##############ECHO OF PROBLEM################# ##############temp/add_sub_sin_c_cos_c_tan_cpostode.ode################# diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #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((sin(0.1) + cos(0.05) - tan(0.02)) * x) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 10.0 estimated_steps 10000000.0 step_error 1.0540925533894597e-21 est_needed_step_err 1.0540925533894597e-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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 10000000.0 step_error 5.684621054069414e-21 est_needed_step_err 5.684621054069414e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 5000000.0 step_error 8.039268191616604e-21 est_needed_step_err 8.039268191616604e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 2500000.0 step_error 1.1369242108138828e-20 est_needed_step_err 1.1369242108138828e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 1250000.0 step_error 1.607853638323321e-20 est_needed_step_err 1.607853638323321e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 625000.0 step_error 2.2738484216277656e-20 est_needed_step_err 2.2738484216277656e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 312500.0 step_error 3.215707276646642e-20 est_needed_step_err 3.215707276646642e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 156250.0 step_error 4.547696843255531e-20 est_needed_step_err 4.547696843255531e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 78125.0 step_error 6.431414553293283e-20 est_needed_step_err 6.431414553293283e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 39062.5 step_error 9.095393686511062e-20 est_needed_step_err 9.095393686511062e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 19531.25 step_error 1.2862829106586567e-19 est_needed_step_err 1.2862829106586567e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 9765.625 step_error 1.8190787373022125e-19 est_needed_step_err 1.8190787373022125e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 4882.8125 step_error 2.5725658213173134e-19 est_needed_step_err 2.5725658213173134e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 2441.40625 step_error 3.638157474604425e-19 est_needed_step_err 3.638157474604425e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 1220.703125 step_error 5.145131642634627e-19 est_needed_step_err 5.145131642634627e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 0.016384 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 610.3515625 step_error 7.27631494920885e-19 est_needed_step_err 7.27631494920885e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 0.032768 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 305.17578125 step_error 1.0290263285269254e-18 est_needed_step_err 1.0290263285269254e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 5.392905049741961 $glob_desired_digits_correct 16 estimated_h 0.065536 estimated_answer 5.392905049741961 desired_abs_gbl_error 5.39290504974196e-16 range 10.0 estimated_steps 152.587890625 step_error 1.45526298984177e-18 est_needed_step_err 1.45526298984177e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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] -5.0 y[1] (closed_form) -5.392905049741961 y[1] (numeric) -5.392905049741961 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] -4.9 y[1] (closed_form) -5.285046948747122 y[1] (numeric) -5.285046948747121 absolute error 8.881784197001252e-16 relative error 1.6805497251271866e-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] -4.800000000000001 y[1] (closed_form) -5.177188847752283 y[1] (numeric) -5.177188847752282 absolute error 8.881784197001252e-16 relative error 1.715561177734003e-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] -4.700000000000001 y[1] (closed_form) -5.069330746757444 y[1] (numeric) -5.069330746757442 absolute error 1.7763568394002505e-15 relative error 3.504124958775835e-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] -4.600000000000001 y[1] (closed_form) -4.961472645762606 y[1] (numeric) -4.961472645762603 absolute error 2.6645352591003757e-15 relative error 5.37045238247166e-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] -4.500000000000002 y[1] (closed_form) -4.853614544767766 y[1] (numeric) -4.853614544767764 absolute error 2.6645352591003757e-15 relative error 5.489795768748808e-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] -4.400000000000002 y[1] (closed_form) -4.745756443772928 y[1] (numeric) -4.745756443772924 absolute error 3.552713678800501e-15 relative error 7.48608513920292e-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] -4.3000000000000025 y[1] (closed_form) -4.637898342778088 y[1] (numeric) -4.637898342778085 absolute error 3.552713678800501e-15 relative error 7.660180142440196e-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] -4.200000000000003 y[1] (closed_form) -4.53004024178325 y[1] (numeric) -4.5300402417832455 absolute error 4.440892098500626e-15 relative