##############ECHO OF PROBLEM################# ##############temp/add_lin_fullpostode.ode################# diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-5.0 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(0.05 * x * x + 0.2 * x - cos(0.3 * x + 0.1) / 0.3) 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 10.0 estimated_steps 10000000.0 step_error 7.905694150420948e-22 est_needed_step_err 7.905694150420948e-22 opt_iter 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.3165571430008035 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 10.0 estimated_steps 10000000.0 step_error 7.905694150420948e-22 est_needed_step_err 7.905694150420948e-22 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.2859869688048747e-277 estimated_step_error 2.2859869688048747e-277 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 0.3165571430008035 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 10.0 estimated_steps 5000000.0 step_error 1.1180339887498947e-21 est_needed_step_err 1.1180339887498947e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.570918320140187e-266 estimated_step_error 1.570918320140187e-266 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 0.3165571430008035 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 10.0 estimated_steps 2500000.0 step_error 1.5811388300841896e-21 est_needed_step_err 1.5811388300841896e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.07952690029871e-255 estimated_step_error 1.07952690029871e-255 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 0.3165571430008035 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 10.0 estimated_steps 1250000.0 step_error 2.2360679774997895e-21 est_needed_step_err 2.2360679774997895e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.418453068577198e-245 estimated_step_error 7.418453068577198e-245 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 0.3165571430008035 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 10.0 estimated_steps 625000.0 step_error 3.1622776601683792e-21 est_needed_step_err 3.1622776601683792e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.097923089242376e-234 estimated_step_error 5.097923089242376e-234 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 0.3165571430008035 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 10.0 estimated_steps 312500.0 step_error 4.472135954999579e-21 est_needed_step_err 4.472135954999579e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.503267388835152e-223 estimated_step_error 3.503267388835152e-223 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 0.3165571430008035 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 10.0 estimated_steps 156250.0 step_error 6.3245553203367584e-21 est_needed_step_err 6.3245553203367584e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.407428829034187e-212 estimated_step_error 2.407428829034187e-212 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 0.3165571430008035 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 10.0 estimated_steps 78125.0 step_error 8.944271909999158e-21 est_needed_step_err 8.944271909999158e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6543749827984765e-201 estimated_step_error 1.6543749827984765e-201 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 0.3165571430008035 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 10.0 estimated_steps 39062.5 step_error 1.2649110640673517e-20 est_needed_step_err 1.2649110640673517e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1368812518657298e-190 estimated_step_error 1.1368812518657298e-190 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 0.3165571430008035 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 10.0 estimated_steps 19531.25 step_error 1.7888543819998316e-20 est_needed_step_err 1.7888543819998316e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.812635484011038e-180 estimated_step_error 7.812635484011038e-180 Double H and LOOP opt_iter 11 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5583135835931752 Order of pole (three term test) 32.971111170334325 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] -5.0 y[1] (closed_form) -0.3165571430008035 y[1] (numeric) -0.3165571430008035 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.000512 NO POLE (given) for Equation 1 NO 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] -4.899648000000074 y[1] (closed_form) -0.4447794010600288 y[1] (numeric) -0.4447794010601226 absolute error 9.381384558082573e-14 relative error 2.1092219054489065e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -4.799808000000147 