##############ECHO OF PROBLEM################# ##############temp/mtest1postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ; diff ( y2 , x , 1 ) = y1 - 1.0 ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=10.0; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(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_y1 (double x) { return(1.0 + cos(x)); } double exact_soln_y2 (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 = 9.9 estimated_steps = 9900000 step_error = 7.945521577046603e-22 est_needed_step_err = 7.945521577046603e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.995004165278026 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 9.9 estimated_steps = 9900000 step_error = 8.738750143124259e-22 est_needed_step_err = 8.738750143124259e-22 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.995004165278026 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 9.9 estimated_steps = 4950000 step_error = 1.235845897059615e-21 est_needed_step_err = 1.235845897059615e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.995004165278026 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 9.9 estimated_steps = 2475000 step_error = 1.747750028624852e-21 est_needed_step_err = 1.747750028624852e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.995004165278026 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 9.9 estimated_steps = 1237500 step_error = 2.47169179411923e-21 est_needed_step_err = 2.47169179411923e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.995004165278026 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 9.9 estimated_steps = 618750 step_error = 3.495500057249703e-21 est_needed_step_err = 3.495500057249703e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.995004165278026 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 9.9 estimated_steps = 309375 step_error = 4.943383588238461e-21 est_needed_step_err = 4.943383588238461e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.995004165278026 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 9.9 estimated_steps = 154687.5 step_error = 6.991000114499407e-21 est_needed_step_err = 6.991000114499407e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 1.995004165278026 min_size = 1.099833416646828 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1.099833416646828 desired_abs_gbl_error = 1.099833416646828e-16 range = 9.9 estimated_steps = 77343.75 step_error = 9.886767176476921e-21 est_needed_step_err = 9.886767176476921e-21 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09933 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y1[1] (closed_form) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.000128 y2[1] (closed_form) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2000959999999943 y1[1] (closed_form) = 1.980047501069369 y1[1] (numeric) = 1.980047501069369 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.000128 y2[1] (closed_form) = 1.198763416270916 y2[1] (numeric) = 1.198763416270922 absolute error = 6.883382752675971e-15 relative error = 5.742069418575212e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3000639999999968 y1[1] (closed_form) = 1.955317573875865 y1[1] (numeric) = 1.955317573875863 absolute error = 1.332267629550188e-15 relative error = 6.813561374121666e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.000128 y2[1] (closed_form) = 1.295581347591373 y2[1] (numeric) = 1.295581347591377 absolute error = 3.33066907387547e-15 relative error = 2.570791158785626e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.40003200000001 y1[1] (closed_form) = 1.921048532144346 y1[1] (numeric) = 1.921048532144348 absolute error = 1.554312234475219e-15 relative error = 8.090957664355506e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.000128 y2[1] (closed_form) = 1.389447816061081 y2[1] (numeric) = 1.389447816061071 absolute error = 9.103828801926284e-15 relative error = 6.552119983702991e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5000000000000233 y1[1] (closed_form) = 1.877582561890362 y1[1] (numeric) = 1.877582561890368 absolute error = 5.995204332975845e-15 relative error = 3.193044319148255e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000128 y2[1] (closed_form) = 1.479425538604223 y2[1] (numeric) = 1.479425538604204 absolute error = 1.931788062847772e-14 relative error = 1.305769038346015e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6000960000000366 y1[1] (closed_form) = 1.825281405429148 y1[1] (numeric) = 1.825281405429164 absolute error = 1.598721155460225e-14 relative error = 8.758765364644387e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000128 y2[1] (closed_form) = 1.564721703012103 y2[1] (numeric) = 1.564721703012072 absolute error = 3.064215547965432e-14 relative error = 1.958313444535722e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7000640000000499 y1[1] (closed_form) = 1.764800955786104 y1[1] (numeric) = 1.764800955786132 absolute error = 2.753353101070388e-14 relative error = 1.560149370977617e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 y2[1] (closed_form) = 1.644266635818324 y2[1] (numeric) = 1.644266635818287 absolute error = 3.752553823233029e-14 relative error = 2.282205173715907e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8000320000000631 y1[1] (closed_form) = 1.696683753595501 y1[1] (numeric) = 1.696683753595541 absolute error = 3.952393967665557e-14 relative error = 