##############ECHO OF PROBLEM################# ##############temp/expt_lin_sinpostode.ode################# diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , sin ( 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=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=0 #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(0.0) 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 4.9 estimated_steps 4900000.000000001 step_error 1.5058465048420852e-21 est_needed_step_err 1.5058465048420852e-21 opt_iter 1 NO INFO (given) for Equation 1 NO 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 0.0 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 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0008294884127135e-167 estimated_step_error 1.0008294884127135e-167 Double H and LOOP opt_iter 2 NO INFO (given) for Equation 1 NO 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 0.0 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 7.094233389451058e-156 estimated_step_error 7.094233389451058e-156 Double H and LOOP opt_iter 3 NO INFO (given) for Equation 1 NO 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 0.0 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 4.76085662689039e-148 estimated_step_error 4.76085662689039e-148 Double H and LOOP opt_iter 4 NO INFO (given) for Equation 1 NO 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 0.0 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 3.1949530270890467e-140 estimated_step_error 3.1949530270890467e-140 Double H and LOOP opt_iter 5 NO INFO (given) for Equation 1 NO 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 0.0 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 2.144091619291599e-132 estimated_step_error 2.144091619291599e-132 Double H and LOOP opt_iter 6 NO INFO (given) for Equation 1 NO 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 0.0 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 1.438868734072728e-124 estimated_step_error 1.438868734072728e-124 Double H and LOOP opt_iter 7 NO INFO (given) for Equation 1 NO 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 0.0 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 9.655993422536634e-117 estimated_step_error 9.655993422536634e-117 Double H and LOOP opt_iter 8 NO INFO (given) for Equation 1 NO 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 0.0 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 6.479905095602406e-109 estimated_step_error 6.479905095602406e-109 Double H and LOOP opt_iter 9 NO INFO (given) for Equation 1 NO 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 0.0 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 4.348426427213213e-101 estimated_step_error 4.348426427213213e-101 Double H and LOOP opt_iter 10 NO INFO (given) for Equation 1 NO 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 0.0 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 2.91795912178219e-93 estimated_step_error 2.91795912178219e-93 Double H and LOOP opt_iter 11 NO INFO (given) for Equation 1 NO 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 0.0 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 1.9579133955776604e-85 estimated_step_error 1.9579133955776604e-85 Double H and LOOP opt_iter 12 NO INFO (given) for Equation 1 NO 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 0.0 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 1.3135365711845686e-77 estimated_step_error 1.3135365711845686e-77 Double H and LOOP opt_iter 13 NO INFO (given) for Equation 1 NO 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 0.0 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 8.809672890700116e-70 estimated_step_error 8.809672890700116e-70 Double H and LOOP opt_iter 14 NO INFO (given) for Equation 1 NO 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 0.0 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 5.904941520155846e-62 estimated_step_error 5.904941520155846e-62 Double H and LOOP opt_iter 15 NO INFO (given) for Equation 1 NO 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 0.0 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 3.953204221322505e-54 estimated_step_error 3.953204221322505e-54 Double H and LOOP opt_iter 16 NO INFO (given) for Equation 1 NO 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 0.0 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 2.6402449537010124e-46 estimated_step_error 2.6402449537010124e-46 Double H and LOOP opt_iter 17 NO INFO (given) for Equation 1 NO 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 0.0 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 1.755028345390252e-38 estimated_step_error 1.755028345390252e-38 Double H and LOOP opt_iter 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL NO INFO (given) for Equation 1 NO 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) 0.0 y[1] (numeric) 0.0 absolute error 0.0 relative error -1.0% Desired digits 16 Estimated correct digits -16 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.08494521191206113 absolute error 0.08494521191206113 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.16213721225208197 absolute error 0.16213721225208197 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.23330216314602015 absolute error 0.23330216314602015 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.2997404540332474 absolute error 0.2997404540332474 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.362526861674144 absolute error 0.362526861674144 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.4225626836591664 absolute error 0.4225626836591664 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.48061537892501976 absolute error 0.48061537892501976 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.5373488055956528 absolute error 0.5373488055956528 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.5933462691641715 absolute error 0.5933462691641715 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.6491279717125857 absolute error 0.6491279717125857 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.7051640070005472 absolute error 0.7051640070005472 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.7618837261875883 absolute error 0.7618837261875883 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.8196820716805805 absolute error 0.8196820716805805 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.8789233204782909 absolute error 0.8789233204782909 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 0.9399425790449967 absolute error 0.9399425790449967 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 1.0030453192147355 absolute error 1.0030453192147355 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 1.0685052311912384 absolute error 1.0685052311912384 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 1.136560688227431 absolute error 1.136560688227431 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 1.2074101602006804 absolute error 1.2074101602006804 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 1.2812069706558162 absolute error 1.2812069706558162 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 1.3580538527201724 absolute error 1.3580538527201724 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 1.4379978108265359 absolute error 1.4379978108265359 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 1.5210258241105434 absolute error 1.5210258241105434 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 1.6070619214652178 absolute error 1.6070619214652178 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 1.6959661083979778 absolute error 1.6959661083979778 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 1.7875355279706695 absolute error 1.7875355279706695 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 1.8815080947288105 absolute error 1.8815080947288105 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 1.9775686613575914 absolute error 1.9775686613575914 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 2.0753575791160337 absolute error 2.0753575791160337 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 2.174481315788618 absolute error 2.174481315788618 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 2.274524621447059 absolute error 2.274524621447059 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 2.3750636032726455 absolute error 2.3750636032726455 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 2.4756790012553735 absolute error 2.4756790012553735 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 2.5759689541246233 absolute error 2.5759689541246233 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 2.6755606078037366 absolute error 2.6755606078037366 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 2.7741200370167185 absolute error 2.7741200370167185 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 2.871360107939668 absolute error 2.871360107939668 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 2.967046085974104 absolute error 2.967046085974104 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 3.0609989675307085 absolute error 3.0609989675307085 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 3.153096670496545 absolute error 3.153096670496545 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 3.243273341899766 absolute error 3.243273341899766 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 3.331517126017397 absolute error 3.331517126017397 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 3.417866780317607 absolute error 3.417866780317607 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 3.5024075334813336 absolute error 3.5024075334813336 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 3.585266555931982 absolute error 3.585266555931982 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 3.6666083671653538 absolute error 3.6666083671653538 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 3.746630444324623 absolute error 3.746630444324623 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 3.825559230645346 absolute error 3.825559230645346 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) 0.0 y[1] (numeric) 3.903646676755391 absolute error 3.903646676755391 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.1 NO INFO (given) for Equation 1 NO 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 ) = expt ( ( 0.2 * x + 0.3 ) , sin ( x ) ) ; 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%