error 9.803206729908583e-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] -4.100000000000003 y[1] (closed_form) -4.422182140788411 y[1] (numeric) -4.422182140788406 absolute error 5.329070518200751e-15 relative error 1.20507711996925e-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] -4.0000000000000036 y[1] (closed_form) -4.314324039793572 y[1] (numeric) -4.314324039793567 absolute error 5.329070518200751e-15 relative error 1.2352040479684813e-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] -3.9000000000000035 y[1] (closed_form) -4.206465938798733 y[1] (numeric) -4.206465938798727 absolute error 5.329070518200751e-15 relative error 1.2668759466343397e-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] -3.8000000000000034 y[1] (closed_form) -4.098607837803893 y[1] (numeric) -4.098607837803888 absolute error 5.329070518200751e-15 relative error 1.3002147873352435e-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] -3.7000000000000033 y[1] (closed_form) -3.9907497368090543 y[1] (numeric) -3.9907497368090485 absolute error 5.773159728050814e-15 relative error 1.4466353714946178e-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] -3.600000000000003 y[1] (closed_form) -3.882891635814215 y[1] (numeric) -3.882891635814209 absolute error 5.773159728050814e-15 relative error 1.4868196873694682e-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] -3.500000000000003 y[1] (closed_form) -3.775033534819376 y[1] (numeric) -3.7750335348193698 absolute error 6.217248937900877e-15 relative error 1.6469387306246416e-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] -3.400000000000003 y[1] (closed_form) -3.6671754338245366 y[1] (numeric) -3.6671754338245304 absolute error 6.217248937900877e-15 relative error 1.6953781050547781e-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] -3.300000000000003 y[1] (closed_form) -3.559317332829697 y[1] (numeric) -3.559317332829691 absolute error 6.217248937900877e-15 relative error 1.7467531991473472e-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] -3.200000000000003 y[1] (closed_form) -3.451459231834858 y[1] (numeric) -3.4514592318348516 absolute error 6.217248937900877e-15 relative error 1.8013392366207017e-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] -3.1000000000000028 y[1] (closed_form) -3.3436011308400184 y[1] (numeric) -3.343601130840012 absolute error 6.217248937900877e-15 relative error 1.8594469539310472e-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] -3.0000000000000027 y[1] (closed_form) -3.235743029845179 y[1] (numeric) -3.235743029845173 absolute error 6.217248937900877e-15 relative error 1.921428519062082e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.9000000000000026 y[1] (closed_form) -3.12788492885034 y[1] (numeric) -3.1278849288503334 absolute error 6.661338147750939e-15 relative error 2.1296621516697952e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.8000000000000025 y[1] (closed_form) -3.0200268278555007 y[1] (numeric) -3.020026827855494 absolute error 6.661338147750939e-15 relative error 2.2057215142294308e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.7000000000000024 y[1] (closed_form) -2.9121687268606613 y[1] (numeric) -2.9121687268606546 absolute error 6.661338147750939e-15 relative error 2.2874149036453357e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.6000000000000023 y[1] (closed_form) -2.804310625865822 y[1] (numeric) -2.8043106258658153 absolute error 6.661338147750939e-15 relative error 2.375392399939387e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.500000000000002 y[1] (closed_form) -2.6964525248709825 y[1] (numeric) -2.696452524870976 absolute error 6.661338147750939e-15 relative error 2.4704080959369626e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.400000000000002 y[1] (closed_form) -2.5885944238761436 y[1] (numeric) -2.5885944238761365 absolute error 7.105427357601002e-15 relative error 2.7448978843744025e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.300000000000002 y[1] (closed_form) -2.480736322881304 y[1] (numeric) -2.480736322881297 absolute error 7.105427357601002e-15 relative error 2.8642412706515506e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.200000000000002 y[1] (closed_form) -2.372878221886465 y[1] (numeric) -2.3728782218864577 absolute error 7.105427357601002e-15 relative error 2.9944340556811664e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.100000000000002 y[1] (closed_form) -2.2650201208916254 y[1] (numeric) -2.2650201208916183 absolute error 7.105427357601002e-15 relative error 3.1370261535707463e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.0000000000000018 y[1] (closed_form) -2.157162019896786 y[1] (numeric) -2.157162019896779 absolute error 7.105427357601002e-15 relative error 3.2938774612492837e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.9000000000000017 y[1] (closed_form) -2.0493039189019466 y[1] (numeric) -2.0493039189019395 absolute error 7.105427357601002e-15 