closed_form) = 1.999570642437716 y[1] (numeric) = 1.999570642437718 absolute error = 1.77635683940025e-15 relative error = 8.883691337029527e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.0001831554384666301 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] = 1.7001040862488 y[1] (closed_form) = 1.991651394140581 y[1] (numeric) = 1.991651394140579 absolute error = 2.220446049250313e-15 relative error = 1.114876858361279e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.0001831554384666301 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] = 1.800106955651557 y[1] (closed_form) = 1.973823324759998 y[1] (numeric) = 1.97382332475999 absolute error = 7.771561172376096e-15 relative error = 3.937313474254875e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.0001831554384666301 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2214 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.900109825054313 y[1] (closed_form) = 1.946264576686327 y[1] (numeric) = 1.946264576686308 absolute error = 1.865174681370263e-14 relative error = 9.583356259537302e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.0001831554384666301 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.306 Order of pole (three term test) = 32.11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.00011269445707 y[1] (closed_form) = 1.909250523609918 y[1] (numeric) = 1.909250523609891 absolute error = 2.708944180085382e-14 relative error = 1.418852134168041e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.0001831554384666301 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] = 2.100115563859947 y[1] (closed_form) = 1.863151018920394 y[1] (numeric) = 1.863151018920414 absolute error = 2.020605904817785e-14 relative error = 1.084509996397731e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.0001831554384666301 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] = 2.200118433262825 y[1] (closed_form) = 1.808426700042098 y[1] (numeric) = 1.80842670004217 absolute error = 7.216449660063518e-14 relative error = 3.990457373746764e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.0001831554384666301 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] = 2.300121302665703 y[1] (closed_form) = 1.745624385633165 y[1] (numeric) = 1.7456243856333 absolute error = 1.352251643993441e-13 relative error = 7.746521274122544e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.0001831554384666301 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] = 2.40012417206858 y[1] (closed_form) = 1.675371611640986 y[1] (numeric) = 1.675371611641192 absolute error = 2.05835348765504e-13 relative error = 1.228595180527699e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.0001831554384666301 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] = 2.500127041471458 y[1] (closed_form) = 1.598370360810931 y[1] (numeric) = 1.598370360811213 absolute error = 2.817746036498647e-13 relative error = 1.76288681621265e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.0001831554384666301 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] = 2.600129910874335 y[1] (closed_form) = 1.515390048304603 y[1] (numeric) = 1.515390048304965 absolute error = 3.623767952376511e-13 relative error = 2.391310380077216e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.0001831554384666301 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4416 Order of pole (three term test) = 32.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700132780277213 y[1] (closed_form) = 1.427259833517063 y[1] (numeric) = 1.427259833517512 absolute error = 4.496403249731884e-13 relative error = 3.150374685912528e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.0001831554384666301 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] = 2.800135649680091 y[1] (closed_form) = 1.33486033491518 y[1] (numeric) = 1.334860334915719 absolute error = 5.39346345362901e-13 relative error = 4.040470236889407e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.0001831554384666301 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] = 2.900138519082968 y[1] (closed_form) = 1.239114830684473 y[1] (numeric) = 1.239114830685106 absolute error = 6.328271240363392e-13 relative error = 5.107090225744234e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.0001831554384666301 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] = 3.000141388485846 y[1] (closed_form) = 1.140980033109696 y[1] (numeric) = 1.140980033110425 absolute error = 7.291944825738028e-13 relative error = 6.390948670560096e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.0001831554384666301 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] = 3.100144257888723 y[1] (closed_form) = 1.041436528873809 y[1] (numeric) = 1.041436528874634 absolute error = 8.251177519014163e-13 relative error = 7.922880838390452e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.0001831554384666301 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] = 3.200147127291601 y[1] (closed_form) = 0.9414789807981639 y[1] (numeric) = 0.9414789807990865 absolute error = 9.225953334635051e-13 relative error = 9.799425715073854e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.0001831554384666301 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] = 3.300149996694479 