y[1] (closed_form) -0.5707500252851385 y[1] (numeric) -0.5707500252853249 absolute error 1.8640644583456378e-13 relative error 3.265991021926592e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -4.69996800000022 y[1] (closed_form) -0.6950396662696058 y[1] (numeric) -0.6950396662698838 absolute error 2.779998453661392e-13 relative error 3.9997694931313906e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -4.599616000000294 y[1] (closed_form) -0.8181850698145494 y[1] (numeric) -0.818185069814918 absolute error 3.6859404417555197e-13 relative error 4.5050204137689516e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -4.4997760000003675 y[1] (closed_form) -0.9388431089896553 y[1] (numeric) -0.9388431089901121 absolute error 4.568567746332519e-13 relative error 4.8661674166720204e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -4.399936000000441 y[1] (closed_form) -1.0575612829958354 y[1] (numeric) -1.0575612829963787 absolute error 5.433431482515516e-13 relative error 5.137698939889153e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -4.2995840000005145 y[1] (closed_form) -1.1748481040567251 y[1] (numeric) -1.1748481040573528 absolute error 6.277200981230635e-13 relative error 5.342989412465829e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -4.199744000000588 y[1] (closed_form) -1.289422779080057 y[1] (numeric) -1.28942277908077 absolute error 7.129852264142755e-13 relative error 5.529491474650054e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -4.099904000000661 y[1] (closed_form) -1.4018063422860085 y[1] (numeric) -1.4018063422868041 absolute error 7.955858194463872e-13 relative error 5.6754331568294824e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -3.9995520000007345 y[1] (closed_form) -1.5124759086229125 y[1] (numeric) -1.5124759086237891 absolute error 8.766321002440236e-13 relative error 5.796007032219009e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -3.8997120000007213 y[1] (closed_form) -1.6202214403852142 y[1] (numeric) -1.620221440386077 absolute error 8.628653347386717e-13 relative error 5.325601261846788e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -3.799872000000708 y[1] (closed_form) -1.72553428311963 y[1] (numeric) -1.7255342831204792 absolute error 8.490985692333197e-13 relative error 4.920786434322339e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -3.7000320000006948 y[1] (closed_form) -1.8283365324952245 y[1] (numeric) -1.8283365324960608 absolute error 8.362199821476679e-13 relative error 4.5736655549207656e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -3.5996800000006814 y[1] (closed_form) -1.9290587680356654 y[1] (numeric) -1.9290587680364888 absolute error 8.233413950620161e-13 relative error 4.268099078704655e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -3.499840000000668 y[1] (closed_form) -2.0265977745126875 y[1] (numeric) -2.0265977745134993 absolute error 8.117950756059145e-13 relative error 4.005703972516783e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -3.400000000000655 y[1] (closed_form) -2.1214005221442633 y[1] (numeric) -2.1214005221450614 absolute error 7.980283101005625e-13 relative error 3.761799347979483e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -3.2996480000006416 y[1] (closed_form) -2.2138593599398284 y[1] (numeric) -2.213859359940619 absolute error 7.904787935331115e-13 relative error 3.5705917360287796e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -3.1998080000006284 y[1] (closed_form) -2.3029601008673652 y[1] (numeric) -2.302960100868142 absolute error 7.767120280277595e-13 relative error 3.372668192276653e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -3.099968000000615 y[1] (closed_form) -2.3891130005527166 y[1] (numeric) -2.3891130005534835 absolute error 7.669420654110581e-13 relative error 3.210153999553925e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -2.999616000000602 y[1] (closed_form) -2.4726695397788516 y[1] (numeric) -2.472669539779609 absolute error 7.571721027943568e-13 relative error 3.0621645578328113e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -2.8997760000005885 y[1] (closed_form) -2.552711651750601 y[1] (numeric) -2.5527116517513493 absolute error 7.482903185973555e-13 relative error 2.9313546560740314e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -2.7999360000005753 y[1] (closed_form) -2.629610136199352 y[1] (numeric) -2.629610136200092 absolute error 7.402967128200544e-13 relative error 2.815233720881627e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -2.699584000000562 y[1] (closed_form) -2.7036731744773355 