##############ECHO OF PROBLEM################# ##############temp/lin_exppostode.ode################# diff ( y , x , 1 ) = exp ( 0.1 * x + 0.2 ) ; ! #BEGIN FIRST INPUT BLOCK max_terms=30 # Digits:=32; ELIMINATED in preodein.rb ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=1.0 x_end=10.0 $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(10.0 * exp(0.1 * x + 0.2)) 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 9.0 estimated_steps 9000000.0 step_error 1.111111111111111e-21 est_needed_step_err 1.111111111111111e-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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 9000000.0 step_error 1.4998431195288927e-20 est_needed_step_err 1.4998431195288927e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.3471048613448756e-208 estimated_step_error 3.3471048613448756e-208 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 4500000.0 step_error 2.1210984810697308e-20 est_needed_step_err 2.1210984810697308e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.2462040534969583e-200 estimated_step_error 2.2462040534969583e-200 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 2250000.0 step_error 2.9996862390577853e-20 est_needed_step_err 2.9996862390577853e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.5074020290067314e-192 estimated_step_error 1.5074020290067314e-192 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 1125000.0 step_error 4.2421969621394616e-20 est_needed_step_err 4.2421969621394616e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0116003850727042e-184 estimated_step_error 1.0116003850727042e-184 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 562500.0 step_error 5.999372478115571e-20 est_needed_step_err 5.999372478115571e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.788735366993033e-177 estimated_step_error 6.788735366993033e-177 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 281250.0 step_error 8.484393924278923e-20 est_needed_step_err 8.484393924278923e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.5558433197432086e-169 estimated_step_error 4.5558433197432086e-169 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 140625.0 step_error 1.1998744956231141e-19 est_needed_step_err 1.1998744956231141e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.0573748786773353e-161 estimated_step_error 3.0573748786773353e-161 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 70312.5 step_error 1.6968787848557846e-19 est_needed_step_err 1.6968787848557846e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.05176979247448e-153 estimated_step_error 2.05176979247448e-153 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 35156.25 step_error 2.3997489912462282e-19 est_needed_step_err 2.3997489912462282e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.376919726005822e-145 estimated_step_error 1.376919726005822e-145 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 17578.125 step_error 3.3937575697115693e-19 est_needed_step_err 3.3937575697115693e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.240356243759382e-138 estimated_step_error 9.240356243759382e-138 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 8789.0625 step_error 4.7994979824924565e-19 est_needed_step_err 4.7994979824924565e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.201103984310229e-130 estimated_step_error 6.201103984310229e-130 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 4394.53125 step_error 6.787515139423139e-19 est_needed_step_err 6.787515139423139e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.1614983307765654e-122 estimated_step_error 4.1614983307765654e-122 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 2197.265625 step_error 9.598995964984913e-19 est_needed_step_err 9.598995964984913e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.7927448469424014e-114 estimated_step_error 2.7927448469424014e-114 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 1098.6328125 step_error 1.3575030278846277e-18 est_needed_step_err 1.3575030278846277e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.874193557403069e-106 estimated_step_error 1.874193557403069e-106 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 0.016384 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 549.31640625 step_error 1.9197991929969826e-18 est_needed_step_err 1.9197991929969826e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2577690866157239e-98 estimated_step_error 1.2577690866157239e-98 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 0.032768 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 274.658203125 step_error 2.7150060557692554e-18 est_needed_step_err 2.7150060557692554e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.441001570888194e-91 estimated_step_error 8.441001570888194e-91 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 