relative error 3.467239432893983e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8000000000000016 y[1] (closed_form) -1.9414458179071075 y[1] (numeric) -1.9414458179071004 absolute error 7.105427357601002e-15 relative error 3.659863845832537e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.7000000000000015 y[1] (closed_form) -1.8335877169122683 y[1] (numeric) -1.8335877169122612 absolute error 7.105427357601002e-15 relative error 3.8751499544109214e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.6000000000000014 y[1] (closed_form) -1.725729615917429 y[1] (numeric) -1.725729615917422 absolute error 6.8833827526759706e-15 relative error 3.988679738231554e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.5000000000000013 y[1] (closed_form) -1.6178715149225895 y[1] (numeric) -1.6178715149225829 absolute error 6.661338147750939e-15 relative error 4.117346826561604e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.4000000000000012 y[1] (closed_form) -1.5100134139277503 y[1] (numeric) -1.5100134139277437 absolute error 6.661338147750939e-15 relative error 4.4114430284588615e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3000000000000012 y[1] (closed_form) -1.402155312932911 y[1] (numeric) -1.4021553129329045 absolute error 6.439293542825908e-15 relative error 4.592425306549482e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.200000000000001 y[1] (closed_form) -1.2942972119380718 y[1] (numeric) -1.2942972119380654 absolute error 6.439293542825908e-15 relative error 4.975127415428604e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.100000000000001 y[1] (closed_form) -1.1864391109432324 y[1] (numeric) -1.1864391109432262 absolute error 6.217248937900877e-15 relative error 5.240259597442041e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.0000000000000009 y[1] (closed_form) -1.078581009948393 y[1] (numeric) -1.078581009948387 absolute error 5.995204332975845e-15 relative error 5.558418215858166e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9000000000000009 y[1] (closed_form) -0.9707229089535538 y[1] (numeric) -0.9707229089535478 absolute error 5.995204332975845e-15 relative error 6.176020239842406e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8000000000000009 y[1] (closed_form) -0.8628648079587147 y[1] (numeric) -0.8628648079587087 absolute error 5.995204332975845e-15 relative error 6.948022769822705e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.700000000000001 y[1] (closed_form) -0.7550067069638755 y[1] (numeric) -0.7550067069638695 absolute error 5.995204332975845e-15 relative error 7.940597451225947e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.600000000000001 y[1] (closed_form) -0.6471486059690363 y[1] (numeric) -0.6471486059690303 absolute error 5.995204332975845e-15 relative error 9.264030359763603e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.500000000000001 y[1] (closed_form) -0.5392905049741972 y[1] (numeric) -0.5392905049741912 absolute error 5.995204332975845e-15 relative error 1.1116836431716318e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.400000000000001 y[1] (closed_form) -0.43143240397935795 y[1] (numeric) -0.43143240397935195 absolute error 5.995204332975845e-15 relative error 1.389604553964539e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.30000000000000104 y[1] (closed_form) -0.3235743029845188 y[1] (numeric) -0.32357430298451273 absolute error 6.050715484207103e-15 relative error 1.869961683730057e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.20000000000000104 y[1] (closed_form) -0.21571620198967956 y[1] (numeric) -0.2157162019896735 absolute error 6.050715484207103e-15 relative error 2.8049425255950807e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.10000000000000103 y[1] (closed_form) -0.10785810099484032 y[1] (numeric) -0.10785810099483428 absolute error 6.036837696399289e-15 relative error 5.597018342357128e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.0269562977782698e-15 y[1] (closed_form) -1.107655560830548e-15 y[1] (numeric) 4.9404924595819466e-15 absolute error 6.0481480204124944e-15 relative error 546.0314771387453% Desired digits 16 Estimated correct digits -1 Correct digits 1 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] 0.09999999999999898 y[1] (closed_form) 0.10785810099483811 y[1] (numeric) 0.10785810099484416 absolute error 6.050715484207103e-15 relative error 5.609885051190248e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19999999999999898 y[1] (closed_form) 0.21571620198967734 y[1] (numeric) 0.2157162019896834 absolute error 6.050715484207103e-15 relative error 2.8049425255951094e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.299999999999999 y[1] (closed_form) 0.32357430298451656 y[1] (numeric) 0.3235743029845226 absolute error 6.050715484207103e-15 relative error 1.86996168373007e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.399999999999999 y[1] (closed_form) 0.4314324039793558 y[1] (numeric) 0.43143240397936183 