##############ECHO OF PROBLEM################# ##############temp/div_lin_exppostode.ode################# diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=1.0 # ELIMINATED in preodein.rb x_end=5.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $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 def exact_soln_y (x) return(-(0.1 * (5.0 + 2.0*x))/exp(x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 4000000.0 step_error 1.6666666666666666e-21 est_needed_step_err 1.6666666666666666e-21 opt_iter 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 4000000.0 step_error 1.6666666666666666e-21 est_needed_step_err 1.6666666666666666e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.104860300807793e-183 estimated_step_error 4.104860300807793e-183 Double H and LOOP opt_iter 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 2000000.0 step_error 2.3570226039551582e-21 est_needed_step_err 2.3570226039551582e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.754725063378627e-175 estimated_step_error 2.754725063378627e-175 Double H and LOOP opt_iter 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 1000000.0 step_error 3.3333333333333333e-21 est_needed_step_err 3.3333333333333333e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8486646248448497e-167 estimated_step_error 1.8486646248448497e-167 Double H and LOOP opt_iter 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 500000.0 step_error 4.7140452079103165e-21 est_needed_step_err 4.7140452079103165e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2406177329217022e-159 estimated_step_error 1.2406177329217022e-159 Double H and LOOP opt_iter 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 250000.0 step_error 6.6666666666666666e-21 est_needed_step_err 6.6666666666666666e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.325643383220975e-152 estimated_step_error 8.325643383220975e-152 Double H and LOOP opt_iter 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 125000.0 step_error 9.428090415820633e-21 est_needed_step_err 9.428090415820633e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.587242966122243e-144 estimated_step_error 5.587242966122243e-144 Double H and LOOP opt_iter 7 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 62500.0 step_error 1.3333333333333333e-20 est_needed_step_err 1.3333333333333333e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.7495329627969775e-136 estimated_step_error 3.7495329627969775e-136 Double H and LOOP opt_iter 8 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 31250.0 step_error 1.8856180831641266e-20 est_needed_step_err 1.8856180831641266e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.5162658618700373e-128 estimated_step_error 2.5162658618700373e-128 Double H and LOOP opt_iter 9 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 15625.0 step_error 2.6666666666666666e-20 est_needed_step_err 2.6666666666666666e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6886332545641444e-120 estimated_step_error 1.6886332545641444e-120 Double H and LOOP opt_iter 10 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 7812.5 step_error 3.771236166328253e-20 est_needed_step_err 3.771236166328253e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1332169832561895e-112 estimated_step_error 1.1332169832561895e-112 Double H and LOOP opt_iter 11 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 3906.25 step_error 5.333333333333333e-20 est_needed_step_err 5.333333333333333e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.604815132584679e-105 estimated_step_error 7.604815132584679e-105 Double H and LOOP opt_iter 12 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 1953.125 step_error 7.542472332656506e-20 est_needed_step_err 7.542472332656506e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.103403970178271e-97 estimated_step_error 5.103403970178271e-97 Double H and LOOP opt_iter 13 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 976.5625 step_error 1.0666666666666666e-19 est_needed_step_err 1.0666666666666666e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.424700777444561e-89 estimated_step_error 3.424700777444561e-89 Double H and LOOP opt_iter 14 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 488.28125 step_error 1.5084944665313013e-19 est_needed_step_err 1.5084944665313013e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.298095738565798e-81 estimated_step_error 2.298095738565798e-81 Double H and LOOP opt_iter 15 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.016384 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 244.140625 step_error 2.1333333333333333e-19 est_needed_step_err 2.1333333333333333e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.5419816582009884e-73 estimated_step_error 1.5419816582009884e-73 Double H and LOOP opt_iter 16 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.032768 