##############ECHO OF PROBLEM################# ##############temp/multpostode.ode################# diff ( y , x , 1 ) = x * x ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=10.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=3 # ELIMINATED in preodein.rb #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(1.0 + x * x * x / 3.0) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 9.9 estimated_steps 9900000.0 step_error 1.059402876939547e-21 est_needed_step_err 1.059402876939547e-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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 9900000.0 step_error 1.0597560112318603e-21 est_needed_step_err 1.0597560112318603e-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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 4950000.0 step_error 1.4987213238905107e-21 est_needed_step_err 1.4987213238905107e-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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 2475000.0 step_error 2.1195120224637207e-21 est_needed_step_err 2.1195120224637207e-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 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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 1237500.0 step_error 2.9974426477810213e-21 est_needed_step_err 2.9974426477810213e-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 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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 618750.0 step_error 4.239024044927441e-21 est_needed_step_err 4.239024044927441e-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 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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 309375.0 step_error 5.994885295562043e-21 est_needed_step_err 5.994885295562043e-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 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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 154687.5 step_error 8.478048089854883e-21 est_needed_step_err 8.478048089854883e-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 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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 77343.75 step_error 1.1989770591124085e-20 est_needed_step_err 1.1989770591124085e-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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 38671.875 step_error 1.6956096179709765e-20 est_needed_step_err 1.6956096179709765e-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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 19335.9375 step_error 2.397954118224817e-20 est_needed_step_err 2.397954118224817e-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 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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 9667.96875 step_error 3.391219235941953e-20 est_needed_step_err 3.391219235941953e-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 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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 4833.984375 step_error 4.795908236449634e-20 est_needed_step_err 4.795908236449634e-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 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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 2416.9921875 step_error 6.782438471883906e-20 est_needed_step_err 6.782438471883906e-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 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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 1208.49609375 step_error 9.591816472899268e-20 est_needed_step_err 9.591816472899268e-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 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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 0.016384 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 604.248046875 step_error 1.3564876943767812e-19 est_needed_step_err 1.3564876943767812e-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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 0.032768 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 302.1240234375 step_error 1.9183632945798537e-19 est_needed_step_err 1.9183632945798537e-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 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 1.0003333333333333 $glob_desired_digits_correct 16 estimated_h 0.065536 estimated_answer 1.0003333333333333 desired_abs_gbl_error 1.0003333333333333e-16 range 9.9 estimated_steps 151.06201171875 step_error 2.7129753887535624e-19 est_needed_step_err 2.7129753887535624e-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 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] 0.1 y[1] (closed_form) 1.0003333333333333 y[1] (numeric) 1.0003333333333333 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] 0.2 y[1] (closed_form) 1.0026666666666666 y[1] (numeric) 1.0026666666666666 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] 0.30000000000000004 y[1] (closed_form) 1.009 y[1] (numeric) 1.009 