##############ECHO OF PROBLEM################# ##############temp/sub_c_sinpostode.ode################# diff ( y , x , 1 ) = 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(2.0 + cos(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 = 3.095004165278026 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 3.095004165278026 desired_abs_gbl_error = 3.095004165278026e-16 range = 4.9 estimated_steps = 4900000.000000001 step_error = 3.495450903566708e-21 est_needed_step_err = 3.495450903566708e-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 = 3.095004165278026 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 3.095004165278026 desired_abs_gbl_error = 3.095004165278026e-16 range = 4.9 estimated_steps = 2450000 step_error = 4.943314074433328e-21 est_needed_step_err = 4.943314074433328e-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 = 3.095004165278026 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 3.095004165278026 desired_abs_gbl_error = 3.095004165278026e-16 range = 4.9 estimated_steps = 1225000 step_error = 6.990901807133415e-21 est_needed_step_err = 6.990901807133415e-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 = 3.095004165278026 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 3.095004165278026 desired_abs_gbl_error = 3.095004165278026e-16 range = 4.9 estimated_steps = 612500.0000000001 step_error = 9.886628148866656e-21 est_needed_step_err = 9.886628148866656e-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 = 3.095004165278026 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 3.095004165278026 desired_abs_gbl_error = 3.095004165278026e-16 range = 4.9 estimated_steps = 306250.0000000001 step_error = 1.398180361426683e-20 est_needed_step_err = 1.398180361426683e-20 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 = 3.095004165278026 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 3.095004165278026 desired_abs_gbl_error = 3.095004165278026e-16 range = 4.9 estimated_steps = 153125 step_error = 1.977325629773331e-20 est_needed_step_err = 1.977325629773331e-20 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 = 3.095004165278026 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 3.095004165278026 desired_abs_gbl_error = 3.095004165278026e-16 range = 4.9 estimated_steps = 76562.50000000001 step_error = 2.796360722853366e-20 est_needed_step_err = 2.796360722853366e-20 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 = 3.095004165278026 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 3.095004165278026 desired_abs_gbl_error = 3.095004165278026e-16 range = 4.9 estimated_steps = 38281.25000000001 step_error = 3.954651259546662e-20 est_needed_step_err = 3.954651259546662e-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) = 3.095004165278026 y[1] (numeric) = 3.095004165278026 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) = 3.180143501069363 y[1] (numeric) = 3.18014350106937 absolute error = 6.217248937900877e-15 relative error = 1.955021506359775e-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) = 3.255381573875861 y[1] (numeric) = 3.255381573875864 absolute error = 3.108624468950438e-15 relative error = 9.549186165753547e-14 % Desired digits = 16 Estimated correct digits = 12 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] = 0.40003200000001 y[1] (closed_form) = 3.321080532144356 y[1] (numeric) = 3.321080532144348 absolute error = 7.993605777301127e-15 relative error = 2.406929220755696e-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) = 3.377582561890385 y[1] (numeric) = 3.377582561890368 absolute error = 1.687538997430238e-14 relative error = 4.996292367419574e-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) = 3.425377405429185 y[1] (numeric) = 3.425377405429165 absolute error = 1.953992523340276e-14 relative error = 5.704459077248595e-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] = 0.7000640000000499 y[1] (closed_form) = 3.464864955786155 y[1] (numeric) = 3.464864955786125 absolute error = 2.97539770599542e-14 relative error = 8.587341047813858e-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] = 0.8000320000000631 y[1] (closed_form) = 3.496715753595565 y[1] (numeric) = 3.49671575359553 absolute error = 3.508304757815495e-14 relative error = 1.003314254013359e-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) = 3.521609968270681 y[1] (numeric) = 3.521609968270641 absolute error = 3.996802888650564e-14 relative error = 1.134936271949852e-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) = 3.540317522164023 y[1] (numeric) = 3.540317522163983 absolute error = 4.04121180963557e-14 relative error = 1.141482871052022e-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) = 3.553603083225609 y[1] (numeric) = 3.553603083225581 absolute error = 2.842170943040401e-14 relative error = 7.997997740537076e-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] = 1.200031999999943 y[1] (closed_form) = 3.562359929040396 y[1] (numeric) = 3.562359929040372 absolute error = 2.442490654175344e-14 relative error = 6.856383697402765e-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) = 3.567498828624583 y[1] (numeric) = 3.567498828624557 absolute error = 2.620126338115369e-14 relative error = 7.344435034125956e-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) = 3.569968538943096 y[1] (numeric) = 3.569968538943068 absolute error = 2.797762022055394e-14 relative error = 7.836937473078359e-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] = 1.500063999999722 y[1] (closed_form) = 3.570737361843733 y[1] (numeric) = 3.570737361843701 absolute error = 3.241851231905457e-14 relative error = 9.078940575544159e-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] = 1.600031999999649 y[1] (closed_form) = 3.570800491358369 y[1] (numeric) = 3.570800491358335 absolute error = 3.419486915845482e-14 relative error = 9.576247466418024e-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] = 1.699999999999575 y[1] (closed_form) = 3.571155505704472 y[1] (numeric) = 3.571155505704438 absolute error = 3.419486915845482e-14 relative error = 9.575295476165298e-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] = 1.800095999999502 y[1] (closed_form) = 3.572800416981426 y[1] (numeric) = 3.572800416981389 absolute error = 3.730349362740526e-14 relative error = 