2.329481825525766e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y2[1] (closed_form) = 1.717378385146976 y2[1] (numeric) = 1.71737838514693 absolute error = 4.529709940470639e-14 relative error = 2.637572464895661e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9000000000000764 y1[1] (closed_form) = 1.621609968270604 y1[1] (numeric) = 1.621609968270658 absolute error = 5.306866057708248e-14 relative error = 3.2725909198547e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y2[1] (closed_form) = 1.783326909627531 y2[1] (numeric) = 1.783326909627479 absolute error = 5.173639294753229e-14 relative error = 2.901116596638923e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.00009600000009 y1[1] (closed_form) = 1.540221522163934 y1[1] (numeric) = 1.540221522164003 absolute error = 6.905587213168474e-14 relative error = 4.483502609070461e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y2[1] (closed_form) = 1.84152284995173 y2[1] (numeric) = 1.841522849951676 absolute error = 5.373479439185758e-14 relative error = 2.917954256894834e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.100064000000016 y1[1] (closed_form) = 1.453539083225593 y1[1] (numeric) = 1.453539083225604 absolute error = 1.043609643147647e-14 relative error = 7.179783847516098e-13 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y2[1] (closed_form) = 1.891236388388001 y2[1] (numeric) = 1.891236388387988 absolute error = 1.332267629550188e-14 relative error = 7.044426797888277e-13 % Desired digits = 16 Estimated correct digits = 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.200031999999943 y1[1] (closed_form) = 1.362327929040454 y1[1] (numeric) = 1.362327929040397 absolute error = 5.706546346573305e-14 relative error = 4.188819905199088e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y2[1] (closed_form) = 1.932050680938143 y2[1] (numeric) = 1.932050680938156 absolute error = 1.332267629550188e-14 relative error = 6.895614295704089e-13 % Desired digits = 16 Estimated correct digits = 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.299999999999869 y1[1] (closed_form) = 1.267498828624713 y1[1] (numeric) = 1.267498828624586 absolute error = 1.27675647831893e-13 relative error = 1.007303872386424e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.963558185417158 y2[1] (numeric) = 1.963558185417188 absolute error = 3.042011087472929e-14 relative error = 1.549233992689987e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.400095999999796 y1[1] (closed_form) = 1.1698725389433 y1[1] (numeric) = 1.169872538943099 absolute error = 2.009503674571533e-13 relative error = 1.717711637531589e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.985466042293166 y2[1] (numeric) = 1.985466042293197 absolute error = 3.019806626980426e-14 relative error = 1.520956069081202e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.500063999999722 y1[1] (closed_form) = 1.070673361844011 y1[1] (numeric) = 1.070673361843734 absolute error = 2.76889622341514e-13 relative error = 2.586126004523262e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.997499511742069 y2[1] (numeric) = 1.99749951174208 absolute error = 1.176836406102666e-14 relative error = 5.891547903690439e-13 % Desired digits = 16 Estimated correct digits = 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.600031999999649 y1[1] (closed_form) = 0.9707684913587206 y1[1] (numeric) = 0.9707684913583713 absolute error = 3.492761635470742e-13 relative error = 3.597934694586301e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.99957266814502 y2[1] (numeric) = 1.999572668145002 absolute error = 1.798561299892754e-14 relative error = 8.994728366442703e-13 % Desired digits = 16 Estimated correct digits = 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.699999999999575 y1[1] (closed_form) = 0.8711555057048963 y1[1] (numeric) = 0.8711555057044799 absolute error = 4.164446565368962e-13 relative error = 4.780371056714262e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.991664810452523 y2[1] (numeric) = 1.991664810452461 absolute error = 6.283862319378386e-14 relative error = 3.155080255673463e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.800095999999502 y1[1] (closed_form) = 0.7727044169819246 y1[1] (numeric) = 0.7727044169814439 absolute error = 4.807265696626928e-13 relative error = 6.2213513873823e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.973825814989762 y2[1] (numeric) = 1.973825814989642 absolute error = 1.199040866595169e-13 relative error = 6.074704553407559e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.900063999999428 y1[1] (closed_form) = 0.6766498705935637 y1[1] (numeric) = 0.6766498705930278 absolute error = 5.359046539865631e-13 relative error = 7.919969799395105e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.946279395217312 y2[1] (numeric) = 1.94627939521712 absolute error = 1.91180404840452e-13 relative error = 9.822865376381675e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.000031999999355 y1[1] (closed_form) = 0.5838240661488576 y1[1] (numeric) = 0.5838240661482764 absolute error = 5.812017533912694e-13 relative error = 9.955083853002395e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.909284109661622 y2[1] (numeric) = 1.909284109661346 absolute error = 2.76667577736589e-13 relative error = 1.449064475719237e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.099999999999455 y1[1] (closed_form) = 0.4951538954006128 y1[1] (numeric) = 0.4951538954001461 absolute error = 4.667377595524158e-13 relative error = 9.426115070240809e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.863209366649149 y2[1] (numeric) = 1.863209366648868 absolute error = 2.802202914153895e-13 relative error = 1.503965665003853e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.200095999999555 y1[1] (closed_form) = 0.4114212698021795 y1[1] (numeric) = 0.4114212698018239 absolute error = 3.556599459386689e-13 relative error = 8.64466599185983e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.808439903987131 y2[1] (numeric) = 1.808439903986865 absolute error = 2.653433028854124e-13 relative error = 1.467249767605773e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.300063999999655 y1[1] (closed_form) = 0.3336762549514194 y1[1] (numeric) = 0.3336762549511675 absolute error = 2.51909604287448e-13 relative error = 7.549521446293026e-11 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.745662568984413 y2[1] (numeric) = 1.745662568984179 absolute error = 2.33812968986058e-13 relative error = 1.33939383899424e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.400031999999755 y1[1] (closed_form) = 0.2625846700146914 y1[1] (numeric) = 0.2625846700145319 absolute error = 1.59539048638635e-13 relative error = 6.075718305631052e-11 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.675439583606601 y2[1] (numeric) = 1.675439583606416 absolute error = 1.854072451124011e-13 relative error = 1.106618507325033e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.499999999999855 y1[1] (closed_form) = 0.1988563844531529 y1[1] (numeric) = 0.1988563844530729 absolute error = 8.004708007547379e-14 relative error = 4.02537139029255e-11 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.598472144104072 y2[1] (numeric) = 1.598472144103952 absolute error = 1.199040866595169e-13 relative error = 7.501168356407107e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.600095999999955 y1[1] (closed_form) = 0.1430617624480003 y1[1] (numeric) = 0.1430617624479844 absolute error = 1.584843367652411e-14 relative error = 1.107803609107965e-11 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.515419108125875 y2[1] (numeric) = 1.515419108125831 absolute error = 4.352074256530614e-14 relative error = 2.871861805882098e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.700064000000055 y1[1] (closed_form) = 0.09590050752213863 y1[1] (numeric) = 0.09590050752216998 absolute error = 3.134992265785286e-14 relative error = 3.269004874725582e-11 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.427322018741456 y2[1] (numeric) = 1.427322018741502 absolute error = 4.596323321948148e-14 relative error = 3.22024270738916e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.800032000000155 y1[1] (closed_form) = 0.05776694019290451 y1[1] (numeric) = 0.05776694019296466 absolute error = 6.014633235906786e-14 relative error = 1.041189513555984e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.334957998869348 y2[1] (numeric) = 1.334957998869492 absolute error = 1.432187701766452e-13 relative error = 1.072833529578798e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.900000000000255 y1[1] (closed_form) = 0.02904183485034839 y1[1] (numeric) = 0.02904183485041817 absolute error = 6.978098654464304e-14 relative error = 2.402774718065238e-10 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.239249329213735 y2[1] (numeric) = 1.239249329213977 absolute error = 2.420286193682841e-13 relative error = 1.953026026827417e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.000096000000355 y1[1] (closed_form) = 0.00999396044063694 y1[1] (numeric) = 0.009993960440696193 absolute error = 5.92529497689398e-14 relative error = 5.928875756602801e-10 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.141024968129707 y2[1] (numeric) = 1.141024968130056 absolute error = 3.497202527569243e-13 relative error = 3.064965820425146e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.100064000000455 y1[1] (closed_form) = 0.0008621906105364952 y1[1] (numeric) = 0.0008621906105647492 absolute error = 2.825409177453775e-14 relative error = 3.277012232475686e-09 % Desired digits = 16 Estimated correct digits = 8 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 1.041516717698105 y2[1] (numeric) = 1.041516717698559 absolute error = 4.54081217071689e-13 relative error = 4.359807282549156e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.200032000000555 y1[1] (closed_form) = 0.001707092688995604 y1[1] (numeric) = 0.001707092688972456 absolute error = 2.314815006343451e-14 relative error = 1.355998430117705e-09 % Desired digits = 16 Estimated correct digits = 8 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 0.9415939111689333 y2[1] (numeric) = 0.9415939111694895 absolute error = 5.562217353372034e-13 relative error = 5.907235897975242e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.300000000000655 y1[1] (closed_form) = 0.01252023009123848 y1[1] (numeric) = 0.01252023009114406 absolute error = 9.442099879741761e-14 relative error = 7.541474726050951e-10 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.8422543058561045 y2[1] (numeric) = 0.8422543058567552 absolute error = 6.507017147328042e-13 relative error = 7.725715501939788e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.400096000000755 y1[1] (closed_form) = 0.03322634382149503 y1[1] (numeric) = 0.03322634382131044 absolute error = 1.845884556317401e-13 relative error = 5.555485027886962e-10 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.7443660865236267 y2[1] (numeric) = 0.7443660865243622 absolute error = 7.355227538141662e-13 relative error = 9.88119645871078e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.500064000000855 y1[1] (closed_form) = 0.06356576475392384 y1[1] (numeric) = 0.06356576475363157 absolute error = 2.922662112325725e-13 relative error = 4.597855659630544e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.6491568398000376 y2[1] (numeric) = 0.6491568398008458 absolute error = 8.08242361927114e-13 relative error = 1.245064847774045e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.600032000000955 y1[1] (closed_form) = 0.1032557447795991 y1[1] (numeric) = 0.1032557447791831 absolute error = 4.159450561758149e-13 relative error = 4.028299413884e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.5574508606615436 y2[1] (numeric) = 0.5574508606624083 absolute error = 8.647527138805344e-13 relative error = 1.551262676057772e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.700000000001055 y1[1] (closed_form) = 0.151899968290151 y1[1] (numeric) = 0.1518999682895982 absolute error = 5.527522883852498e-13 relative error = 3.638923000493409e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.4701638590906118 y2[1] (numeric) = 0.4701638590915148 absolute error = 9.030554082301023e-13 relative error = 1.920724851069555e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.800096000001155 y1[1] (closed_form) = 0.2090910300885098 y1[1] (numeric) = 0.2090910300878085 absolute error = 7.013001290800958e-13 relative error = 3.354042154669333e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.388066178975581 y2[1] (numeric) = 0.3880661789765036 absolute error = 9.225953334635051e-13 relative error = 2.377417521668538e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.900064000001255 y1[1] (closed_form) = 0.2741117143215904 y1[1] (numeric) = 0.274111714320732 absolute error = 8.58424442640171e-13 relative error = 3.131659092953099e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.3121873825562229 y2[1] (numeric) = 0.3121873825571427 absolute error = 9.197642647507109e-13 relative error = 2.946192947388152e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.000032000001355 y1[1] (closed_form) = 0.3463805971519252 y1[1] (numeric) = 0.3463805971509033 absolute error = 1.021849271864994e-12 relative error = 2.950076535080293e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.2431765884828047 y2[1] (numeric) = 0.2431765884836998 absolute error = 8.951173136040325e-13 relative error = 3.680935402493844e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.100000000001455 y1[1] (closed_form) = 0.425176053467922 y1[1] (numeric) = 0.4251760534667335 absolute error = 1.18849374786123e-12 relative error = 2.795297943445673e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.181722888934753 y2[1] (numeric) = 0.1817228889355991 absolute error = 8.461009670668318e-13 relative error = 4.655995576708126e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.200096000001555 y1[1] (closed_form) = 0.5098228521938013 y1[1] (numeric) = 0.5098228521924468 absolute error = 1.354472090042691e-12 relative error = 2.656750446187942e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.1283771665630942 y2[1] (numeric) = 0.1283771665638663 absolute error = 7.721601136267964e-13 relative error = 6.01477766100484e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.300064000001655 y1[1] (closed_form) = 0.5992594633622901 y1[1] (numeric) = 0.5992594633607724 absolute error = 1.517674874662589e-12 relative error = 2.53258390972636e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.08380841397919381 y2[1] (numeric) = 0.08380841397986727 absolute error = 6.7346128673762e-13 relative error = 8.035724037264478e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.400032000001755 y1[1] (closed_form) = 0.6926975814469645 y1[1] (numeric) = 0.6926975814452911 absolute error = 1.673328142715036e-12 relative error = 2.415669099377608e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.04838809194532723 y2[1] (numeric) = 0.04838809194587665 absolute error = 5.494216193113743e-13 relative error = 1.135447993965448e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.500000000001855 y1[1] (closed_form) = 0.789204200571034 y1[1] (numeric) = 0.7892042005692176 absolute error = 1.816435890589219e-12 relative error = 2.301604438084496e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.02246988233451186 y2[1] (numeric) = 0.0224698823349126 absolute error = 4.007419396323542e-13 relative error = 1.783462564095621e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.600096000001956 y1[1] (closed_form) = 0.8879428679198897 y1[1] (numeric) = 0.8879428679179431 absolute error = 1.946665051377749e-12 relative error = 2.192331423234516e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.006298234302675287 y2[1] (numeric) = 0.006298234302903792 absolute error = 2.285047151495689e-13 relative error = 3.628075809318613e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.700064000002055 y1[1] (closed_form) = 0.9876753316529769 y1[1] (numeric) = 0.9876753316509163 absolute error = 2.060684956006753e-12 relative error = 2.086399133364993e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 7.595160925555344e-05 y2[1] (numeric) = 7.595160928975819e-05 absolute error = 3.42047489507516e-14 relative error = 4.503492327024079e-08 % Desired digits = 16 Estimated correct digits = 7 Correct digits = 10 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.800032000002155 y1[1] (closed_form) = 1.087530860664272 y1[1] (numeric) = 1.08753086066212 absolute error = 2.151612221723553e-12 relative error = 1.978437853624985e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.003838191641853839 y2[1] (numeric) = 0.00383819164167357 absolute error = 1.802689941765578e-13 relative error = 4.696716865588511e-09 % Desired digits = 16 Estimated correct digits = 8 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.900000000002255 y1[1] (closed_form) = 1.186512369424791 y1[1] (numeric) = 1.186512369422571 absolute error = 2.220668093855238e-12 relative error = 1.871592872589938e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.01754738737608819 y2[1] (numeric) = 0.01754738737567541 absolute error = 4.127774511086812e-13 relative error = 2.352358458052695e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.000096000002356 y1[1] (closed_form) = 1.283754240888596 y1[1] (numeric) = 1.283754240886332 absolute error = 2.263522702605769e-12 relative error = 1.763205628079555e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.04110296132601565 y2[1] (numeric) = 0.04110296132535469 absolute error = 6.60964338816683e-13 relative error = 1.608069875000304e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.100064000002456 y1[1] (closed_form) = 1.378036994080784 y1[1] (numeric) = 1.378036994078505 absolute error = 2.279287869555446e-12 relative error = 1.654010653811104e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.07420951014478161 y2[1] (numeric) = 0.07420951014386028 absolute error = 9.21332454772994e-13 relative error = 1.241528818847461e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.200032000002555 y1[1] (closed_form) = 1.468544941611732 y1[1] (numeric) = 1.468544941609469 absolute error = 2.263300658000844e-12 relative error = 1.541185832227147e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.1165603372668519 y2[1] (numeric) = 0.1165603372656612 absolute error = 1.190644804971441e-12 relative error = 1.021483664932775e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.300000000002655 y1[1] (closed_form) = 1.554374336181371 y1[1] (numeric) = 1.554374336179154 absolute error = 2.216893335571513e-12 relative error = 1.426228730086828e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.167732557777571 y2[1] (numeric) = 0.1677325577761049 absolute error = 1.466160526319982e-12 relative error = 8.741061042330536e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.400096000002756 y1[1] (closed_form) = 1.63476705841079 y1[1] (numeric) = 1.634767058408651 absolute error = 2.139399768452677e-12 relative error = 1.308687838701898e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.2272964465226575 y2[1] (numeric) = 0.2272964465209134 absolute error = 1.744077104959274e-12 relative error = 7.673138457030036e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.500064000002856 y1[1] (closed_form) = 1.708714927422724 y1[1] (numeric) = 1.708714927420699 absolute error = 2.025712930731061e-12 relative error = 1.185518367178116e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.2945050307421021 y2[1] (numeric) = 0.2945050307400822 absolute error = 2.01993977100301e-12 relative error = 6.858761515594856e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.600032000002956 y1[1] (closed_form) = 1.775586078647434 y1[1] (numeric) = 1.775586078645554 absolute error = 1.880273714505165e-12 relative error = 1.058959482233313e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 0.3687581805612876 y2[1] (numeric) = 0.3687581805589978 absolute error = 2.289779477138154e-12 relative error = 6.209433709790182e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.700000000003056 y1[1] (closed_form) = 1.834712784840842 y1[1] (numeric) = 1.834712784839145 absolute error = 1.697308960046939e-12 relative error = 9.25108809439172e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 0.4493144574049127 y2[1] (numeric) = 0.4493144574023636 absolute error = 2.549072064539359e-12 relative error = 5.673247371700282e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.800096000003156 y1[1] (closed_form) = 1.885564114671466 y1[1] (numeric) = 1.885564114669989 absolute error = 1.477262756566233e-12 relative error = 7.834593080509629e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 0.53548283260342 y2[1] (numeric) = 0.5354828326006257 absolute error = 2.794320330679056e-12 relative error = 5.218319170184373e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.900064000003256 y1[1] (closed_form) = 1.92750235695231 y1[1] (numeric) = 1.927502356951081 absolute error = 1.228572799050198e-12 relative error = 6.373910748377858e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 0.6261826945580098 y2[1] (numeric) = 0.6261826945549883 absolute error = 3.021471961517364e-12 relative error = 4.825224311971868e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.000032000003356 y1[1] (closed_form) = 1.960179227455637 y1[1] (numeric) = 1.960179227454688 absolute error = 9.490186414495838e-13 relative error = 4.84148912587669e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 0.7206152273965244 y2[1] (numeric) = 0.7206152273932993 absolute error = 3.225086864233617e-12 relative error = 4.475463106553238e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.100000000003456 y1[1] (closed_form) = 1.983268438443214 y1[1] (numeric) = 1.983268438442571 absolute error = 6.434852650727407e-13 relative error = 3.244569684060776e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 0.8178374957313022 y2[1] (numeric) = 0.8178374957278992 absolute error = 3.402944592778567e-12 relative error = 4.160905571755044e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.200096000003556 y1[1] (closed_form) = 1.996550069014105 y1[1] (numeric) = 1.996550069013798 absolute error = 3.070876886113183e-13 relative error = 1.538091597988114e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 0.91700626561009 y2[1] (numeric) = 0.9170062656065406 absolute error = 3.549383009726625e-12 relative error = 3.870620237654755e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.300064000003656 y1[1] (closed_form) = 1.999857558246013 y1[1] (numeric) = 1.99985755824606 absolute error = 4.729550084903167e-14 relative error = 2.36494347579997e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y2[1] (closed_form) = 1.016877891406255 y2[1] (numeric) = 1.016877891402592 absolute error = 3.662847802843316e-12 relative error = 3.602052747727568e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.400032000003756 y1[1] (closed_form) = 1.99318118867469 y1[1] (numeric) = 1.993181188675115 absolute error = 4.249933738265099e-13 relative error = 2.132236528426688e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.116580986711945 y2[1] (numeric) = 1.116580986708204 absolute error = 3.740785459172002e-12 relative error = 3.350214183914855e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.500000000003856 y1[1] (closed_form) = 1.976587625727194 y1[1] (numeric) = 1.976587625728008 absolute error = 8.137934770502397e-13 relative error = 4.117163673686574e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.215119988091581 y2[1] (numeric) = 1.215119988087805 absolute error = 3.775424417540307e-12 relative error = 3.107038362087878e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.600096000003956 y1[1] (closed_form) = 1.950202679607774 y1[1] (numeric) = 1.950202679608993 absolute error = 1.219024881038422e-12 relative error = 6.250759953235185e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.311632584410242 y2[1] (numeric) = 1.311632584406469 absolute error = 3.772759882281207e-12 relative error = 2.876384688153792e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.700064000004056 y1[1] (closed_form) = 1.914357235966119 y1[1] (numeric) = 1.914357235967748 absolute error = 1.62891922173003e-12 relative error = 8.508961604065308e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y2[1] (closed_form) = 1.404908440312621 y2[1] (numeric) = 1.404908440308897 absolute error = 3.723688024592775e-12 relative error = 2.650484485497274e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.800032000004156 y1[1] (closed_form) = 1.869381678275406 y1[1] (numeric) = 1.869381678277449 absolute error = 2.043032409915213e-12 relative error = 1.092892068889863e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.494141171608922 y2[1] (numeric) = 1.494141171605292 absolute error = 3.629985201314412e-12 relative error = 2.42947940281009e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.900000000004256 y1[1] (closed_form) = 1.815725100122895 y1[1] (numeric) = 1.815725100125351 absolute error = 2.455369241260996e-12 relative error = 1.352280276950959e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.578439764391671 y2[1] (numeric) = 1.578439764388181 absolute error = 3.490541189421492e-12 relative error = 2.211387008972587e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.000096000004356 y1[1] (closed_form) = 1.753839180153081 y1[1] (numeric) = 1.753839180155941 absolute error = 2.859490422224553e-12 relative error = 1.630417688567641e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.657058970310984 y2[1] (numeric) = 1.657058970307685 absolute error = 3.298694650766265e-12 relative error = 1.990692371163587e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.100064000004456 y1[1] (closed_form) = 1.68450001101907 y1[1] (numeric) = 1.684500011022316 absolute error = 3.245625990189183e-12 relative error = 1.926759257321512e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.72901284962262 y2[1] (numeric) = 1.729012849619557 absolute error = 3.062439191126032e-12 relative error = 1.771206727465588e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.200032000004556 y1[1] (closed_form) = 1.608325916845524 y1[1] (numeric) = 1.60832591684914 absolute error = 3.61577434659921e-12 relative error = 2.248160219721496e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.793687330687628 y2[1] (numeric) = 1.793687330684845 absolute error = 2.783107078130342e-12 relative error = 1.551612162563143e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.300000000004656 y1[1] (closed_form) = 1.526077517377146 y1[1] (numeric) = 1.526077517381105 absolute error = 3.959277350418233e-12 relative error = 2.594414310763848e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.850436620631014 y2[1] (numeric) = 1.850436620628553 absolute error = 2.461142400989047e-12 relative error = 1.330033341076971e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.400096000004756 y1[1] (closed_form) = 1.438461049572225 y1[1] (numeric) = 1.438461049576498 absolute error = 4.273470466387153e-12 relative error = 2.970862831258457e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.898750192215847 y2[1] (numeric) = 1.898750192213754 absolute error = 2.09365857983812e-12 relative error = 1.102650884998629e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.500064000004856 y1[1] (closed_form) = 1.346575285122089 y1[1] (numeric) = 1.346575285126644 absolute error = 4.554578936222242e-12 relative error = 3.382342589043801e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.938022159515724 y2[1] (numeric) = 1.938022159514033 absolute error = 1.690869666504113e-12 relative error = 8.724717920287508e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.600032000004956 y1[1] (closed_form) = 1.251228869019314 y1[1] (numeric) = 1.251228869024114 absolute error = 4.800604358479177e-12 relative error = 3.836711633932956e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.967927711852118 y2[1] (numeric) = 1.967927711850867 absolute error = 1.250999304147626e-12 relative error = 6.356937282875328e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.700000000005056 y1[1] (closed_form) = 1.153373862032869 y1[1] (numeric) = 1.15337386203787 absolute error = 5.000888592121555e-12 relative error = 4.335878206314893e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.988168233877776 y2[1] (numeric) = 1.988168233876995 absolute error = 7.80486786311485e-13 relative error = 3.925657663231059e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.800096000005156 y1[1] (closed_form) = 1.053859560147866 y1[1] (numeric) = 1.053859560153021 absolute error = 5.155209592544452e-12 relative error = 4.891742493488534e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.998548520493961 y2[1] (numeric) = 1.99854852049368 absolute error = 2.813305144400147e-13 relative error = 1.407674177309846e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.900064000005256 y1[1] (closed_form) = 0.9539339422035915 y1[1] (numeric) = 0.9539339422088462 absolute error = 5.254685575550866e-12 relative error = 5.508437579453898e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.998938395657659 y2[1] (numeric) = 1.998938395657901 absolute error = 2.418065747633591e-13 relative error = 1.2096749719183e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.000032000005355 y1[1] (closed_form) = 0.8544683067966981 y1[1] (numeric) = 0.8544683068019999 absolute error = 5.301870054097435e-12 relative error = 6.204876192510319e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.98935359011497 y2[1] (numeric) = 1.989353590115749 absolute error = 7.789324740770098e-13 relative error = 3.91550540812603e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.100000000005455 y1[1] (closed_form) = 0.7564558462589179 y1[1] (numeric) = 0.756455846264212 absolute error = 5.294098492925059e-12 relative error = 6.998555856375796e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.969889810843758 y2[1] (numeric) = 1.969889810845089 absolute error = 1.330935361920638e-12 relative error = 6.756394974958329e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.200096000005555 y1[1] (closed_form) = 0.6607548304404623 y1[1] (numeric) = 0.6607548304456897 absolute error = 5.227374089145087e-12 relative error = 7.911215852422138e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.940697993476398 y2[1] (numeric) = 1.940697993478284 absolute error = 1.886490963443066e-12 relative error = 9.720682815071963e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.300064000005655 y1[1] (closed_form) = 0.5685654169104171 y1[1] (numeric) = 0.5685654169155199 absolute error = 5.102807065782144e-12 relative error = 8.97488119047195e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 y2[1] (closed_form) = 1.902144223788147 y2[1] (numeric) = 1.902144223790587 absolute error = 2.440048163521169e-12 relative error = 1.282788199236428e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.400032000005755 y1[1] (closed_form) = 0.4806839989792183 y1[1] (numeric) = 0.4806839989841375 absolute error = 4.919176177509144e-12 relative error = 1.023370070140782e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 1.854582290410808 y2[1] (numeric) = 1.854582290413797 absolute error = 2.988276293081071e-12 relative error = 1.61129344787345e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.500000000005855 y1[1] (closed_form) = 0.3979880973105013 y1[1] (numeric) = 0.3979880973151776 absolute error = 4.676314890872391e-12 relative error = 1.174988629678549e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 1.798487112619966 y2[1] (numeric) = 1.798487112623492 absolute error = 3.526512415419347e-12 relative error = 1.960821620946765e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.600096000005955 y1[1] (closed_form) = 0.3212094536818687 y1[1] (numeric) = 0.3212094536862429 absolute error = 4.374167694720654e-12 relative error = 1.36178049698777e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 1.734331937361526 y2[1] (numeric) = 1.734331937365571 absolute error = 4.044542478709445e-12 relative error = 2.332046358358878e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.700064000006055 y1[1] (closed_form) = 0.2513109259011189 y1[1] (numeric) = 0.2513109259051342 absolute error = 4.015232590859341e-12 relative error = 1.597715091957116e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 1.662921315334603 