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] 0.4 y[1] (closed_form) 1.0213333333333334 y[1] (numeric) 1.0213333333333332 absolute error 2.220446049250313e-16 relative error 2.174065975114536e-14% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5 y[1] (closed_form) 1.0416666666666667 y[1] (numeric) 1.0416666666666665 absolute error 2.220446049250313e-16 relative error 2.1316282072803006e-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] 0.6 y[1] (closed_form) 1.072 y[1] (numeric) 1.0719999999999998 absolute error 2.220446049250313e-16 relative error 2.0713116131066354e-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] 0.7 y[1] (closed_form) 1.1143333333333334 y[1] (numeric) 1.1143333333333332 absolute error 2.220446049250313e-16 relative error 1.9926228380948066e-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] 0.7999999999999999 y[1] (closed_form) 1.1706666666666665 y[1] (numeric) 1.1706666666666665 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8999999999999999 y[1] (closed_form) 1.2429999999999999 y[1] (numeric) 1.2429999999999999 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9999999999999999 y[1] (closed_form) 1.3333333333333333 y[1] (numeric) 1.3333333333333333 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0999999999999999 y[1] (closed_form) 1.4436666666666664 y[1] (numeric) 1.4436666666666667 absolute error 2.220446049250313e-16 relative error 1.5380600664398384e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2 y[1] (closed_form) 1.576 y[1] (numeric) 1.576 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3 y[1] (closed_form) 1.7323333333333335 y[1] (numeric) 1.7323333333333335 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4000000000000001 y[1] (closed_form) 1.9146666666666667 y[1] (numeric) 1.914666666666667 absolute error 2.220446049250313e-16 relative error 1.1597037165304559e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5000000000000002 y[1] (closed_form) 2.125000000000001 y[1] (numeric) 2.1250000000000004 absolute error 4.440892098500626e-16 relative error 2.0898315757649997e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6000000000000003 y[1] (closed_form) 2.365333333333334 y[1] (numeric) 2.365333333333334 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7000000000000004 y[1] (closed_form) 2.637666666666668 y[1] (numeric) 2.6376666666666675 absolute error 4.440892098500626e-16 relative error 1.68364416725665e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8000000000000005 y[1] (closed_form) 2.9440000000000017 y[1] (numeric) 2.944000000000001 absolute error 8.881784197001252e-16 relative error 3.016910393003141e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9000000000000006 y[1] (closed_form) 3.2863333333333355 y[1] (numeric) 3.286333333333334 absolute error 1.3322676295501878e-15 relative error 4.053963777919222e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0000000000000004 y[1] (closed_form) 3.6666666666666683 y[1] (numeric) 3.666666666666668 absolute error 4.440892098500626e-16 relative error 1.2111523905001702e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1000000000000005 y[1] (closed_form) 4.0870000000000015 y[1] (numeric) 4.0870000000000015 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2000000000000006 y[1] (closed_form) 4.549333333333337 y[1] (numeric) 4.549333333333335 absolute error 1.7763568394002505e-15 relative error 3.904653076055647e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3000000000000007 y[1] (closed_form) 5.055666666666671 y[1] (numeric) 5.055666666666669 absolute error 1.7763568394002505e-15 relative error 3.5135956472609924e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.400000000000001 y[1] (closed_form) 5.608000000000005 y[1] (numeric) 5.608000000000002 absolute error 2.6645352591003757e-15 relative error 4.751311089693961e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.500000000000001 y[1] (closed_form) 6.208333333333338 y[1] (numeric) 6.208333333333336 absolute error 2.6645352591003757e-15 relative error 4.2918688737187226e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.600000000000001 y[1] (closed_form) 6.8586666666666725 y[1] (numeric) 6.85866666666667 absolute error 2.6645352591003757e-15 relative error 3.88491727123888e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.700000000000001 y[1] (closed_form) 7.561000000000007 y[1] (numeric) 7.5610000000000035 absolute error 3.552713678800501e-15 relative error 4.698735192171006e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.800000000000001 y[1] (closed_form) 8.317333333333341 y[1] (numeric) 8.317333333333337 absolute error 3.552713678800501e-15 relative error 4.2714576131778985e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9000000000000012 y[1] (closed_form) 9.129666666666678 y[1] (numeric) 9.129666666666672 absolute error 5.329070518200751e-15 relative error 5.837092100698176e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.0000000000000013 y[1] (closed_form) 10.000000000000012 y[1] (numeric) 