y[1] (numeric) -2.703673174478066 absolute error 7.30526750203353e-13 relative error 2.7019787639257686e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -2.5997440000005487 y[1] (closed_form) -2.774085382596055 y[1] (numeric) -2.774085382596778 absolute error 7.229772336359019e-13 relative error 2.606182340931852e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -2.4999040000005355 y[1] (closed_form) -2.8411755581634717 y[1] (numeric) -2.841175558164185 absolute error 7.132072710192006e-13 relative error 2.510254141001466e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -2.399552000000522 y[1] (closed_form) -2.905206378088427 y[1] (numeric) -2.905206378089132 absolute error 7.052136652418994e-13 relative error 2.427413317555489e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -2.299712000000509 y[1] (closed_form) -2.9654711211558813 y[1] (numeric) -2.9654711211565785 absolute error 6.972200594645983e-13 relative error 2.3511274633247343e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -2.1998720000004957 y[1] (closed_form) -3.0222542523096836 y[1] (numeric) -3.0222542523103755 absolute error 6.918909889463976e-13 relative error 2.289320921354108e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -2.1000320000004824 y[1] (closed_form) -3.075507071131643 y[1] (numeric) -3.0755070711323307 absolute error 6.87894186057747e-13 relative error 2.2366854315331947e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -1.999680000000469 y[1] (closed_form) -3.1254286038734675 y[1] (numeric) -3.125428603874148 absolute error 6.803446694902959e-13 relative error 2.1768043865955467e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -1.8998400000004558 y[1] (closed_form) -3.171465151086239 y[1] (numeric) -3.1714651510869145 absolute error 6.754596881819452e-13 relative error 2.129803280198736e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -1.8000000000004426 y[1] (closed_form) -3.2138388773996986 y[1] (numeric) -3.2138388774003688 absolute error 6.701306176637445e-13 relative error 2.0851406782593405e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -1.6996480000004293 y[1] (closed_form) -3.2526991366312745 y[1] (numeric) -3.2526991366319398 absolute error 6.652456363553938e-13 relative error 2.0452110951902218e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -1.599808000000416 y[1] (closed_form) -3.287612315006641 y[1] (numeric) -3.287612315007303 absolute error 6.621370118864434e-13 relative error 2.014036171065705e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -1.4999680000004028 y[1] (closed_form) -3.3187517486921627 y[1] (numeric) -3.3187517486928217 absolute error 6.590283874174929e-13 relative error 1.9857718724433052e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -1.3996160000003894 y[1] (closed_form) -3.346215785465345 y[1] (numeric) -3.3462157854659997 absolute error 6.545874953189923e-13 relative error 1.9562022812822317e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -1.2997760000003762 y[1] (closed_form) -3.3696946152863583 y[1] (numeric) -3.3696946152870138 absolute error 6.554756737386924e-13 relative error 1.9452079448540467e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -1.199936000000363 y[1] (closed_form) -3.38931125947175 y[1] (numeric) -3.389311259472405 absolute error 6.550315845288424e-13 relative error 1.9326392130504238e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] -1.0995840000003496 y[1] (closed_form) -3.4051120147397906 y[1] (numeric) -3.4051120147404457 absolute error 6.550315845288424e-13 relative error 1.923671179372048e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9997440000003365 y[1] (closed_form) -3.416913839241493 y[1] (numeric) -3.4169138392421465 absolute error 6.536993168992922e-13 relative error 1.9131278915841912e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8999040000003449 y[1] (closed_form) -3.424788236047418 y[1] (numeric) -3.424788236048077 absolute error 6.590283874174929e-13 relative error 1.9242894508948795e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7995520000003533 y[1] (closed_form) -3.4287287028443765 y[1] (numeric) -3.428728702845035 absolute error 6.585842982076429e-13 relative error 1.9207827602729254e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6997120000003617 y[1] (closed_form) -3.4286811528259946 y[1] (numeric) -3.4286811528266536 absolute error 6.590283874174929e-13 relative error 1.9221046170312665e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5998720000003701 y[1] (closed_form) -3.4246646601539728 y[1] (numeric) -3.424664660154632 absolute error 6.590283874174929e-13 