y2[1] (numeric) = 1.662921315339139 absolute error = 4.536149234013465e-12 relative error = 2.727819525905066e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.800032000006155 y1[1] (closed_form) = 0.1888882689998548 y1[1] (numeric) = 0.1888882690034556 absolute error = 3.600814091342386e-12 relative error = 1.906319598569223e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 1.584891237610847 y2[1] (numeric) = 1.584891237615843 absolute error = 4.996447700023054e-12 relative error = 3.152549261080513e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.900000000006255 y1[1] (closed_form) = 0.1345647907557541 y1[1] (numeric) = 0.1345647907588885 absolute error = 3.134353887546126e-12 relative error = 2.329252600136116e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 1.501020856452472 y2[1] (numeric) = 1.501020856457888 absolute error = 5.416556092541214e-12 relative error = 3.608581499222309e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.000096000006355 y1[1] (closed_form) = 0.08883017893667033 y1[1] (numeric) = 0.08883017893928906 absolute error = 2.61872468154678e-12 relative error = 2.948012390489213e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 1.412031014831918 y2[1] (numeric) = 1.412031014837712 absolute error = 5.794476010123617e-12 relative error = 4.103646413753432e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.100064000006455 y1[1] (closed_form) = 0.05225797751258598 y1[1] (numeric) = 0.05225797751464519 absolute error = 2.059206971605221e-12 relative error = 3.940464345581064e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 1.319037707507226 y2[1] (numeric) = 1.319037707513348 absolute error = 6.122435891597888e-12 relative error = 4.641592773847483e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.200032000006555 y1[1] (closed_form) = 0.0251492466162454 y1[1] (numeric) = 0.02514924661770548 absolute error = 1.460082055260159e-12 relative error = 5.805669161942229e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 1.222858718983858 y2[1] (numeric) = 1.222858718990254 absolute error = 6.396660978680302e-12 relative error = 5.230907609667001e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.300000000006655 y1[1] (closed_form) = 0.007774674546568328 y1[1] (numeric) = 0.00777467454739533 absolute error = 8.270025289580651e-13 relative error = 1.063713373472458e-08 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 10 h = 0.000128 y2[1] (closed_form) = 1.124454423500459 y2[1] (numeric) = 1.124454423507068 absolute error = 6.608935620988632e-12 relative error = 5.877459755473969e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.400096000006755 y1[1] (closed_form) = 0.0003045841303724872 y1[1] (numeric) = 0.0003045841305371201 absolute error = 1.64632901495515e-13 relative error = 5.405170036080978e-08 % Desired digits = 16 Estimated correct digits = 7 Correct digits = 10 h = 0.000128 y2[1] (closed_form) = 1.024679454800552 y2[1] (numeric) = 1.024679454807315 absolute error = 6.763034576806604e-12 relative error = 6.600146558147777e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.500064000006855 y1[1] (closed_form) = 0.002832655518052007 y1[1] (numeric) = 0.002832655517533305 absolute error = 5.18702702317908e-13 relative error = 1.831153484821251e-08 % Desired digits = 16 Estimated correct digits = 8 Correct digits = 10 h = 0.000128 y2[1] (closed_form) = 0.9247850606673116 y2[1] (numeric) = 0.9247850606741571 absolute error = 6.845524147536253e-12 relative error = 7.402286691998053e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.600032000006955 y1[1] (closed_form) = 0.01531772316824409 y1[1] (numeric) = 0.01531772316702741 absolute error = 1.216683004345853e-12 relative error = 7.942975538742059e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 0.8256417088480468 y2[1] (numeric) = 0.8256417088549051 absolute error = 6.858291712319442e-12 relative error = 8.306619734470875e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.700000000007055 y1[1] (closed_form) = 0.03763512017060722 y1[1] (numeric) = 0.03763512016868498 absolute error = 1.922240144835996e-12 relative error = 5.107570099742243e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 0.7282393735822674 y2[1] (numeric) = 0.7282393735890665 absolute error = 6.799116825106921e-12 relative error = 9.336376295697284e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.800096000007155 y1[1] (closed_form) = 0.06960891418162773 y1[1] (numeric) = 0.06960891417899899 absolute error = 2.628744444344022e-12 relative error = 3.776447995561237e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 0.6334315515081662 y2[1] (numeric) = 0.6334315515148321 absolute error = 6.665890062151902e-12 relative error = 1.052345758003494e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.900064000007255 y1[1] (closed_form) = 0.1108381314962039 y1[1] (numeric) = 0.1108381314928773 absolute error = 3.326616759835588e-12 relative error = 3.001328798067586e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 y2[1] (closed_form) = 0.5424071989215324 y2[1] (numeric) = 0.5424071989279924 absolute error = 6.459943691083936e-12 relative error = 1.190976761357193e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ; diff ( y2 , x , 1 ) = y1 - 1.0 ; Iterations = 77344 Total Elapsed Time = 18.0 Seconds Elapsed Time(since restart) = 18.0 Seconds Time to Timeout = 2 Minutes 42.0 Seconds Percent Done = 100 %