##############ECHO OF PROBLEM################# ##############temp/sub_lin_cpostode.ode################# diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) - 0.3 ; ! #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=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 # 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(0.05 * x * x - 0.1 * x) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 4900000.000000001 step_error 1.5058465048420852e-21 est_needed_step_err 1.5058465048420852e-21 opt_iter 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 4900000.000000001 step_error 1.5058465048420852e-21 est_needed_step_err 1.5058465048420852e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 2450000.0000000005 step_error 2.1295885499997994e-21 est_needed_step_err 2.1295885499997994e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 1225000.0000000002 step_error 3.0116930096841704e-21 est_needed_step_err 3.0116930096841704e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 612500.0000000001 step_error 4.259177099999599e-21 est_needed_step_err 4.259177099999599e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 306250.00000000006 step_error 6.023386019368341e-21 est_needed_step_err 6.023386019368341e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 153125.00000000003 step_error 8.518354199999198e-21 est_needed_step_err 8.518354199999198e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 76562.50000000001 step_error 1.2046772038736681e-20 est_needed_step_err 1.2046772038736681e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 38281.25000000001 step_error 1.7036708399998395e-20 est_needed_step_err 1.7036708399998395e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 19140.625000000004 step_error 2.4093544077473363e-20 est_needed_step_err 2.4093544077473363e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 9570.312500000002 step_error 3.407341679999679e-20 est_needed_step_err 3.407341679999679e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 4785.156250000001 step_error 4.8187088154946726e-20 est_needed_step_err 4.8187088154946726e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 2392.5781250000005 step_error 6.814683359999358e-20 est_needed_step_err 6.814683359999358e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 1196.2890625000002 step_error 9.637417630989345e-20 est_needed_step_err 9.637417630989345e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 598.1445312500001 step_error 1.3629366719998716e-19 est_needed_step_err 1.3629366719998716e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.016384 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 299.07226562500006 step_error 1.927483526197869e-19 est_needed_step_err 1.927483526197869e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.032768 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 149.53613281250003 step_error 2.7258733439997433e-19 est_needed_step_err 2.7258733439997433e-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 0.009500000000000001 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.065536 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 74.76806640625001 step_error 3.854967052395738e-19 est_needed_step_err 3.854967052395738e-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) -0.009500000000000001 y[1] (numeric) -0.009500000000000001 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) -0.018000000000000002 y[1] (numeric) -0.018 absolute error 3.469446951953614e-18 relative error 1.9274705288631187e-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] 0.30000000000000004 y[1] (closed_form) -0.025500000000000005 y[1] (numeric) -0.025499999999999995 absolute error 1.0408340855860843e-17 relative error 4.081702296416016e-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] 0.4 y[1] (closed_form) -0.03200000000000001 y[1] (numeric) -0.031999999999999994 absolute error 1.3877787807814457e-17 relative error 4.3368086899420165e-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] 0.5 y[1] (closed_form) -0.037500000000000006 y[1] (numeric) -0.03749999999999999 absolute error 1.3877787807814457e-17 relative error 3.7007434154171876e-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) -0.041999999999999996 y[1] (numeric) -0.04199999999999999 absolute error 6.938893903907228e-18 relative error 1.652117596168388e-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) -0.0455 y[1] (numeric) -0.045499999999999985 absolute error 1.3877787807814457e-17 relative error 3.050063254464716e-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) -0.048 y[1] (numeric) -0.04799999999999998 absolute error 2.0816681711721685e-17 relative error 4.336808689942018e-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] 0.8999999999999999 y[1] (closed_form) -0.0495 y[1] (numeric) -0.049499999999999975 absolute error 2.7755575615628914e-17 relative error 5.607186993056346e-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] 0.9999999999999999 y[1] (closed_form) -0.05 y[1] (numeric) -0.04999999999999997 absolute error 3.469446951953614e-17 relative error 6.938893903907228e-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] 1.0999999999999999 y[1] (closed_form) -0.0495 y[1] (numeric) -0.04949999999999997 absolute error 3.469446951953614e-17 relative error 7.008983741320432e-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) -0.048 y[1] (numeric) -0.047999999999999966 absolute error 3.469446951953614e-17 relative error 7.228014483236696e-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] 1.3 y[1] (closed_form) -0.0455 y[1] (numeric) -0.045499999999999964 absolute error 3.469446951953614e-17 relative error 7.625158136161789e-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] 1.4000000000000001 y[1] (closed_form) -0.041999999999999996 y[1] (numeric) -0.04199999999999996 absolute error 3.469446951953614e-17 relative error 8.26058798084194e-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) -0.03749999999999999 y[1] (numeric) -0.03749999999999996 absolute error 3.469446951953614e-17 relative error 9.251858538542973e-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) -0.03199999999999997 y[1] (numeric) -0.03199999999999995 absolute error 2.0816681711721685e-17 relative error 6.505213034913032e-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] 1.7000000000000004 y[1] (closed_form) -0.025499999999999967 y[1] (numeric) -0.025499999999999946 absolute error 2.0816681711721685e-17 relative error 8.163404592832044e-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) -0.01799999999999996 y[1] (numeric) -0.01799999999999994 absolute error 2.0816681711721685e-17 relative error 1.156482317317874e-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] 1.9000000000000006 y[1] (closed_form) -0.009499999999999953 y[1] (numeric) -0.009499999999999932 absolute error 2.0816681711721685e-17 relative error 2.1912296538654514e-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] 2.0000000000000004 y[1] (closed_form) 5.551115123125783e-17 y[1] (numeric) 7.632783294297951e-17 absolute error 2.0816681711721685e-17 relative error -1.0% Desired digits 16 Estimated correct digits -16 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) 0.010500000000000065 y[1] (numeric) 0.010500000000000086 absolute error 2.0816681711721685e-17 relative error 1.982541115402053e-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] 2.2000000000000006 y[1] (closed_form) 0.022000000000000075 y[1] (numeric) 0.022000000000000096 absolute error 2.0816681711721685e-17 relative error 9.462128050782552e-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) 0.034500000000000086 y[1] (numeric) 0.03450000000000011 absolute error 2.0816681711721685e-17 relative error 6.033820786006271e-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) 0.0480000000000001 y[1] (numeric) 0.04800000000000012 absolute error 2.0816681711721685e-17 relative error 4.336808689942009e-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) 0.06250000000000017 y[1] (numeric) 0.06250000000000014 absolute error 2.7755575615628914e-17 relative error 4.440892098500614e-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) 0.07800000000000018 y[1] (numeric) 0.07800000000000015 absolute error 2.7755575615628914e-17 relative error 3.5584071302088267e-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) 0.0945000000000002 y[1] (numeric) 0.09450000000000017 absolute error 2.7755575615628914e-17 relative error 2.937097948743794e-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) 0.11200000000000021 y[1] (numeric) 0.11200000000000018 absolute error 2.7755575615628914e-17 relative error 2.478176394252577e-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) 0.13050000000000023 y[1] (numeric) 0.1305000000000002 absolute error 2.7755575615628914e-17 relative error 2.126864031848955e-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) 0.1500000000000003 y[1] (numeric) 0.15000000000000022 absolute error 8.326672684688674e-17 relative error 5.5511151231257713e-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) 0.17050000000000032 y[1] (numeric) 0.17050000000000023 absolute error 8.326672684688674e-17 relative error 4.8836789939522926e-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) 0.1920000000000004 y[1] (numeric) 0.19200000000000025 absolute error 1.3877787807814457e-16 relative error 7.228014483236682e-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) 0.21450000000000036 y[1] (numeric) 0.21450000000000027 absolute error 8.326672684688674e-17 relative error 3.881898687500541e-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) 0.23800000000000043 y[1] (numeric) 0.2380000000000003 absolute error 1.3877787807814457e-16 relative error 5.831003280594299e-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) 0.2625000000000005 y[1] (numeric) 0.26250000000000034 absolute error 1.6653345369377348e-16 relative error 6.344131569286596e-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) 0.2880000000000005 y[1] (numeric) 0.28800000000000037 absolute error 1.1102230246251565e-16 relative error 3.854941057726232e-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) 0.31450000000000056 y[1] (numeric) 0.3145000000000004 absolute error 1.6653345369377348e-16 relative error 5.295181357512661e-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) 0.34200000000000064 y[1] (numeric) 0.3420000000000004 absolute error 2.220446049250313e-16 relative error 6.492532307749441e-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) 0.3705000000000006 y[1] (numeric) 0.37050000000000044 absolute error 1.6653345369377348e-16 relative error 4.4948300592111527e-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) 0.4000000000000005 y[1] (numeric) 0.40000000000000047 absolute error 5.551115123125783e-17 relative error 1.387778780781444e-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) 0.43050000000000044 y[1] (numeric) 0.4305000000000005 absolute error 5.551115123125783e-17 relative error 1.2894576360338622e-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] 4.200000000000001 y[1] (closed_form) 0.4620000000000004 y[1] (numeric) 0.4620000000000005 absolute error 1.1102230246251565e-16 relative error 2.403080139881289e-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) 0.49450000000000033 y[1] (numeric) 0.49450000000000055 absolute error 2.220446049250313e-16 relative error 4.4902852360976977e-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) 0.5280000000000001 y[1] (numeric) 0.5280000000000006 absolute error 4.440892098500626e-16 relative error 8.410780489584517e-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) 0.5625 y[1] (numeric) 0.5625000000000006 absolute error 5.551115123125783e-16 relative error 9.86864910777917e-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) 0.5979999999999999 y[1] (numeric) 0.5980000000000005 absolute error 6.661338147750939e-16 relative error 1.1139361451088529e-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) 0.6344999999999998 y[1] (numeric) 0.6345000000000005 absolute error 6.661338147750939e-16 relative error 1.049856288061614e-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] 4.799999999999999 y[1] (closed_form) 0.6719999999999995 y[1] (numeric) 0.6720000000000005 absolute error 9.992007221626409e-16 relative error 1.4869058365515501e-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) 0.7104999999999996 y[1] (numeric) 0.7105000000000005 absolute error 8.881784197001252e-16 relative error 1.2500751860663277e-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) 0.7499999999999993 y[1] (numeric) 0.7500000000000004 absolute error 1.1102230246251565e-15 relative error 1.4802973661668768e-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 ) = ( 0.1 * x + 0.2 ) - 0.3 ; Iterations 50 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 104.08163265306118%