13.498588075760033 $glob_desired_digits_correct 16 estimated_h 0.065536 estimated_answer 13.498588075760033 desired_abs_gbl_error 1.3498588075760032e-15 range 9.0 estimated_steps 137.3291015625 step_error 3.839598385993965e-18 est_needed_step_err 3.839598385993965e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.665004043908942e-83 estimated_step_error 5.665004043908942e-83 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) 13.498588075760033 y[1] (numeric) 13.498588075760033 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) 13.634251141321778 y[1] (numeric) 13.63425114132178 absolute error 1.7763568394002505e-15 relative error 1.3028635170263123e-14% 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] 1.2000000000000002 y[1] (closed_form) 13.771277643359571 y[1] (numeric) 13.771277643359573 absolute error 1.7763568394002505e-15 relative error 1.2898998084297569e-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) 13.909681284637802 y[1] (numeric) 13.909681284637806 absolute error 3.552713678800501e-15 relative error 2.5541301817779293e-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) 14.04947590563594 y[1] (numeric) 14.04947590563594 absolute error 0.0 relative error 0.0% 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) 14.190675485932573 y[1] (numeric) 14.190675485932575 absolute error 1.7763568394002505e-15 relative error 1.2517775078157339e-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) 14.333294145603404 y[1] (numeric) 14.333294145603405 absolute error 1.7763568394002505e-15 relative error 1.2393221135039152e-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) 14.477346146633245 y[1] (numeric) 14.477346146633247 absolute error 1.7763568394002505e-15 relative error 1.2269906524362188e-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) 14.622845894342246 y[1] (numeric) 14.622845894342248 absolute error 1.7763568394002505e-15 relative error 1.2147818914562617e-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) 14.769807938826427 y[1] (numeric) 14.769807938826428 absolute error 1.7763568394002505e-15 relative error 1.2026946096777719e-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] 2.000000000000001 y[1] (closed_form) 14.918246976412705 y[1] (numeric) 14.918246976412705 absolute error 0.0 relative error 0.0% 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] 2.100000000000001 y[1] (closed_form) 15.068177851128537 y[1] (numeric) 15.068177851128539 absolute error 1.7763568394002505e-15 relative error 1.1788796607993378e-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] 2.200000000000001 y[1] (closed_form) 15.21961555618634 y[1] (numeric) 15.21961555618634 absolute error 0.0 relative error 0.0% 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] 2.300000000000001 y[1] (closed_form) 15.372575235482817 y[1] (numeric) 15.372575235482817 absolute error 0.0 relative error 0.0% 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] 2.4000000000000012 y[1] (closed_form) 15.527072185113362 y[1] (numeric) 15.527072185113363 absolute error 1.7763568394002505e-15 relative error 1.1440385014138978e-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] 2.5000000000000013 y[1] (closed_form) 15.683121854901692 y[1] (numeric) 15.68312185490169 absolute error 1.7763568394002505e-15 relative error 1.1326551281274766e-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] 2.6000000000000014 y[1] (closed_form) 15.840739849944821 y[1] (numeric) 15.84073984994482 absolute error 1.7763568394002505e-15 relative error 1.121385021297751e-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] 2.7000000000000015 y[1] (closed_form) 15.999941932173606 y[1] (numeric) 15.999941932173604 absolute error 1.7763568394002505e-15 relative error 1.1102270539046456e-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] 2.8000000000000016 y[1] (closed_form) 16.160744021928938 y[1] (numeric) 16.160744021928934 absolute error 3.552713678800501e-15 relative error 2.1983602202842458e-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] 2.9000000000000017 y[1] (closed_form) 16.323162199553792 y[1] (numeric) 16.323162199553792 absolute error 0.0 relative error 0.0% 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] 3.0000000000000018 y[1] (closed_form) 16.487212707001284 y[1] (numeric) 16.487212707001284 absolute error 0.0 relative error 0.0% 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] 3.100000000000002 y[1] (closed_form) 16.652911949458865 y[1] (numeric) 16.652911949458865 absolute error 0.0 relative error 0.0% 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] 3.200000000000002 y[1] (closed_form) 16.820276496988868 y[1] (numeric) 16.820276496988864 absolute error 3.552713678800501e-15 relative error 2.1121612831016782e-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] 3.300000000000002 y[1] (closed_form) 16.98932308618551 y[1] (numeric) 