y[1] (closed_form) = 0.8421061889305169 y[1] (numeric) = 0.8421061889315354 absolute error = 1.018518602791119e-12 relative error = 1.209489511156125e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.0001831554384666301 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1559 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.400152866097356 y[1] (closed_form) = 0.7443111102928612 y[1] (numeric) = 0.7443111102939742 absolute error = 1.112998582186719e-12 relative error = 1.495340546171335e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.0001831554384666301 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] = 3.500155735500234 y[1] (closed_form) = 0.6490709370141956 y[1] (numeric) = 0.6490709370154012 absolute error = 1.205591182440457e-12 relative error = 1.857410513535426e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.0001831554384666301 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] = 3.600158604903112 y[1] (closed_form) = 0.5573373319899216 y[1] (numeric) = 0.5573373319912172 absolute error = 1.295519247435095e-12 relative error = 2.324479580094811e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.0001831554384666301 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] = 3.700161474305989 y[1] (closed_form) = 0.470026919635533 y[1] (numeric) = 0.4700269196369127 absolute error = 1.379674152701682e-12 relative error = 2.935308798422663e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.0001831554384666301 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] = 3.800164343708867 y[1] (closed_form) = 0.3880121267532866 y[1] (numeric) = 0.3880121267547458 absolute error = 1.459277143567306e-12 relative error = 3.760906020587268e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.0001831554384666301 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] = 3.899984057673278 y[1] (closed_form) = 0.3122454139533981 y[1] (numeric) = 0.3122454139549311 absolute error = 1.532940441251185e-12 relative error = 4.909408986483858e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.0001831554384666301 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] = 3.999986927076155 y[1] (closed_form) = 0.2432060497900179 y[1] (numeric) = 0.2432060497916183 absolute error = 1.600330978845932e-12 relative error = 6.580144614937187e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.0001831554384666301 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] = 4.09998979647879 y[1] (closed_form) = 0.1817287542065158 y[1] (numeric) = 0.1817287542080273 absolute error = 1.511457625724688e-12 relative error = 8.317107726425472e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.0001831554384666301 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] = 4.199992665881426 y[1] (closed_form) = 0.1284278232408488 y[1] (numeric) = 0.1284278232422827 absolute error = 1.433964058605852e-12 relative error = 1.116552490278255e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.0001831554384666301 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] = 4.299995535284061 y[1] (closed_form) = 0.08383585271412841 y[1] (numeric) = 0.08383585271549775 absolute error = 1.36933520078486e-12 relative error = 1.63335274402725e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.0001831554384666301 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] = 4.399998404686696 y[1] (closed_form) = 0.04839841640391129 y[1] (numeric) = 0.04839841640522933 absolute error = 1.318035958153274e-12 relative error = 2.723303893155392e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.0001831554384666301 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] = 4.500001274089331 y[1] (closed_form) = 0.02246961376301726 y[1] (numeric) = 0.02246961376429774 absolute error = 1.280475725451424e-12 relative error = 5.698699314355636e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.0001831554384666301 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] = 4.600004143491966 y[1] (closed_form) = 0.006308531671971318 y[1] (numeric) = 0.006308531673228393 absolute error = 1.257075173122235e-12 relative error = 1.992658891937399e-08 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 10 h = 0.0001831554384666301 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] = 4.700007012894601 y[1] (closed_form) = 7.665558009650741e-05 y[1] (numeric) = 7.665558134451521e-05 absolute error = 1.248007800618359e-12 relative error = 1.628071692950662e-06 % Desired digits = 16 Estimated correct digits = 7 Correct digits = 8 h = 0.0001831554384666301 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] = 4.800009882297236 y[1] (closed_form) = 0.00383625590376413 y[1] (numeric) = 0.003836255905017673 absolute error = 1.253542842444277e-12 relative error = 3.26762049740817e-08 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 10 h = 0.0001831554384666301 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] = 4.900012751699871 y[1] (closed_form) = 0.01754976580530088 y[1] (numeric) = 0.01754976580657429 absolute error = 1.273415400904199e-12 relative error = 7.256025037778942e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 h = 0.0001831554384666301 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 ) = cos ( x ) ; Iterations = 18910 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %