##############ECHO OF PROBLEM################# ##############temp/mtest6postode.ode################# diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ; ! // BEGIN FIRST INPUT BLOCK Digits=64; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK t_start=1.5; t_end=8.0; array_x1_init[0 + 1] = exact_soln_x1(t_start); array_x2_init[0 + 1] = exact_soln_x2(t_start); array_x2_init[1 + 1] = exact_soln_x2p(t_start); glob_look_poles=true; glob_max_h=0.0001; glob_type_given_pole=0; // 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_x1 (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(2.0 * c1 + 6.0 * c3 * exp(-t)); } double exact_soln_x1p (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( - 6.0 * c3 * exp(-t)); } double exact_soln_x2 (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t)); } double exact_soln_x2p (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t)); } // 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 = 6.5 estimated_steps = 6500000 step_error = 9.805806756909201e-22 est_needed_step_err = 9.805806756909201e-22 opt_iter = 1 NO INFO (given) for Equation 1 NO 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 INFO (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 = 2.000401634288267 min_size = 1.004084046432682 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1.004084046432682 desired_abs_gbl_error = 1.004084046432682e-16 range = 6.5 estimated_steps = 6500000 step_error = 9.845854127014326e-22 est_needed_step_err = 9.845854127014326e-22 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.900103781919588e-250 estimated_step_error = 7.900103781919588e-250 Double H and LOOP opt_iter = 2 NO INFO (given) for Equation 1 NO 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 INFO (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 = 2.000401634288267 min_size = 1.004084046432682 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1.004084046432682 desired_abs_gbl_error = 1.004084046432682e-16 range = 6.5 estimated_steps = 3250000 step_error = 1.392414043957077e-21 est_needed_step_err = 1.392414043957077e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.428910127263391e-239 estimated_step_error = 5.428910127263391e-239 Double H and LOOP opt_iter = 3 NO INFO (given) for Equation 1 NO 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 INFO (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 = 2.000401634288267 min_size = 1.004084046432682 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1.004084046432682 desired_abs_gbl_error = 1.004084046432682e-16 range = 6.5 estimated_steps = 1625000 step_error = 1.969170825402865e-21 est_needed_step_err = 1.969170825402865e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.730718833583601e-228 estimated_step_error = 3.730718833583601e-228 Double H and LOOP opt_iter = 4 NO INFO (given) for Equation 1 NO 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 INFO (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 = 2.000401634288267 min_size = 1.004084046432682 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1.004084046432682 desired_abs_gbl_error = 1.004084046432682e-16 range = 6.5 estimated_steps = 812500 step_error = 2.784828087914154e-21 est_needed_step_err = 2.784828087914154e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.563730738090161e-217 estimated_step_error = 2.563730738090161e-217 Double H and LOOP opt_iter = 5 NO INFO (given) for Equation 1 NO 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 INFO (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 = 2.000401634288267 min_size = 1.004084046432682 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1.004084046432682 desired_abs_gbl_error = 1.004084046432682e-16 range = 6.5 estimated_steps = 406250 step_error = 3.93834165080573e-21 est_needed_step_err = 3.93834165080573e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.761782729061621e-206 estimated_step_error = 1.761782729061621e-206 Double H and LOOP opt_iter = 6 NO INFO (given) for Equation 1 NO 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 INFO (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 = 2.000401634288267 min_size = 1.004084046432682 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1.004084046432682 desired_abs_gbl_error = 1.004084046432682e-16 range = 6.5 estimated_steps = 203125 step_error = 5.569656175828308e-21 est_needed_step_err = 5.569656175828308e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.210688396177503e-195 estimated_step_error = 1.210688396177503e-195 Double H and LOOP opt_iter = 7 NO INFO (given) for Equation 1 NO 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 INFO (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 = 2.000401634288267 min_size = 1.004084046432682 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1.004084046432682 desired_abs_gbl_error = 1.004084046432682e-16 range = 6.5 estimated_steps = 101562.5 step_error = 7.876683301611461e-21 est_needed_step_err = 7.876683301611461e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.319794503070188e-185 estimated_step_error = 8.319794503070188e-185 Double H and LOOP opt_iter = 8 SETTING H FOR MAX H NO INFO (given) for Equation 1 NO 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 INFO (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 START of Soultion TOP MAIN SOLVE Loop t[1] = 1.5 x1[1] (closed_form) = 2.000401634288267 x1[1] (numeric) = 2.000401634288267 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.0001 x2[1] (closed_form) = 1.004084046432682 x2[1] (numeric) = 1.004084046432682 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 1.599999999999989 x1[1] (closed_form) = 2.00036341373239 x1[1] (numeric) = 2.000359394041442 absolute error = 4.019690948542376e-06 relative error = 0.0002009480337896308 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 x2[1] (closed_form) = 1.00496707499482 x2[1] (numeric) = 1.004969366676686 absolute error = 2.291681865607131e-06 relative error = 0.0002280355170460628 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 1.699999999999978 x1[1] (closed_form) = 2.000328830343295 x1[1] (numeric) = 2.000312711349069 absolute error = 1.611899422604424e-05 relative error = 0.0008058172227252209 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 6 h = 0.0001 x2[1] (closed_form) = 1.006047625066695 x2[1] (numeric) = 1.006058063756991 absolute error = 1.043869029637712e-05 relative error = 0.001037594049852769 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 1.799999999999967 x1[1] (closed_form) = 2.000297537998799 x1[1] (numeric) = 2.000261118995087 absolute error = 3.641900371231799e-05 relative error = 0.001820679324974496 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 x2[1] (closed_form) = 1.007369236555202 x2[1] (numeric) = 1.007395940396528 absolute error = 2.670384132663628e-05 relative error = 0.002650849396389421 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 1.899999999999956 x1[1] (closed_form) = 2.000269223514601 x1[1] (numeric) = 2.000204100625871 absolute error = 6.512288873006256e-05 relative error = 0.003255706180172961 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 x2[1] (closed_form) = 1.008985107484426 x2[1] (numeric) = 1.009039021625493 absolute error = 5.391414106670211e-05 relative error = 0.005343403055880515 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 1.999999999999945 x1[1] (closed_form) = 2.000243603509826 x1[1] (numeric) = 2.000141085582417 absolute error = 0.0001025179274090071 relative error = 0.005125272103313766 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 x2[1] (closed_form) = 1.010960230591599 x2[1] (numeric) = 1.01105582659539 absolute error = 9.559600379138722e-05 relative error = 0.009455960867565076 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 2.100000000000156 x1[1] (closed_form) = 2.000220421570855 x1[1] (numeric) = 2.000071443188991 absolute error = 0.0001489783818637846 relative error = 0.007448098232433094 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 x2[1] (closed_form) = 1.013374003136665 x2[1] (numeric) = 1.013530144279976 absolute error = 0.0001561411433104176 relative error = 0.01540804706131387 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 2.200000000000367 x1[1] (closed_form) = 2.000199445685052 x1[1] (numeric) = 1.999994476441111 absolute error = 0.0002049692439409778 relative error = 0.01024744029317424 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 x2[1] (closed_form) = 1.016323414680514 x2[1] (numeric) = 1.016564424719792 absolute error = 0.0002410100392775671 relative error = 0.02371391190995336 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 2.300000000000578 x1[1] (closed_form) = 2.000180465918701 x1[1] (numeric) = 1.999909415029699 absolute error = 0.0002710508890018115 relative error = 0.0135513216742328 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 x2[1] (closed_form) = 1.019926940781527 x2[1] (numeric) = 1.020283922198111 absolute error = 0.0003569814165840235 relative error = 0.03500068507951009 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 2.400000000000789 x1[1] (closed_form) = 2.000163292315921 x1[1] (numeric) = 1.999815407631557 absolute error = 0.0003478846843636418 relative error = 0.01739281416172967 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 