16.989323086185507 absolute error 3.552713678800501e-15 relative error 2.091144927186246e-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] 3.400000000000002 y[1] (closed_form) 17.16006862184859 y[1] (numeric) 17.160068621848584 absolute error 7.105427357601002e-15 relative error 4.140675375012318e-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] 3.500000000000002 y[1] (closed_form) 17.332530178673956 y[1] (numeric) 17.332530178673952 absolute error 3.552713678800501e-15 relative error 2.04973748332011e-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] 3.6000000000000023 y[1] (closed_form) 17.506725002961016 y[1] (numeric) 17.506725002961012 absolute error 3.552713678800501e-15 relative error 2.029342254590513e-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] 3.7000000000000024 y[1] (closed_form) 17.682670514337357 y[1] (numeric) 17.682670514337353 absolute error 3.552713678800501e-15 relative error 2.009149961777499e-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] 3.8000000000000025 y[1] (closed_form) 17.860384307500738 y[1] (numeric) 17.860384307500734 absolute error 3.552713678800501e-15 relative error 1.9891585856349606e-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] 3.9000000000000026 y[1] (closed_form) 18.039884153978576 y[1] (numeric) 18.03988415397857 absolute error 7.105427357601002e-15 relative error 3.938732254017245e-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] 4.000000000000003 y[1] (closed_form) 18.221188003905095 y[1] (numeric) 18.22118800390509 absolute error 3.552713678800501e-15 relative error 1.94977060663613e-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] 4.100000000000002 y[1] (closed_form) 18.40431398781638 y[1] (numeric) 18.404313987816376 absolute error 3.552713678800501e-15 relative error 1.9303700649491148e-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] 4.200000000000002 y[1] (closed_form) 18.589280418463424 y[1] (numeric) 18.58928041846342 absolute error 3.552713678800501e-15 relative error 1.911162561877242e-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] 4.300000000000002 y[1] (closed_form) 18.776105792643435 y[1] (numeric) 18.77610579264343 absolute error 3.552713678800501e-15 relative error 1.8921461766541978e-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] 4.400000000000001 y[1] (closed_form) 18.964808793049517 y[1] (numeric) 18.964808793049514 absolute error 3.552713678800501e-15 relative error 1.8733190076256122e-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] 4.500000000000001 y[1] (closed_form) 19.15540829013896 y[1] (numeric) 19.15540829013896 absolute error 0.0 relative error 0.0% 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] 4.6000000000000005 y[1] (closed_form) 19.347923344020316 y[1] (numeric) 19.347923344020316 absolute error 0.0 relative error 0.0% 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] 4.7 y[1] (closed_form) 19.542373206359397 y[1] (numeric) 19.542373206359397 absolute error 0.0 relative error 0.0% 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] 4.8 y[1] (closed_form) 19.738777322304475 y[1] (numeric) 19.73877732230448 absolute error 3.552713678800501e-15 relative error 1.7998651186899992e-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] 4.8999999999999995 y[1] (closed_form) 19.937155332430823 y[1] (numeric) 19.937155332430827 absolute error 3.552713678800501e-15 relative error 1.7819561615299604e-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] 4.999999999999999 y[1] (closed_form) 20.137527074704767 y[1] (numeric) 20.137527074704767 absolute error 0.0 relative error 0.0% 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] 5.099999999999999 y[1] (closed_form) 20.339912586467506 y[1] (numeric) 20.33991258646751 absolute error 3.552713678800501e-15 relative error 1.7466710654224654e-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] 5.199999999999998 y[1] (closed_form) 20.544332106438876 y[1] (numeric) 20.54433210643888 absolute error 3.552713678800501e-15 relative error 1.729291397935994e-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] 5.299999999999998 y[1] (closed_form) 20.75080607674122 y[1] (numeric) 20.750806076741227 absolute error 7.105427357601002e-15 relative error 3.4241693220607955e-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] 5.399999999999998 y[1] (closed_form) 20.95935514494364 y[1] (numeric) 20.959355144943647 absolute error 7.105427357601002e-15 relative error 3.3900982680352917e-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] 5.499999999999997 y[1] (closed_form) 21.170000166126744 y[1] (numeric) 21.170000166126748 absolute error 3.552713678800501e-15 relative error 1.6781831133308415e-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] 5.599999999999997 y[1] (closed_form) 21.38276220496818 y[1] (numeric) 21.382762204968188 absolute error 7.105427357601002e-15 