relative error 1.9243588871205365e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5000320000003785 y[1] (closed_form) -3.416670735111901 y[1] (numeric) -3.416670735112559 absolute error 6.581402089977928e-13 relative error 1.926261732610994e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.39968000000037607 y[1] (closed_form) -3.4046218679850497 y[1] (numeric) -3.4046218679857114 absolute error 6.616929226765933e-13 relative error 1.9435136950118977e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.29984000000037364 y[1] (closed_form) -3.388637862962477 y[1] (numeric) -3.3886378629631384 absolute error 6.612488334667432e-13 relative error 1.9513706102801263e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.20000000000037121 y[1] (closed_form) -3.3686670222033417 y[1] (numeric) -3.368667022204006 absolute error 6.643574579356937e-13 relative error 1.972167191226748e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.09964800000036947 y[1] (closed_form) -3.3445784762268604 y[1] (numeric) -3.3445784762275252 absolute error 6.648015471455437e-13 relative error 1.9876990534709485e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.00019199999963030203 y[1] (closed_form) -3.316622975565703 y[1] (numeric) -3.316622975566366 absolute error 6.630251903061435e-13 relative error 1.9990972600467315e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10003199999963008 y[1] (closed_form) -3.284695443886685 y[1] (numeric) -3.284695443887347 absolute error 6.621370118864434e-13 relative error 2.0158246729351438e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20038399999963186 y[1] (closed_form) -3.248611923852337 y[1] (numeric) -3.248611923853 absolute error 6.625811010962934e-13 relative error 2.0395821865684025e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3002239999996343 y[1] (closed_form) -3.2087536160988552 y[1] (numeric) -3.20875361609952 absolute error 6.648015471455437e-13 relative error 2.0718373134357304e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4000639999996367 y[1] (closed_form) -3.164962170268584 y[1] (numeric) -3.164962170269251 absolute error 6.67021993194794e-13 relative error 2.1075196394470313e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5004159999996391 y[1] (closed_form) -3.117001118517997 y[1] (numeric) -3.117001118518669 absolute error 6.719069745031447e-13 relative error 2.1556199338889177e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6002559999996308 y[1] (closed_form) -3.0653808079324456 y[1] (numeric) -3.065380807933114 absolute error 6.683542608243442e-13 relative error 2.1803302842335577e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7000959999996224 y[1] (closed_form) -3.009890025546195 y[1] (numeric) -3.009890025546859 absolute error 6.639133687258436e-13 relative error 2.2057728458213866e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8004479999996139 y[1] (closed_form) -2.950240671127167 y[1] (numeric) -2.9502406711278275 absolute error 6.603606550470431e-13 relative error 2.2383280845855402e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9002879999996055 y[1] (closed_form) -2.8870701376959182 y[1] (numeric) -2.8870701376965733 absolute error 6.550315845288424e-13 relative error 2.2688454152056134e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 1.0001279999995971 y[1] (closed_form) -2.8201150647126254 y[1] (numeric) -2.8201150647132747 absolute error 6.492584248007915e-13 relative error 2.3022409011773856e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 1.0999679999996104 y[1] (closed_form) -2.749409091924761 y[1] (numeric) -2.74940909192542 absolute error 6.590283874174929e-13 relative error 2.3969819164165603e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 1.2003199999996237 y[1] (closed_form) -2.6745971761413276 y[1] (numeric) -2.6745971761419955 absolute error 6.679101716144942e-13 relative error 2.4972365093800628e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 1.300159999999637 y[1] (closed_form) -2.5964814238904594 y[1] (numeric) -2.59648142389114 absolute error 6.803446694902959e-13 relative error 2.620256256141035e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 1.3999999999996502 y[1] (closed_form) -2.5147305989257926 y[1] (numeric) -2.5147305989264837 absolute error 6.910028105266974e-13 relative error 2.7478204258614037e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 1.5003519999996635 y[1] (closed_form) -2.4289411989211915 y[1] (numeric) -2.428941198921892 absolute error 7.003286839335487e-13 relative error 2.883267343995804e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 