absolute error 6.050715484207103e-15 relative error 1.402471262797551e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.499999999999999 y[1] (closed_form) 0.539290504974195 y[1] (numeric) 0.5392905049742011 absolute error 6.106226635438361e-15 relative error 1.1322703773044444e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.599999999999999 y[1] (closed_form) 0.6471486059690341 y[1] (numeric) 0.6471486059690403 absolute error 6.217248937900877e-15 relative error 9.607142595310435e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.699999999999999 y[1] (closed_form) 0.7550067069638734 y[1] (numeric) 0.7550067069638795 absolute error 6.106226635438361e-15 relative error 8.087645552174599e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7999999999999989 y[1] (closed_form) 0.8628648079587126 y[1] (numeric) 0.8628648079587187 absolute error 6.106226635438361e-15 relative error 7.076689858152772e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8999999999999989 y[1] (closed_form) 0.9707229089535517 y[1] (numeric) 0.9707229089535578 absolute error 6.106226635438361e-15 relative error 6.290390985024686e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9999999999999989 y[1] (closed_form) 1.078581009948391 y[1] (numeric) 1.078581009948397 absolute error 5.995204332975845e-15 relative error 5.558418215858176e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.099999999999999 y[1] (closed_form) 1.1864391109432302 y[1] (numeric) 1.1864391109432362 absolute error 5.995204332975845e-15 relative error 5.053107468961978e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.199999999999999 y[1] (closed_form) 1.2942972119380696 y[1] (numeric) 1.2942972119380753 absolute error 5.773159728050814e-15 relative error 4.4604590621084116e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2999999999999992 y[1] (closed_form) 1.402155312932909 y[1] (numeric) 1.4021553129329145 absolute error 5.551115123125783e-15 relative error 3.9589873332323176e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3999999999999992 y[1] (closed_form) 1.5100134139277481 y[1] (numeric) 1.5100134139277537 absolute error 5.551115123125783e-15 relative error 3.676202523715723e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4999999999999993 y[1] (closed_form) 1.6178715149225875 y[1] (numeric) 1.6178715149225928 absolute error 5.329070518200751e-15 relative error 3.2938774612492877e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5999999999999994 y[1] (closed_form) 1.7257296159174267 y[1] (numeric) 1.725729615917432 absolute error 5.329070518200751e-15 relative error 3.088010119921207e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6999999999999995 y[1] (closed_form) 1.833587716912266 y[1] (numeric) 1.8335877169122712 absolute error 5.10702591327572e-15 relative error 2.7852640297328533e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7999999999999996 y[1] (closed_form) 1.9414458179071055 y[1] (numeric) 1.9414458179071103 absolute error 4.884981308350689e-15 relative error 2.5161563940098716e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8999999999999997 y[1] (closed_form) 2.049303918901945 y[1] (numeric) 2.0493039189019497 absolute error 4.884981308350689e-15 relative error 2.383727110114615e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9999999999999998 y[1] (closed_form) 2.157162019896784 y[1] (numeric) 2.157162019896789 absolute error 5.329070518200751e-15 relative error 2.470408095936965e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0999999999999996 y[1] (closed_form) 2.265020120891623 y[1] (numeric) 2.2650201208916285 absolute error 5.329070518200751e-15 relative error 2.3527696151780617e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1999999999999997 y[1] (closed_form) 2.3728782218864626 y[1] (numeric) 2.372878221886468 absolute error 5.329070518200751e-15 relative error 2.245825541760877e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3 y[1] (closed_form) 2.4807363228813015 y[1] (numeric) 2.4807363228813073 absolute error 5.773159728050814e-15 relative error 2.327196032404387e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4 y[1] (closed_form) 2.588594423876141 y[1] (numeric) 2.5885944238761467 absolute error 5.773159728050814e-15 relative error 2.2302295310542043e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5 y[1] (closed_form) 2.6964525248709803 y[1] (numeric) 2.696452524870986 absolute error 5.773159728050814e-15 relative error 2.1410203498120361e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6 y[1] (closed_form) 2.8043106258658197 y[1] (numeric) 2.8043106258658255 absolute error 5.773159728050814e-15 relative error 2.0586734132808036e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7 y[1] (closed_form) 2.912168726860659 y[1] (numeric) 2.912168726860665 absolute error 5.773159728050814e-15 relative error 1.982426249825959e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8000000000000003 y[1] (closed_form) 3.020026827855498 