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 122.0703125 step_error 3.0169889330626025e-19 est_needed_step_err 3.0169889330626025e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.034478649272839e-65 estimated_step_error 1.034478649272839e-65 Double H and LOOP opt_iter 17 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.2575156088200097 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.065536 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 61.03515625 step_error 4.2666666666666666e-19 est_needed_step_err 4.2666666666666666e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.937874073288147e-58 estimated_step_error 6.937874073288147e-58 Double H and LOOP opt_iter 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL 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 START of Soultion TOP MAIN SOLVE Loop x[1] 1.0 y[1] (closed_form) -0.2575156088200097 y[1] (numeric) -0.2575156088200097 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1 y[1] (closed_form) -0.2396671802626173 y[1] (numeric) -0.23966718026261732 absolute error 2.7755575615628914e-17 relative error 1.1580882949937289e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2000000000000002 y[1] (closed_form) -0.22288371681502955 y[1] (numeric) -0.2228837168150296 absolute error 5.551115123125783e-17 relative error 2.4905880081552278e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3000000000000003 y[1] (closed_form) -0.20712416270584955 y[1] (numeric) -0.20712416270584963 absolute error 8.326672684688674e-17 relative error 4.020135833458466e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4000000000000004 y[1] (closed_form) -0.192345631874453 y[1] (numeric) -0.1923456318744531 absolute error 1.1102230246251565e-16 relative error 5.77202099057709e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5000000000000004 y[1] (closed_form) -0.17850412811874378 y[1] (numeric) -0.17850412811874392 absolute error 1.3877787807814457e-16 relative error 7.774491242344116e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6000000000000005 y[1] (closed_form) -0.1655551447556174 y[1] (numeric) -0.1655551447556175 absolute error 1.1102230246251565e-16 relative error 6.706061755217583e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7000000000000006 y[1] (closed_form) -0.15345416020429706 y[1] (numeric) -0.15345416020429717 absolute error 1.1102230246251565e-16 relative error 7.234883845098048e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8000000000000007 y[1] (closed_form) -0.14215704387056435 y[1] (numeric) -0.1421570438705645 absolute error 1.3877787807814457e-16 relative error 9.762293467814613e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9000000000000008 y[1] (closed_form) -0.13162038491591876 y[1] (numeric) -0.13162038491591893 absolute error 1.6653345369377348e-16 relative error 1.265255786937242e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.000000000000001 y[1] (closed_form) -0.12180175491295135 y[1] (numeric) -0.1218017549129515 absolute error 1.5265566588595902e-16 relative error 1.2533125322788508e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.100000000000001 y[1] (closed_form) -0.11265991399274328 y[1] (numeric) -0.11265991399274344 absolute error 1.6653345369377348e-16 relative error 1.4781961728152957e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.200000000000001 y[1] (closed_form) -0.10415496886059376 y[1] (numeric) -0.10415496886059394 absolute error 1.8041124150158794e-16 relative error 1.7321424361718104e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.300000000000001 y[1] (closed_form) -0.09624848997389149 y[1] (numeric) -0.09624848997389168 absolute error 1.942890293094024e-16 relative error 2.0186189867716942e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4000000000000012 y[1] (closed_form) -0.08890359422362418 y[1] (numeric) -0.08890359422362436 absolute error 1.8041124150158794e-16 relative error 2.0292907511454427e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5000000000000013 y[1] (closed_form) -0.08208499862389873 y[1] (numeric) -0.08208499862389891 absolute error 1.8041124150158794e-16 relative error 2.1978588600361125e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6000000000000014 y[1] (closed_form) -0.07575904977862047 y[1] (numeric) -0.07575904977862068 absolute error 2.0816681711721685e-16 relative error 2.747748522790507e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7000000000000015 y[1] (closed_form) -0.06989373324933967 y[1] (numeric) -0.06989373324933988 absolute error 2.0816681711721685e-16 relative error 2.9783330699277466e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8000000000000016 y[1] (closed_form) -0.06445866638273096 y[1] (numeric) -0.06445866638273118 absolute error 2.220446049250313e-16 relative error 3.4447595239810766e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9000000000000017 