relative error 3.322969824707722e-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] 5.699999999999997 y[1] (closed_form) 21.597662537849146 y[1] (numeric) 21.597662537849153 absolute error 7.105427357601002e-15 relative error 3.289905722505382e-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] 5.799999999999996 y[1] (closed_form) 21.814722654982003 y[1] (numeric) 21.814722654982013 absolute error 1.0658141036401503e-14 relative error 4.8857559204253365e-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] 5.899999999999996 y[1] (closed_form) 22.033964262559355 y[1] (numeric) 22.03396426255937 absolute error 1.4210854715202004e-14 relative error 6.449522449008158e-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] 5.999999999999996 y[1] (closed_form) 22.255409284924667 y[1] (numeric) 22.255409284924678 absolute error 1.0658141036401503e-14 relative error 4.78901147130154e-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] 6.099999999999995 y[1] (closed_form) 22.479079866764703 y[1] (numeric) 22.479079866764717 absolute error 1.4210854715202004e-14 relative error 6.321813347979931e-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] 6.199999999999995 y[1] (closed_form) 22.70499837532405 y[1] (numeric) 22.70499837532406 absolute error 1.0658141036401503e-14 relative error 4.6941826906206015e-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] 6.2999999999999945 y[1] (closed_form) 22.933187402641817 y[1] (numeric) 22.93318740264183 absolute error 1.4210854715202004e-14 relative error 6.196633056582866e-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] 6.399999999999994 y[1] (closed_form) 23.1636697678109 y[1] (numeric) 23.16366976781092 absolute error 1.7763568394002505e-14 relative error 7.668719409343083e-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] 6.499999999999994 y[1] (closed_form) 23.396468519259894 y[1] (numeric) 23.396468519259912 absolute error 1.7763568394002505e-14 relative error 7.592414376289138e-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] 6.599999999999993 y[1] (closed_form) 23.631606937057935 y[1] (numeric) 23.631606937057953 absolute error 1.7763568394002505e-14 relative error 7.516868590999854e-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] 6.699999999999993 y[1] (closed_form) 23.869108535242756 y[1] (numeric) 23.86910853524277 absolute error 1.4210854715202004e-14 relative error 5.953659599066998e-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] 6.799999999999993 y[1] (closed_form) 24.10899706417208 y[1] (numeric) 24.1089970641721 absolute error 2.1316282072803006e-14 relative error 8.841629544383132e-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] 6.899999999999992 y[1] (closed_form) 24.351296512898728 y[1] (numeric) 24.35129651289875 absolute error 2.1316282072803006e-14 relative error 8.753653860488252e-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] 6.999999999999992 y[1] (closed_form) 24.596031111569477 y[1] (numeric) 24.5960311115695 absolute error 2.1316282072803006e-14 relative error 8.666553549274158e-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] 7.099999999999992 y[1] (closed_form) 24.843225333848146 y[1] (numeric) 24.843225333848167 absolute error 2.1316282072803006e-14 relative error 8.580319900637142e-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] 7.199999999999991 y[1] (closed_form) 25.09290389936296 y[1] (numeric) 25.092903899362977 absolute error 1.7763568394002505e-14 relative error 7.079120242617066e-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] 7.299999999999991 y[1] (closed_form) 25.345091776178524 y[1] (numeric) 25.345091776178545 absolute error 2.1316282072803006e-14 relative error 8.410418183152077e-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] 7.399999999999991 y[1] (closed_form) 25.59981418329269 y[1] (numeric) 25.599814183292715 absolute error 2.4868995751603507e-14 relative error 9.714521977989145e-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] 7.49999999999999 y[1] (closed_form) 25.85709659315844 y[1] (numeric) 25.857096593158463 absolute error 2.4868995751603507e-14 relative error 9.617860869260792e-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] 7.59999999999999 y[1] (closed_form) 26.116964734231153 y[1] (numeric) 26.11696473423118 absolute error 2.4868995751603507e-14 relative error 9.522161554634275e-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] 7.6999999999999895 y[1] (closed_form) 26.379444593541503 y[1] (numeric) 26.379444593541525 absolute error 2.1316282072803006e-14 relative error 8.080640969227186e-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] 7.799999999999989 y[1] (closed_form) 26.644562419294143 y[1] (numeric) 26.64456241929417 absolute error 2.842170943040401e-14 relative error 1.0666982997560125e-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] 7.899999999999989 