1.6001919999996768 y[1] (closed_form) -2.3400344859866067 y[1] (numeric) -2.3400344859873194 absolute error 7.127631818093505e-13 relative error 3.0459516134388715e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 1.70003199999969 y[1] (closed_form) -2.247629887549403 y[1] (numeric) -2.2476298875501284 absolute error 7.251976796851523e-13 relative error 3.226499539369612e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 1.8003839999997033 y[1] (closed_form) -2.151277258118415 y[1] (numeric) -2.1512772581191566 absolute error 7.416289804496046e-13 relative error 3.447389115702641e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 1.9002239999997166 y[1] (closed_form) -2.052012417000638 y[1] (numeric) -2.0520124170013894 absolute error 7.513989430663059e-13 relative error 3.6617660636021013e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 2.0000639999997296 y[1] (closed_form) -1.9494071270085445 y[1] (numeric) -1.949407127009309 absolute error 7.644995747568828e-13 relative error 3.9217029842813944e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 2.100415999999743 y[1] (closed_form) -1.8429666687194015 y[1] (numeric) -1.8429666687201802 absolute error 7.787104294720848e-13 relative error 4.225309348720763e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 2.200255999999756 y[1] (closed_form) -1.7338361415112848 y[1] (numeric) -1.7338361415120775 absolute error 7.926992395823618e-13 relative error 4.571938608289775e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 2.3000959999997694 y[1] (closed_form) -1.621541576826445 y[1] (numeric) -1.6215415768272528 absolute error 8.077982727172639e-13 relative error 4.981668581685237e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 2.4004479999997828 y[1] (closed_form) -1.5055459870543564 y[1] (numeric) -1.50554598705518 absolute error 8.235634396669411e-13 relative error 5.470197833533245e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 2.500287999999796 y[1] (closed_form) -1.3870978385019952 y[1] (numeric) -1.3870978385028352 absolute error 8.399947404313934e-13 relative error 6.05577138912242e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 2.6001279999998093 y[1] (closed_form) -1.2656796103672983 y[1] (numeric) -1.2656796103681545 absolute error 8.562039965909207e-13 relative error 6.764776722147335e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 2.6999679999998225 y[1] (closed_form) -1.1413594689371271 y[1] (numeric) -1.1413594689379998 absolute error 8.72635297355373e-13 relative error 7.645578111933489e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 2.800319999999836 y[1] (closed_form) -1.0135480506663288 y[1] (numeric) -1.0135480506672194 absolute error 8.906209103543006e-13 relative error 8.787160211780653e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 2.900159999999849 y[1] (closed_form) -0.8836213853698789 y[1] (numeric) -0.8836213853707876 absolute error 9.087175456556906e-13 relative error 1.0284014858641143e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000512 NO POLE (given) for Equation 1 NO 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] 2.9999999999998623 y[1] (closed_form) -0.7510076862273172 y[1] (numeric) -0.7510076862282434 absolute error 9.262590694447681e-13 relative error 1.2333549794913887e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000512 NO POLE (given) for Equation 1 NO 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] 3.1003519999998757 y[1] (closed_form) -0.6150815115596373 y[1] (numeric) -0.6150815115605816 absolute error 9.442446824436956e-13 relative error 1.53515373929776e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000512 NO POLE (given) for Equation 1 NO 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] 3.200191999999889 y[1] (closed_form) -0.47730626940292864 y[1] (numeric) -0.4773062694038913 absolute error 9.626743846524732e-13 relative error 2.0168902995066472e-10% Desired digits 16 Estimated correct digits 10 Correct digits 12 h 0.000512 NO POLE (given) for Equation 1 NO 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] 3.300031999999902 y[1] (closed_form) -0.3370725574009752 y[1] (numeric) -0.33707255740195663 absolute error 9.814371537686384e-13 relative error 2.9116495312940565e-10% Desired digits 16 Estimated correct digits 10 Correct digits 12 h 0.000512 NO POLE (given) for Equation 1 NO 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] 3.4003839999999155 y[1] (closed_form) -0.19372180534406525 y[1] (numeric) -0.1937218053450663 absolute error 1.001060345728888e-12 relative error 5.16751505567959e-10% Desired digits 