10.000000000000007 absolute error 5.329070518200751e-15 relative error 5.329070518200745e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.1000000000000014 y[1] (closed_form) 10.930333333333346 y[1] (numeric) 10.93033333333334 absolute error 5.329070518200751e-15 relative error 4.87548765045355e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.2000000000000015 y[1] (closed_form) 11.92266666666668 y[1] (numeric) 11.922666666666675 absolute error 5.329070518200751e-15 relative error 4.4696968112844544e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.3000000000000016 y[1] (closed_form) 12.979000000000019 y[1] (numeric) 12.97900000000001 absolute error 8.881784197001252e-15 relative error 6.843196083674582e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.4000000000000017 y[1] (closed_form) 14.101333333333352 y[1] (numeric) 14.101333333333343 absolute error 8.881784197001252e-15 relative error 6.29854212154967e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.5000000000000018 y[1] (closed_form) 15.291666666666687 y[1] (numeric) 15.291666666666679 absolute error 8.881784197001252e-15 relative error 5.808251245995361e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.600000000000002 y[1] (closed_form) 16.55200000000002 y[1] (numeric) 16.552000000000014 absolute error 7.105427357601002e-15 relative error 4.2927908153703436e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.700000000000002 y[1] (closed_form) 17.88433333333336 y[1] (numeric) 17.88433333333335 absolute error 1.0658141036401503e-14 relative error 5.959484671724686e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.800000000000002 y[1] (closed_form) 19.290666666666695 y[1] (numeric) 19.290666666666684 absolute error 1.0658141036401503e-14 relative error 5.5250247285741744e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.900000000000002 y[1] (closed_form) 20.77300000000003 y[1] (numeric) 20.77300000000002 absolute error 1.0658141036401503e-14 relative error 5.1307663969583046e-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] 4.000000000000002 y[1] (closed_form) 22.33333333333336 y[1] (numeric) 22.333333333333357 absolute error 3.552713678800501e-15 relative error 1.590767318865894e-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] 4.100000000000001 y[1] (closed_form) 23.97366666666669 y[1] (numeric) 23.97366666666669 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.200000000000001 y[1] (closed_form) 25.696000000000016 y[1] (numeric) 25.696000000000026 absolute error 1.0658141036401503e-14 relative error 4.1477821592471577e-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] 4.300000000000001 y[1] (closed_form) 27.502333333333343 y[1] (numeric) 27.50233333333336 absolute error 1.7763568394002505e-14 relative error 6.458931385459111e-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] 4.4 y[1] (closed_form) 29.394666666666676 y[1] (numeric) 29.394666666666694 absolute error 1.7763568394002505e-14 relative error 6.043126324730959e-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] 4.5 y[1] (closed_form) 31.375 y[1] (numeric) 31.37500000000003 absolute error 2.842170943040401e-14 relative error 9.05871216905307e-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] 4.6 y[1] (closed_form) 33.44533333333332 y[1] (numeric) 33.44533333333336 absolute error 3.552713678800501e-14 relative error 1.0622449605726265e-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] 4.699999999999999 y[1] (closed_form) 35.60766666666665 y[1] (numeric) 35.60766666666669 absolute error 3.552713678800501e-14 relative error 9.977384118028427e-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] 4.799999999999999 y[1] (closed_form) 37.86399999999997 y[1] (numeric) 37.86400000000002 absolute error 4.973799150320701e-14 relative error 1.3135958034863472e-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] 4.899999999999999 y[1] (closed_form) 40.2163333333333 y[1] (numeric) 40.21633333333335 absolute error 4.973799150320701e-14 relative error 1.236760971989997e-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] 4.999999999999998 y[1] (closed_form) 42.66666666666662 y[1] (numeric) 42.666666666666686 absolute error 6.394884621840902e-14 relative error 1.4988010832439628e-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] 5.099999999999998 y[1] (closed_form) 45.216999999999935 y[1] (numeric) 45.21700000000002 absolute error 8.526512829121202e-14 relative error 1.8856874248891378e-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] 5.1999999999999975 y[1] (closed_form) 47.869333333333266 y[1] (numeric) 47.86933333333335 absolute error 8.526512829121202e-14 relative error 1.7812056770767397e-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] 5.299999999999997 y[1] (closed_form) 50.625666666666596 y[1] (numeric) 50.62566666666668 absolute error 8.526512829121202e-14 relative error 1.6842272686031225e-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] 5.399999999999997 y[1] (closed_form) 53.48799999999991 y[1] (numeric) 53.488000000000014 absolute error 1.0658141036401503e-13 relative error 1.9926228380948102e-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] 5.4999999999999964 y[1] (closed_form) 56.45833333333323 y[1] (numeric) 56.45833333333334 absolute error 1.1368683772161603e-13 relative error 2.0136414061393283e-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] 5.599999999999996 y[1] (closed_form) 59.53866666666655 y[1] (numeric) 59.53866666666667 absolute error 1.2079226507921703e-13 relative error 2.0288036639363315e-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] 5.699999999999996 y[1] (closed_form) 62.73099999999986 y[1] (numeric) 62.731 absolute error 1.4210854715202004e-13 relative error 2.2653639692021546e-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] 5.799999999999995 y[1] (closed_form) 66.03733333333317 y[1] (numeric) 66.03733333333334 absolute error 1.7053025658242404e-13 relative error 2.582331053885042e-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] 5.899999999999995 y[1] (closed_form) 69.45966666666648 y[1] (numeric) 69.45966666666666 absolute error 1.8474111129762605e-13 relative error 2.659688998857273e-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] 5.999999999999995 y[1] (closed_form) 72.99999999999982 y[1] (numeric) 72.99999999999999 absolute error 1.7053025658242404e-13 relative error 2.3360309120880064e-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] 6.099999999999994 y[1] (closed_form) 76.66033333333313 y[1] (numeric) 76.66033333333331 absolute error 1.8474111129762605e-13 relative error 2.409865744965365e-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] 6.199999999999994 y[1] (closed_form) 80.44266666666644 y[1] (numeric) 80.44266666666664 absolute error 1.9895196601282805e-13 relative error 2.4732144551750556e-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] 6.299999999999994 y[1] (closed_form) 84.34899999999975 y[1] (numeric) 84.34899999999996 absolute error 2.1316282072803006e-13 relative error 2.527152909080495e-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] 6.399999999999993 y[1] (closed_form) 88.38133333333307 y[1] (numeric) 88.38133333333329 absolute error 2.1316282072803006e-13 relative error 2.411853416196829e-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] 6.499999999999993 y[1] (closed_form) 92.54166666666636 y[1] (numeric) 92.54166666666661 absolute error 2.5579538487363607e-13 relative error 2.7641104173648293e-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] 6.5999999999999925 y[1] (closed_form) 96.83199999999967 y[1] (numeric) 96.83199999999994 absolute error 2.7000623958883807e-13 relative error 2.788398872158367e-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] 6.699999999999992 y[1] (closed_form) 101.25433333333298 y[1] (numeric) 101.25433333333326 absolute error 2.8421709430404007e-13 relative error 2.8069622795143687e-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] 6.799999999999992 y[1] (closed_form) 105.8106666666663 y[1] (numeric) 105.81066666666659 absolute error 2.984279490192421e-13 relative error 2.8203956975280673e-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] 6.8999999999999915 y[1] (closed_form) 110.5029999999996 y[1] (numeric) 110.50299999999991 absolute error 3.126388037344441e-13 relative error 2.829233629262963e-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] 6.999999999999991 y[1] (closed_form) 115.3333333333329 y[1] (numeric) 115.33333333333324 absolute error 3.410605131648481e-13 relative error 2.957172079464012e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 7.099999999999991 y[1] (closed_form) 120.30366666666619 y[1] (numeric) 120.30366666666656 absolute error 3.694822225952521e-13 relative error 3.0712465615782305e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 7.19999999999999 y[1] (closed_form) 125.4159999999995 y[1] (numeric) 125.41599999999988 absolute error 3.836930773104541e-13 relative error 3.0593630582258693e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 7.29999999999999 y[1] (closed_form) 130.6723333333328 y[1] (numeric) 130.6723333333332 absolute error 3.979039320256561e-13 relative error 3.045051097470194e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 7.39999999999999 y[1] (closed_form) 136.0746666666661 y[1] (numeric) 136.07466666666653 absolute error 4.263256414560601e-13 relative error 3.1330272702442423e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 7.499999999999989 y[1] (closed_form) 141.6249999999994 y[1] (numeric) 141.62499999999986 absolute error 4.547473508864641e-13 relative error 3.210925690283961e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 7.599999999999989 y[1] (closed_form) 147.3253333333327 y[1] (numeric) 147.32533333333316 absolute error 4.547473508864641e-13 relative error 3.0866880841027527e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 7.699999999999989 y[1] (closed_form) 153.177666666666 y[1] (numeric) 153.17766666666648 absolute error 4.831690603168681e-13 relative error 3.1543048724479214e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 