1.044096766505701e-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] = 1.900063999999428 y[1] (closed_form) = 3.576713870592992 y[1] (numeric) = 3.576713870592961 absolute error = 3.108624468950438e-14 relative error = 8.691286419383197e-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] = 2.000031999999355 y[1] (closed_form) = 3.583856066148213 y[1] (numeric) = 3.583856066148183 absolute error = 2.97539770599542e-14 relative error = 8.302224339029495e-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] = 2.099999999999455 y[1] (closed_form) = 3.595153895400068 y[1] (numeric) = 3.595153895400025 absolute error = 4.352074256530614e-14 relative error = 1.210539070969677e-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] = 2.200095999999555 y[1] (closed_form) = 3.611517269801735 y[1] (numeric) = 3.611517269801678 absolute error = 5.639932965095795e-14 relative error = 1.561651943977944e-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] = 2.300063999999655 y[1] (closed_form) = 3.633740254951075 y[1] (numeric) = 3.633740254950998 absolute error = 7.682743330406083e-14 relative error = 2.114279720444555e-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] = 2.400031999999755 y[1] (closed_form) = 3.662616670014446 y[1] (numeric) = 3.662616670014344 absolute error = 1.021405182655144e-13 relative error = 2.788730775506232e-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) = 3.698856384453008 y[1] (numeric) = 3.698856384452872 absolute error = 1.358912982141192e-13 relative error = 3.673873329748512e-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) = 3.743157762447956 y[1] (numeric) = 3.743157762447778 absolute error = 1.77635683940025e-13 relative error = 4.745610396711001e-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) = 3.795964507522194 y[1] (numeric) = 3.795964507521966 absolute error = 2.273736754432321e-13 relative error = 5.989878856682189e-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] = 2.800032000000155 y[1] (closed_form) = 3.85779894019306 y[1] (numeric) = 3.857798940192776 absolute error = 2.833289158843399e-13 relative error = 7.344315250140046e-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] = 2.900000000000255 y[1] (closed_form) = 3.929041834850604 y[1] (numeric) = 3.929041834850247 absolute error = 3.561595462997502e-13 relative error = 9.064793943923294e-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] = 3.000096000000355 y[1] (closed_form) = 4.010089960440992 y[1] (numeric) = 4.01008996044055 absolute error = 4.423128530106624e-13 relative error = 1.102999826373025e-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) = 4.100926190610991 y[1] (numeric) = 4.100926190610451 absolute error = 5.400124791776761e-13 relative error = 1.316806141046934e-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) = 4.201739092689551 y[1] (numeric) = 4.201739092688897 absolute error = 6.536993168992922e-13 relative error = 1.55578274252354e-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) = 4.312520230091893 y[1] (numeric) = 4.31252023009114 absolute error = 7.531752999057062e-13 relative error = 1.746485256231847e-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) = 4.43332234382225 y[1] (numeric) = 4.433322343821374 absolute error = 8.757439218243235e-13 relative error = 1.975367126292217e-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) = 4.563629764754779 y[1] (numeric) = 4.563629764753769 absolute error = 1.009858863199042e-12 relative error = 2.212841346154437e-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) = 4.703287744780555 y[1] (numeric) = 4.703287744779398 absolute error = 1.157296480869263e-12 relative error = 2.460611690521308e-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) = 4.851899968291207 y[1] (numeric) = 4.851899968289895 absolute error = 1.311839525897085e-12 relative error = 2.703764575672203e-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) = 5.009187030089665 y[1] (numeric) = 5.009187030088199 absolute error = 1.465494392505207e-12 relative error = 2.925613245626754e-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) = 5.174175714322846 y[1] (numeric) = 5.174175714321218 absolute error = 1.62803104331033e-12 relative error = 3.146454881313193e-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) = 5.346412597153281 y[1] (numeric) = 5.346412597151479 absolute error = 1.801225835151854e-12 relative error = 3.369036344316045e-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) = 5.525176053469377 y[1] (numeric) = 5.525176053467399 absolute error = 1.978861519091879e-12 relative error = 3.581535683101553e-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) = 5.709918852195357 y[1] (numeric) = 5.709918852193204 absolute error = 2.152944489353104e-12 relative error = 3.770534301946054e-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) = 5.899323463363945 y[1] (numeric) = 5.899323463361602 absolute error = 2.34301467116893e-12 relative error = 3.971666727073961e-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) = 6.09272958144872 y[1] (numeric) = 6.092729581446179 absolute error = 2.540190280342358e-12 relative error = 4.169215532028184e-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) = 6.28920420057289 y[1] (numeric) = 6.289204200570154 absolute error = 2.735589532676386e-12 relative error = 4.349659265996163e-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) = 6.488038867921845 y[1] (numeric) = 6.488038867918915 absolute error = 2.930100606590713e-12 relative error = 4.516157603613803e-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) = 6.687739331655033 y[1] (numeric) = 6.687739331651898 absolute error = 3.134381643121742e-12 relative error = 4.686758092208818e-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) = 6.887562860666427 y[1] (numeric) = 6.887562860663094 absolute error = 3.33333360913457e-12 relative error = 4.839641650562073e-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) = 7.086512369427046 y[1] (numeric) = 7.086512369423512 absolute error = 3.534061931986798e-12 relative error = 4.987025701434755e-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 ) = 1.0 - sin ( x ) ; Iterations = 38282 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Time to Timeout = 2 Minutes 59.0 Seconds Percent Done = 100 %