y[1] (closed_form) -0.059425077660919735 y[1] (numeric) -0.05942507766091995 absolute error 2.1510571102112408e-16 relative error 3.619780057310485e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.0000000000000018 y[1] (closed_form) -0.05476577520465026 y[1] (numeric) -0.05476577520465049 absolute error 2.2898349882893854e-16 relative error 4.18114229139032e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.100000000000002 y[1] (closed_form) -0.050455106680784664 y[1] (numeric) -0.0504551066807849 absolute error 2.3592239273284576e-16 relative error 4.675887303647194e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.200000000000002 y[1] (closed_form) -0.046468912535337414 y[1] (numeric) -0.04646891253533765 absolute error 2.3592239273284576e-16 relative error 5.076994056046349e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.300000000000002 y[1] (closed_form) -0.04278447418543834 y[1] (numeric) -0.04278447418543858 absolute error 2.3592239273284576e-16 relative error 5.51420573057181e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.400000000000002 y[1] (closed_form) -0.0393804585531847 y[1] (numeric) -0.03938045855318495 absolute error 2.498001805406602e-16 relative error 6.343252204727283e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.500000000000002 y[1] (closed_form) -0.03623686010678213 y[1] (numeric) -0.036236860106782384 absolute error 2.5673907444456745e-16 relative error 7.085025404740183e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.6000000000000023 y[1] (closed_form) -0.03333494138569686 y[1] (numeric) -0.03333494138569711 absolute error 2.498001805406602e-16 relative error 7.493643911065728e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.7000000000000024 y[1] (closed_form) -0.03065717282322079 y[1] (numeric) -0.03065717282322104 absolute error 2.498001805406602e-16 relative error 8.148180589941843e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.8000000000000025 y[1] (closed_form) -0.028187172538768596 y[1] (numeric) -0.02818717253876885 absolute error 2.5326962749261384e-16 relative error 8.985279638965815e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.9000000000000026 y[1] (closed_form) -0.02590964665062956 y[1] (numeric) -0.02590964665062982 absolute error 2.6020852139652106e-16 relative error 1.0042920496185093e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.000000000000003 y[1] (closed_form) -0.023810330555354385 y[1] (numeric) -0.023810330555354642 absolute error 2.5673907444456745e-16 relative error 1.0782675773765469e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.100000000000002 y[1] (closed_form) -0.021875931530324806 y[1] (numeric) -0.02187593153032506 absolute error 2.5326962749261384e-16 relative error 1.1577547092864456e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.200000000000002 y[1] (closed_form) -0.020094072939440096 y[1] (numeric) -0.020094072939440343 absolute error 2.463307335887066e-16 relative error 1.2258875257948098e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.300000000000002 y[1] (closed_form) -0.018453240256593242 y[1] (numeric) -0.018453240256593485 absolute error 2.42861286636753e-16 relative error 1.3160902002019942e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.400000000000001 y[1] (closed_form) -0.016942729066234435 y[1] (numeric) -0.016942729066234667 absolute error 2.3245294578089215e-16 relative error 1.371992344752494e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.500000000000001 y[1] (closed_form) -0.015552595153539218 y[1] (numeric) -0.01555259515353945 absolute error 2.3071822230491534e-16 relative error 1.4834708936174686e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.6000000000000005 y[1] (closed_form) -0.01427360675737968 y[1] (numeric) -0.014273606757379907 absolute error 2.2724877535296173e-16 relative error 1.5920907673561241e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.7 y[1] (closed_form) -0.013097199026441976 y[1] (numeric) -0.013097199026442198 absolute error 2.220446049250313e-16 relative error 1.6953594770663923e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.8 y[1] (closed_form) -0.012015430691569245 y[1] (numeric) -0.012015430691569464 absolute error 2.185751579730777e-16 relative error 1.8191204592145274e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.8999999999999995 y[1] (closed_form) -0.01102094294496803 y[1] (numeric) -0.011020942944968245 absolute error 2.1510571102112408e-16 relative error 1.951790442026901e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.999999999999999 y[1] (closed_form) -0.01010692049862821 y[1] (numeric) -0.010106920498628422 absolute error 2.1163626406917047e-16 relative error 2.0939737687448456e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; Iterations 41 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 104.99999999999996%