x2[1] (closed_form) = 1.024329298889772 x2[1] (numeric) = 1.024841756943653 absolute error = 0.0005124580538806711 relative error = 0.05002864356570715 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 2.500000000001 x1[1] (closed_form) = 2.000147752997523 x1[1] (numeric) = 1.999711513389051 absolute error = 0.0004362396084716114 relative error = 0.02181036914987108 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 x2[1] (closed_form) = 1.029707257320162 x2[1] (numeric) = 1.030425098852398 absolute error = 0.0007178415322357523 relative error = 0.06971316625503372 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 2.600000000001211 x1[1] (closed_form) = 2.000133692440786 x1[1] (numeric) = 1.99959669249367 absolute error = 0.0005369999471158682 relative error = 0.02684820265492159 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 x2[1] (closed_form) = 1.036276730448582 x2[1] (numeric) = 1.03726272178796 absolute error = 0.000985991339377934 relative error = 0.09514749394701925 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 2.700000000001422 x1[1] (closed_form) = 2.000120969922931 x1[1] (numeric) = 1.999469795779309 absolute error = 0.0006511741436221463 relative error = 0.03255673798806466 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 x2[1] (closed_form) = 1.044301444894785 x2[1] (numeric) = 1.045634232066643 absolute error = 0.00133278717185803 relative error = 0.1276247560868126 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 2.800000000001633 x1[1] (closed_form) = 2.000109458112725 x1[1] (numeric) = 1.999329553220999 absolute error = 0.0007799048917265239 relative error = 0.03899311053018224 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 x2[1] (closed_form) = 1.054103524504195 x2[1] (numeric) = 1.055881341968907 absolute error = 0.001777817464711839 relative error = 0.168656818176189 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 2.900000000001844 x1[1] (closed_form) = 2.000099041796101 x1[1] (numeric) = 1.999174561224077 absolute error = 0.0009244805720243221 relative error = 0.04622173965915872 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 x2[1] (closed_form) = 1.06607641894819 x2[1] (numeric) = 1.068421641242624 absolute error = 0.002345222294433347 relative error = 0.2199863211257579 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 3.000000000002055 x1[1] (closed_form) = 2.000089616723062 x1[1] (numeric) = 1.999003268576545 absolute error = 0.001086348146516869 relative error = 0.05431497356087159 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 x2[1] (closed_form) = 1.080700694819389 x2[1] (numeric) = 1.083765419871191 absolute error = 0.003064725051801886 relative error = 0.283586849392567 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 3.100000000002266 x1[1] (closed_form) = 2.000081088564308 x1[1] (numeric) = 1.998813960924013 absolute error = 0.001267127640295573 relative error = 0.06335381337989346 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 x2[1] (closed_form) = 1.098563322979816 x2[1] (numeric) = 1.102536217898149 absolute error = 0.003972894918333303 relative error = 0.3616445984703876 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 3.200000000002477 x1[1] (closed_form) = 2.000073371967161 x1[1] (numeric) = 1.998604743611865 absolute error = 0.001468628355296486 relative error = 0.07342872395986279 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 x2[1] (closed_form) = 1.120381236236206 x2[1] (numeric) = 1.125495927746337 absolute error = 0.005114691510130553 relative error = 0.4565134924351982 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 3.300000000002688 x1[1] (closed_form) = 2.000066389701322 x1[1] (numeric) = 1.99837352272292 absolute error = 0.00169286697840243 relative error = 0.08464053929005988 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 x2[1] (closed_form) = 1.147030102799405 x2[1] (numeric) = 1.153575457251221 absolute error = 0.006545354451815699 relative error = 0.5706349324086015 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 3.400000000002899 x1[1] (closed_form) = 2.000060071885928 x1[1] (numeric) = 1.998117984120811 absolute error = 0.001942087765117284 relative error = 0.09710147172159785 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 4 h = 0.0001 x2[1] (closed_form) = 1.179579470312113 x2[1] (numeric) = 1.187912184880409 absolute error = 0.008332714568295874 relative error = 0.7064140041442959 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 3.50000000000311 x1[1] (closed_form) = 2.00005435529016 x1[1] (numeric) = 1.997835570289306 absolute error = 0.002218785000853929 relative error = 0.1109362350570736 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 1.219335690902083 x2[1] (numeric) = 1.229895711295798 absolute error = 0.01056002039371529 relative error = 0.8660470182663829 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 3.600000000003321 x1[1] (closed_form) = 2.000049182700405 x1[1] (numeric) = 1.997523454735874 absolute error = 0.002525727964530766 relative error = 0.1262832927498616 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 1.267894349997397 x2[1] (numeric) = 1.281223744475792 absolute error = 0.01332939447839476 relative error = 1.05130167023949 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 3.700000000003532 x1[1] (closed_form) = 2.000044502347647 x1[1] (numeric) = 1.997178513703137 absolute error = 0.002865988644509043 relative error = 0.143296243715825 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 1.327204303059438 x2[1] (numeric) = 1.343970362420416 absolute error = 0.01676605936097775 relative error = 1.263261377493205 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 3.800000000003743 x1[1] (closed_form) = 2.000040267389341 x1[1] (numeric) = 1.996797294905307 absolute error = 0.003242972484034601 relative error = 0.1621453596165673 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 1.399645890255373 x2[1] (numeric) = 1.420669394339641 absolute error = 0.02102350408426834 relative error = 1.502058787200275 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 3.900000000003955 x1[1] (closed_form) = 2.000036435440602 x1[1] (numeric) = 1.996375982976521 absolute error = 0.003660452464081088 relative error = 0.1830192890098375 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 1.488126468102194 x2[1] (numeric) = 1.514416268117512 absolute error = 0.02628980001531822 relative error = 1.766637485377542 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 4.000000000004166 x1[1] (closed_form) = 2.00003296815 x1[1] (numeric) = 1.995910361285389 absolute error = 0.004122606864610745 relative error = 0.2061269454185095 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 1.596197092104979 x2[1] (numeric) = 1.628992413109794 absolute error = 0.03279532100481442 relative error = 2.054590950392329 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 4.100000000003932 x1[1] (closed_form) = 2.000029830815723 x1[1] (numeric) = 1.995395769733524 absolute error = 0.004634061082198881 relative error = 0.2316995982159353 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 1.728195033274819 x2[1] (numeric) = 1.769017212721645 absolute error = 0.04082217944682665 relative error = 2.362128038840109 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 4.200000000003699 x1[1] (closed_form) = 2.000026992038277 x1[1] (numeric) = 1.994827058115714 absolute error = 0.005199933922563016 relative error = 0.2599931872551197 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 1.889417848219598 x2[1] (numeric) = 1.940133607062835 absolute error = 0.05071575884323654 relative error = 2.684200262584906 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 4.300000000003466 x1[1] (closed_form) = 2.000024423406222 x1[1] (numeric) = 1.994198534574938 absolute error = 0.005825888831283432 relative error = 0.2912908844063723 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 2.086335988847831 x2[1] (numeric) = 2.14923479667431 absolute error = 0.06289880782647872 relative error = 3.014797624289378 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 4.400000000003233 x1[1] (closed_form) = 2.000022099211825 x1[1] (numeric) = 1.993503908636344 absolute error = 0.006518190575481198 relative error = 0.3259059276419948 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 2.326852484466128 x2[1] (numeric) = 2.404741148071861 absolute error = 0.07788866360573232 relative error = 3.347382961563335 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 4.500000000003 x1[1] (closed_form) = 2.000019996193769 x1[1] (numeric) = 1.992736228250071 absolute error = 0.00728376794369745 relative error = 0.3641847560303979 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 2.620620118223763 x2[1] (numeric) = 2.716938416872795 absolute error = 0.09631829864903185 relative error = 3.675401023568257 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 4.600000000002767 x1[1] (closed_form) = 2.00001809330434 x1[1] (numeric) = 1.991887810212789 absolute error = 0.008130283091551505 relative error = 0.4065104770186861 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 2.979428827310462 x2[1] (numeric) = 3.098390865432158 absolute error = 0.1189620381216963 relative error = 3.992779992972129 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 4.700000000002534 x1[1] (closed_form) = 2.000016371498783 x1[1] (numeric) = 1.990950163271613 absolute error = 0.009066208227170192 relative error = 0.4533067007034602 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 3.417678874638781 x2[1] (numeric) = 3.564445857993969 absolute error = 0.1467669833551883 relative error = 4.29434679905965 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 4.800000000002301 x1[1] (closed_form) = 2.000014813544688 x1[1] (numeric) = 1.989913903140796 absolute error = 0.01010091040389183 relative error = 0.5050417794651066 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 3.952958782053159 x2[1] (numeric) = 4.13385018800727 absolute error = 0.1808914059541111 relative error = 4.576101495805542 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 4.900000000002068 x1[1] (closed_form) = 2.000013403849528 x1[1] (numeric) = 1.988768658580661 absolute error = 0.01124474526886643 relative error = 0.5622334953967356 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 4.606751219555541 x2[1] (numeric) = 4.829502876826574 absolute error = 0.2227516572710329 relative error = 4.835330727768797 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 5.000000000001835 x1[1] (closed_form) = 2.000012128304598 x1[1] (numeric) = 1.987502967598706 absolute error = 0.01250916070589203 relative error = 0.6254542424448192 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 5.405295180361611 x2[1] (numeric) = 5.679374660495869 absolute error = 0.2740794801342581 relative error = 5.070573779763908 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 5.100000000001602 x1[1] (closed_form) = 2.000010974143818 x1[1] (numeric) = 1.986104162734179 absolute error = 0.01390681140963945 relative error = 0.6953367551191962 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 6.380639043900721 x2[1] (numeric) = 6.717631071539758 absolute error = 0.3369920276390372 relative error = 5.28147769087752 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 5.200000000001369 x1[1] (closed_form) = 2.000009929815957 x1[1] (numeric) = 1.98455824427783 absolute error = 0.01545168553812704 relative error = 0.7725804411155555 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 7.571926789875981 x2[1] (numeric) = 7.98600419416124 absolute error = 0.4140774042852593 relative error = 5.468587002701875 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 5.300000000001136 x1[1] (closed_form) = 2.000008984869032 x1[1] (numeric) = 1.982849740158163 absolute error = 0.01715924471086905 relative error = 0.8579583812216072 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 9.026968983671566 x2[1] (numeric) = 9.535468151927578 absolute error = 0.5084991682560123 relative error = 5.633110839040336 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 5.400000000000903 x1[1] (closed_form) = 2.000008129845697 x1[1] (numeric) = 1.980961551091705 absolute error = 0.01904657875399196 relative error = 0.9523250665716759 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 10.80416158226833 x2[1] (numeric) = 11.42828557747957 absolute error = 0.6241239952112458 relative error = 5.776699936027903 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 5.50000000000067 x1[1] (closed_form) = 2.000007356188589 x1[1] (numeric) = 1.978874779447631 absolute error = 0.0211325767409587 relative error = 1.056624950681732 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 12.97482956908703 x2[1] (numeric) = 13.74050720327682 absolute error = 0.7656776341897871 relative error = 5.901253886324947 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 5.600000000000437 x1[1] (closed_form) = 2.00000665615469 x1[1] (numeric) = 1.976568540113927 absolute error = 0.02343811604076285 relative error = 1.171901901857972 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 15.62608947605499 x2[1] (numeric) = 16.5650248984652 absolute error = 0.9389354224102089 relative error = 6.008767733277153 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 5.700000000000204 x1[1] (closed_form) = 2.000006022737824 x1[1] (numeric) = 1.974019751472196 absolute error = 0.0259862712656278 relative error = 1.299309650580702 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 18.86434567595802 x2[1] (numeric) = 20.01530068950266 absolute error = 1.150955013544635 relative error = 6.101218845939029 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 5.799999999999971 x1[1] (closed_form) = 2.000005449598542 x1[1] (numeric) = 1.97120290438902 absolute error = 0.02880254520952152 relative error = 1.440123336429059 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 22.81956076356665 x2[1] (numeric) = 24.22992143267976 absolute error = 1.410360669113107 relative error = 6.180489991572784 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 5.899999999999737 x1[1] (closed_form) = 2.000004931000674 x1[1] (numeric) = 1.968089806912034 absolute error = 0.03191512408863995 relative error = 1.595752270104237 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 27.65047141092564 x2[1] (numeric) = 29.37816194397498 absolute error = 1.727690533049341 relative error = 6.248322161938518 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 5.999999999999504 x1[1] (closed_form) = 2.000004461753918 x1[1] (numeric) = 1.964649302115365 absolute error = 0.03535515963855329 relative error = 1.767754038285911 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 33.55095902739418 x2[1] (numeric) = 35.66677986571522 absolute error = 2.115820838321042 relative error = 6.306290191566464 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 6.099999999999271 x1[1] (closed_form) = 2.000004037161895 x1[1] (numeric) = 1.960846956270622 absolute error = 0.0391570808912729 relative error = 1.95785009248475 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 40.75783090139328 x2[1] (numeric) = 43.3483149846489 absolute error = 2.590484083255618 relative error = 6.355794766220161 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 6.199999999999038 x1[1] (closed_form) = 2.000003652975145 x1[1] (numeric) = 1.956644714222528 absolute error = 0.04335893875261765 relative error = 2.167942977909975 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 49.56032410840049 x2[1] (numeric) = 52.73122609630015 absolute error = 3.170901987899654 relative error = 6.398065478676289 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 6.299999999998805 x1[1] (closed_form) = 2.000003305348599 x1[1] (numeric) = 1.95200051852031 absolute error = 0.04800278682828862 relative error = 2.400135374772382 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 60.3117136103903 x2[1] (numeric) = 64.19227225913124 absolute error = 3.880558648740944 relative error = 6.434170771218835 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 6.399999999998572 x1[1] (closed_form) = 2.000002990803092 x1[1] (numeric) = 1.94686788849245 absolute error = 0.05313510231064145 relative error = 2.656751142622307 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 73.44349042050989 x2[1] (numeric) = 78.19163535893249 absolute error = 4.748144938422598 relative error = 6.465031701566062 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 6.499999999998339 x1[1] (closed_form) = 2.000002706190547 x1[1] (numeric) = 1.94119545505242 absolute error = 0.05880725113812724 relative error = 2.940358578321067 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 89.48267885252194 x2[1] (numeric) = 95.2913909240641 absolute error = 5.808712071542161 relative error = 6.491437388810864 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 6.599999999998106 x1[1] (closed_form) = 2.000002448662467 x1[1] (numeric) = 1.934926446579657 absolute error = 0.06507600208281072 relative error = 3.253796120416318 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 109.0729878570394 x2[1] (numeric) = 116.1780685112453 absolute error = 7.105080654205864 relative error = 6.514060716406157 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 6.699999999997873 x1[1] (closed_form) = 2.000002215641425 x1[1] (numeric) = 1.927998120730415 absolute error = 0.07200409491101012 relative error = 3.600200757173538 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 133.0006453219434 x2[1] (numeric) = 141.6902071126161 absolute error = 8.689561790672713 relative error = 6.533473405064034 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 6.79999999999764 x1[1] (closed_form) = 2.000002004795266 x1[1] (numeric) = 1.920341136490891 absolute error = 0.07966086830437491 relative error = 3.983039422629456 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 162.2259521581696 x2[1] (numeric) = 172.852011504988 absolute error = 10.62605934681841 relative error = 6.550159950029479 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 6.899999999997407 x1[1] (closed_form) = 2.000001814013772 x1[1] (numeric) = 1.911878860189363 absolute error = 0.08812295382440882 relative error = 4.40614369481777 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 197.9218225471213 x2[1] (numeric) = 210.9144603171308 absolute error = 12.99263777000951 relative error = 6.564530178028355 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 6.999999999997174 x1[1] (closed_form) = 2.000001641387538 x1[1] (numeric) = 1.902526598520262 absolute error = 0.09747504286727615 relative error = 4.873748143509075 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 241.5208571051604 x2[1] (numeric) = 257.4055156575309 absolute error = 15.8846585523705 relative error = 6.576930349934195 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 7.099999999996941 x1[1] (closed_form) = 2.000001485188862 x1[1] (numeric) = 1.892190750905448 absolute error = 0.107810734283414 relative error = 5.390532711191131 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 294.7728381765531 x2[1] (numeric) = 314.1914494259473 absolute error = 19.41861124939425 relative error = 6.587652841257898 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 7.199999999996708 x1[1] (closed_form) = 2.000001343854455 x1[1] (numeric) = 1.880767872708023 absolute error = 0.1192334711464318 relative error = 5.961669551513495 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 359.814954742856 x2[1] (numeric) = 383.5517475872705 absolute error = 23.73679284441454 relative error = 6.596944493699042 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 7.299999999996475 x1[1] (closed_form) = 2.000001215969796 x1[1] (numeric) = 1.868143639922981 absolute error = 0.1318575760468141 relative error = 6.592874793972399 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 439.2575753209335 x2[1] (numeric) = 468.2705986215513 absolute error = 29.01302330061776 relative error = 6.605013762009695 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 7.399999999996242 x1[1] (closed_form) = 2.00000110025497 x1[1] (numeric) = 1.854191704986024 absolute error = 0.1458093952689463 relative error = 7.290465752761726 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 536.2890112171716 x2[1] (numeric) = 571.7486379496928 absolute error = 35.4596267325212 relative error = 6.612036791886033 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 7.499999999996009 x1[1] (closed_form) = 2.000000995551866 x1[1] (numeric) = 1.838772432243467 absolute error = 0.161228563308399 relative error = 8.061424152637017 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 654.8034746551281 x2[1] (numeric) = 698.1394330826961 absolute error = 43.33595842756802 relative error = 6.618162564026131 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 7.599999999995775 x1[1] (closed_form) = 2.00000090081258 x1[1] (numeric) = 1.821731500430406 absolute error = 0.1782694003821745 relative error = 8.913466004427573 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 799.5573671855778 x2[1] (numeric) = 852.5161871798693 absolute error = 52.9588199942915 relative error = 6.623517231878587 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 7.699999999995542 x1[1] (closed_form) = 2.000000815088929 x1[1] (numeric) = 1.802898358173942 absolute error = 0.1971024569149873 relative error = 9.855118829350236 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 x2[1] (closed_form) = 976.3601707816059 x2[1] (numeric) = 1041.075351478263 absolute error = 64.7151806966566 relative error = 6.6282077693573 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 7.799999999995309 x1[1] (closed_form) = 2.000000737522962 x1[1] (numeric) = 1.7820845170562 absolute error = 0.2179162204667622 relative error = 10.89580700538418 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 0.0001 x2[1] (closed_form) = 1192.307602748668 x2[1] (numeric) = 1271.385318344864 absolute error = 79.07771559619596 relative error = 6.632325032055099 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 7.899999999995076 x1[1] (closed_form) = 2.000000667338373 x1[1] (numeric) = 1.759081665160731 absolute error = 0.2409190021776424 relative error = 12.04594608952109 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 0.0001 x2[1] (closed_form) = 1456.066391774812 x2[1] (numeric) = 1552.690175954089 absolute error = 96.62378417927721 relative error = 6.635946322578165 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 t[1] = 7.999999999994843 x1[1] (closed_form) = 2.00000060383273 x1[1] (numeric) = 1.73365958221445 absolute error = 0.2663410216182804 relative error = 13.31704706027958 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 2 h = 0.0001 x2[1] (closed_form) = 1778.222104183884 x2[1] (numeric) = 1896.280715417553 absolute error = 118.0586112336684 relative error = 6.639137538325198 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 NO 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 INFO (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 ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ; Iterations = 65001 Total Elapsed Time = 8.0 Seconds Elapsed Time(since restart) = 8.0 Seconds Time to Timeout = 2 Minutes 52.0 Seconds Percent Done = 100 %