16 Estimated correct digits 10 Correct digits 12 h 0.000512 NO POLE (given) for Equation 1 NO 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] 3.5002239999999287 y[1] (closed_form) -0.048797138241590376 y[1] (numeric) -0.04879713824261073 absolute error 1.0203504707817501e-12 relative error 2.0910047341917552e-09% Desired digits 16 Estimated correct digits 9 Correct digits 11 h 0.000512 NO POLE (given) for Equation 1 NO 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] 3.600063999999942 y[1] (closed_form) 0.09834560066727249 y[1] (numeric) 0.0983456006662326 absolute error 1.0398903960151529e-12 relative error 1.0573837456475145e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.000512 NO POLE (given) for Equation 1 NO 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] 3.7004159999999553 y[1] (closed_form) 0.24839501667442 y[1] (numeric) 0.2483950166733602 absolute error 1.0597911437315588e-12 relative error 4.2665555771622585e-10% Desired digits 16 Estimated correct digits 10 Correct digits 12 h 0.000512 NO POLE (given) for Equation 1 NO 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] 3.8002559999999685 y[1] (closed_form) 0.3997363257106632 y[1] (numeric) 0.3997363257095833 absolute error 1.0799139360528898e-12 relative error 2.7015656736549685e-10% Desired digits 16 Estimated correct digits 10 Correct digits 12 h 0.000512 NO POLE (given) for Equation 1 NO 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] 3.900095999999982 y[1] (closed_form) 0.553045420801412 y[1] (numeric) 0.5530454208003115 absolute error 1.1004530620084552e-12 relative error 1.9898059374830387e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000512 NO POLE (given) for Equation 1 NO 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] 4.000447999999995 y[1] (closed_form) 0.7090377300722147 y[1] (numeric) 0.7090377300710942 absolute error 1.1205480987541705e-12 relative error 1.580378661428982e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000512 NO POLE (given) for Equation 1 NO 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] 4.100287999999922 y[1] (closed_form) 0.8660351997341827 y[1] (numeric) 0.8660351997331779 absolute error 1.0048628595882292e-12 relative error 1.1603025603308706e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000512 NO POLE (given) for Equation 1 NO 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] 4.200127999999848 y[1] (closed_form) 1.0247423083641993 y[1] (numeric) 1.0247423083633105 absolute error 8.888445535149003e-13 relative error 8.673834838865654e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 4.299967999999775 y[1] (closed_form) 1.1850717694090513 y[1] (numeric) 1.1850717694082804 absolute error 7.709388682997087e-13 relative error 6.505419234517294e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 4.400319999999701 y[1] (closed_form) 1.347769609618318 y[1] (numeric) 1.3477696096176666 absolute error 6.514788708500419e-13 relative error 4.8337554593958946e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 4.500159999999628 y[1] (closed_form) 1.5110869379294034 y[1] (numeric) 1.511086937928872 absolute error 5.313527395855999e-13 relative error 3.516361145399724e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 4.599999999999555 y[1] (closed_form) 1.6757612517848977 y[1] (numeric) 1.6757612517844866 absolute error 4.1100456371623295e-13 relative error 2.4526439149876578e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 4.700351999999481 y[1] (closed_form) 1.8425575929286206 y[1] (numeric) 1.842557592928333 absolute error 2.8754776337791554e-13 relative error 1.5605903689603418e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000512 NO POLE (given) for Equation 1 NO 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] 4.800191999999408 y[1] (closed_form) 2.0096842740302865 y[1] (numeric) 2.0096842740301204 absolute error 1.6608936448392342e-13 relative error 8.2644506219299e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000512 NO POLE (given) for Equation 1 NO 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] 4.900031999999334 y[1] (closed_form) 2.17789965767094 y[1] (numeric) 2.177899657670899 absolute error 4.085620730620576e-14 relative error 1.875945347725416e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000512 NO POLE (given) for Equation 1 NO 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 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ; Iterations 19532 Total Elapsed Time 3 Seconds Elapsed Time(since restart) 3 Seconds Time to Timeout 2 Minutes 57.0 Seconds Percent Done 100.0089599999926%