y[1] (numeric) 3.0200268278555042 absolute error 6.217248937900877e-15 relative error 2.0586734132808039e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9000000000000004 y[1] (closed_form) 3.1278849288503374 y[1] (numeric) 3.1278849288503436 absolute error 6.217248937900877e-15 relative error 1.9876846748918105e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.0000000000000004 y[1] (closed_form) 3.235743029845177 y[1] (numeric) 3.235743029845183 absolute error 6.217248937900877e-15 relative error 1.9214285190620834e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.1000000000000005 y[1] (closed_form) 3.343601130840016 y[1] (numeric) 3.3436011308400224 absolute error 6.217248937900877e-15 relative error 1.8594469539310482e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.2000000000000006 y[1] (closed_form) 3.4514592318348556 y[1] (numeric) 3.451459231834862 absolute error 6.217248937900877e-15 relative error 1.801339236620703e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.3000000000000007 y[1] (closed_form) 3.559317332829695 y[1] (numeric) 3.559317332829701 absolute error 6.217248937900877e-15 relative error 1.7467531991473482e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.400000000000001 y[1] (closed_form) 3.667175433824534 y[1] (numeric) 3.6671754338245406 absolute error 6.661338147750939e-15 relative error 1.8164765411301208e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.500000000000001 y[1] (closed_form) 3.7750335348193733 y[1] (numeric) 3.77503353481938 absolute error 6.661338147750939e-15 relative error 1.7645772113835458e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.600000000000001 y[1] (closed_form) 3.8828916358142127 y[1] (numeric) 3.8828916358142194 absolute error 6.661338147750939e-15 relative error 1.7155611777340028e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.700000000000001 y[1] (closed_form) 3.990749736809052 y[1] (numeric) 3.9907497368090588 absolute error 6.661338147750939e-15 relative error 1.6691946594168674e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.800000000000001 y[1] (closed_form) 4.0986078378038915 y[1] (numeric) 4.098607837803898 absolute error 6.217248937900877e-15 relative error 1.5169172518911181e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.9000000000000012 y[1] (closed_form) 4.206465938798731 y[1] (numeric) 4.206465938798737 absolute error 6.217248937900877e-15 relative error 1.4780219377400638e-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] 4.000000000000001 y[1] (closed_form) 4.314324039793569 y[1] (numeric) 4.3143240397935765 absolute error 7.105427357601002e-15 relative error 1.6469387306246428e-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] 4.1000000000000005 y[1] (closed_form) 4.422182140788408 y[1] (numeric) 4.422182140788416 absolute error 7.993605777301127e-15 relative error 1.8076156799538765e-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] 4.2 y[1] (closed_form) 4.530040241783247 y[1] (numeric) 4.530040241783255 absolute error 7.993605777301127e-15 relative error 1.764577211383546e-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] 4.3 y[1] (closed_form) 4.637898342778086 y[1] (numeric) 4.637898342778095 absolute error 8.881784197001252e-15 relative error 1.9150450356100503e-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] 4.3999999999999995 y[1] (closed_form) 4.745756443772925 y[1] (numeric) 4.745756443772934 absolute error 8.881784197001252e-15 relative error 1.871521284800731e-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] 4.499999999999999 y[1] (closed_form) 4.853614544767764 y[1] (numeric) 4.853614544767773 absolute error 9.769962616701378e-15 relative error 2.0129251152078974e-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] 4.599999999999999 y[1] (closed_form) 4.961472645762602 y[1] (numeric) 4.961472645762613 absolute error 1.0658141036401503e-14 relative error 2.1481809529886656e-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] 4.699999999999998 y[1] (closed_form) 5.0693307467574416 y[1] (numeric) 5.069330746757452 absolute error 1.0658141036401503e-14 relative error 2.1024749752655024e-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] 4.799999999999998 y[1] (closed_form) 5.17718884775228 y[1] (numeric) 5.177188847752292 absolute error 1.1546319456101628e-14 relative error 2.230229531054205e-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] 4.899999999999998 y[1] (closed_form) 5.2850469487471186 y[1] (numeric) 5.285046948747131 absolute error 1.2434497875801753e-14 relative error 2.3527696151780627e-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] 4.999999999999997 y[1] (closed_form) 5.392905049741958 y[1] (numeric) 5.39290504974197 absolute error 1.2434497875801753e-14 relative error 2.3057142228745017e-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 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; Iterations 101 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 101.99999999999996%