7.799999999999988 y[1] (closed_form) 159.1839999999993 y[1] (numeric) 159.1839999999998 absolute error 5.115907697472721e-13 relative error 3.213832858498809e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 7.899999999999988 y[1] (closed_form) 165.34633333333258 y[1] (numeric) 165.34633333333312 absolute error 5.400124791776761e-13 relative error 3.2659477128472475e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 7.999999999999988 y[1] (closed_form) 171.66666666666586 y[1] (numeric) 171.66666666666643 absolute error 5.684341886080801e-13 relative error 3.311267118105337e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 8.099999999999987 y[1] (closed_form) 178.14699999999914 y[1] (numeric) 178.14699999999974 absolute error 5.968558980384842e-13 relative error 3.3503561555259817e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 8.199999999999987 y[1] (closed_form) 184.78933333333245 y[1] (numeric) 184.78933333333305 absolute error 5.968558980384842e-13 relative error 3.2299261395236756e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 8.299999999999986 y[1] (closed_form) 191.59566666666572 y[1] (numeric) 191.59566666666635 absolute error 6.252776074688882e-13 relative error 3.2635268758804107e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 8.399999999999986 y[1] (closed_form) 198.567999999999 y[1] (numeric) 198.56799999999967 absolute error 6.821210263296962e-13 relative error 3.435201172040307e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 8.499999999999986 y[1] (closed_form) 205.70833333333232 y[1] (numeric) 205.70833333333297 absolute error 6.536993168992922e-13 relative error 3.177796962848509e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 8.599999999999985 y[1] (closed_form) 213.01866666666558 y[1] (numeric) 213.0186666666663 absolute error 7.105427357601002e-13 relative error 3.3355890677504186e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 8.699999999999985 y[1] (closed_form) 220.50099999999887 y[1] (numeric) 220.5009999999996 absolute error 7.389644451905042e-13 relative error 3.351297477972925e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 8.799999999999985 y[1] (closed_form) 228.15733333333216 y[1] (numeric) 228.15733333333293 absolute error 7.673861546209082e-13 relative error 3.3634078002646367e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 8.899999999999984 y[1] (closed_form) 235.98966666666544 y[1] (numeric) 235.98966666666624 absolute error 7.958078640513122e-13 relative error 3.372214874032548e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 8.999999999999984 y[1] (closed_form) 243.99999999999872 y[1] (numeric) 243.99999999999955 absolute error 8.242295734817162e-13 relative error 3.377990055252953e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 9.099999999999984 y[1] (closed_form) 252.19033333333198 y[1] (numeric) 252.19033333333286 absolute error 8.810729923425242e-13 relative error 3.4936826511029193e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 9.199999999999983 y[1] (closed_form) 260.5626666666652 y[1] (numeric) 260.5626666666662 absolute error 9.663381206337363e-13 relative error 3.7086591605617903e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 9.299999999999983 y[1] (closed_form) 269.1189999999985 y[1] (numeric) 269.1189999999995 absolute error 1.0231815394945443e-12 relative error 3.8019669346814976e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 9.399999999999983 y[1] (closed_form) 277.8613333333318 y[1] (numeric) 277.8613333333328 absolute error 1.0231815394945443e-12 relative error 3.682345892535905e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 9.499999999999982 y[1] (closed_form) 286.79166666666504 y[1] (numeric) 286.7916666666661 absolute error 1.0800249583553523e-12 relative error 3.76588682268322e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 9.599999999999982 y[1] (closed_form) 295.91199999999833 y[1] (numeric) 295.9119999999994 absolute error 1.0800249583553523e-12 relative error 3.6498180484581846e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 9.699999999999982 y[1] (closed_form) 305.22433333333163 y[1] (numeric) 305.2243333333327 absolute error 1.0800249583553523e-12 relative error 3.5384628301435936e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 9.799999999999981 y[1] (closed_form) 314.7306666666649 y[1] (numeric) 314.730666666666 absolute error 1.1368683772161603e-12 relative error 3.6121944812585787e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 9.89999999999998 y[1] (closed_form) 324.4329999999981 y[1] (numeric) 324.4329999999993 absolute error 1.1937117960769683e-12 relative error 3.679378472834068e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 9.99999999999998 y[1] (closed_form) 334.3333333333314 y[1] (numeric) 334.33333333333263 absolute error 1.2505552149377763e-12 relative error 3.740444311877718e-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 ) = x * x ; Iterations 100 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 102.02020202020181%