y[1] (closed_form) 26.912344723492595 y[1] (numeric) 26.912344723492623 absolute error 2.842170943040401e-14 relative error 1.0560844743339603e-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] 7.9999999999999885 y[1] (closed_form) 27.182818284590425 y[1] (numeric) 27.182818284590454 absolute error 2.842170943040401e-14 relative error 1.0455762582394149e-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] 8.099999999999989 y[1] (closed_form) 27.456010150169135 y[1] (numeric) 27.456010150169167 absolute error 3.197442310920451e-14 relative error 1.1645691757222613e-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] 8.199999999999989 y[1] (closed_form) 27.73194763964295 y[1] (numeric) 27.731947639642982 absolute error 3.197442310920451e-14 relative error 1.1529815188132304e-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] 8.299999999999988 y[1] (closed_form) 28.01065834699076 y[1] (numeric) 28.010658346990795 absolute error 3.552713678800501e-14 relative error 1.2683435122410024e-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] 8.399999999999988 y[1] (closed_form) 28.292170143515563 y[1] (numeric) 28.292170143515598 absolute error 3.552713678800501e-14 relative error 1.2557232834310403e-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] 8.499999999999988 y[1] (closed_form) 28.576511180631602 y[1] (numeric) 28.57651118063164 absolute error 3.907985046680551e-14 relative error 1.3675514907954472e-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] 8.599999999999987 y[1] (closed_form) 28.863709892679545 y[1] (numeric) 28.863709892679587 absolute error 4.263256414560601e-14 relative error 1.4770299557514103e-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] 8.699999999999987 y[1] (closed_form) 29.15379499976993 y[1] (numeric) 29.15379499976997 absolute error 4.263256414560601e-14 relative error 1.4623332621342249e-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] 8.799999999999986 y[1] (closed_form) 29.4467955106552 y[1] (numeric) 29.446795510655242 absolute error 4.263256414560601e-14 relative error 1.4477828030618678e-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] 8.899999999999986 y[1] (closed_form) 29.742740725630618 y[1] (numeric) 29.742740725630657 absolute error 3.907985046680551e-14 relative error 1.313929029853281e-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] 8.999999999999986 y[1] (closed_form) 30.041660239464285 y[1] (numeric) 30.041660239464335 absolute error 4.973799150320701e-14 relative error 1.6556339132638417e-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] 9.099999999999985 y[1] (closed_form) 30.343583944356713 y[1] (numeric) 30.34358394435676 absolute error 4.618527782440651e-14 relative error 1.5220772176780401e-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] 9.199999999999985 y[1] (closed_form) 30.648542032929974 y[1] (numeric) 30.648542032930024 absolute error 4.973799150320701e-14 relative error 1.6228501652628892e-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] 9.299999999999985 y[1] (closed_form) 30.95656500124707 y[1] (numeric) 30.956565001247117 absolute error 4.618527782440651e-14 relative error 1.4919380694384522e-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] 9.399999999999984 y[1] (closed_form) 31.267683651861514 y[1] (numeric) 31.26768365186156 absolute error 4.618527782440651e-14 relative error 1.4770930376115943e-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] 9.499999999999984 y[1] (closed_form) 31.581929096897625 y[1] (numeric) 31.581929096897678 absolute error 5.3290705182007514e-14 relative error 1.6873796726762457e-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] 9.599999999999984 y[1] (closed_form) 31.899332761161794 y[1] (numeric) 31.899332761161848 absolute error 5.3290705182007514e-14 relative error 1.6705899644048428e-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] 9.699999999999983 y[1] (closed_form) 32.21992638528495 y[1] (numeric) 32.219926385285 absolute error 4.973799150320701e-14 relative error 1.5437028287539068e-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] 9.799999999999983 y[1] (closed_form) 32.54374202889665 y[1] (numeric) 32.54374202889671 absolute error 5.684341886080802e-14 relative error 1.7466774045324868e-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] 9.899999999999983 y[1] (closed_form) 32.87081207383113 y[1] (numeric) 32.87081207383118 absolute error 4.973799150320701e-14 relative error 1.5131354647244647e-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] 9.999999999999982 y[1] (closed_form) 33.20116922736541 y[1] (numeric) 33.201169227365476 absolute error 6.394884621840902e-14 relative error 1.9261022339448345e-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 Finished! diff ( y , x , 1 ) = exp ( 0.1 * x + 0.2 ) ; Iterations 91 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 102.22222222222202%