##############ECHO OF PROBLEM################# ##############temp/mtest5postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.5 x_end=5.0 $array_y1_init[0 + 1] = exact_soln_y1(x_start) $array_y2_init[0 + 1] = exact_soln_y2(x_start) $array_y2_init[1 + 1] = exact_soln_y2p(x_start) $glob_look_poles=true # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=3 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=16 $glob_max_minutes=3.0 $glob_subiter_method=3 $glob_max_iter=100000000 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y1 (x) return( - cos(x)) end def exact_soln_y2 (x) return( - sin(x)) end def exact_soln_y2p (x) return( - cos(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 4.5 estimated_steps 4500000.0 step_error 1.5713484026367722e-21 est_needed_step_err 1.5713484026367722e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 4500000.0 step_error 1.5713484026367722e-21 est_needed_step_err 1.5713484026367722e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 2250000.0 step_error 2.222222222222222e-21 est_needed_step_err 2.222222222222222e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 1125000.0 step_error 3.1426968052735444e-21 est_needed_step_err 3.1426968052735444e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 562500.0 step_error 4.444444444444444e-21 est_needed_step_err 4.444444444444444e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 281250.0 step_error 6.285393610547089e-21 est_needed_step_err 6.285393610547089e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 140625.0 step_error 8.888888888888888e-21 est_needed_step_err 8.888888888888888e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 70312.5 step_error 1.2570787221094178e-20 est_needed_step_err 1.2570787221094178e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 35156.25 step_error 1.7777777777777775e-20 est_needed_step_err 1.7777777777777775e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 17578.125 step_error 2.5141574442188355e-20 est_needed_step_err 2.5141574442188355e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 8789.0625 step_error 3.555555555555555e-20 est_needed_step_err 3.555555555555555e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 4394.53125 step_error 5.028314888437671e-20 est_needed_step_err 5.028314888437671e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 2197.265625 step_error 7.11111111111111e-20 est_needed_step_err 7.11111111111111e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 1098.6328125 step_error 1.0056629776875342e-19 est_needed_step_err 1.0056629776875342e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 14 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 549.31640625 step_error 1.422222222222222e-19 est_needed_step_err 1.422222222222222e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 274.658203125 step_error 2.0113259553750684e-19 est_needed_step_err 2.0113259553750684e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 137.3291015625 step_error 2.844444444444444e-19 est_needed_step_err 2.844444444444444e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 0.8775825618903728 min_size 0.479425538604203 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 4.5 estimated_steps 68.66455078125 step_error 4.022651910750137e-19 est_needed_step_err 4.022651910750137e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 START of Soultion TOP MAIN SOLVE Loop x[1] 0.5 y1[1] (closed_form) -0.8775825618903728 y1[1] (numeric) -0.8775825618903728 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 y2[1] (closed_form) -0.479425538604203 y2[1] (numeric) -0.479425538604203 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6 y1[1] (closed_form) -0.8253356149096783 y1[1] (numeric) -0.8253356149094621 absolute error 2.162714451969805e-13 relative error 2.6204060662116035e-11% Desired digits 16 Estimated correct digits 13 Correct digits 13 h 0.1 y2[1] (closed_form) -0.5646424733950354 y2[1] (numeric) -0.5646424734123264 absolute error 1.7291057474722038e-11 relative error 3.062301950251068e-09% Desired digits 16 Estimated correct digits 13 Correct digits 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7 y1[1] (closed_form) -0.7648421872844885 y1[1] (numeric) -0.7648421872763022 absolute error 8.186340494376054e-12 relative error 1.0703306682704057e-09% Desired digits 16 Estimated correct digits 13 Correct digits 11 h 0.1 y2[1] (closed_form) -0.644217687237691 y2[1] (numeric) -0.6442176873918414 absolute error 1.5415035914401187e-10 relative error 2.392830283890303e-08% Desired digits 16 Estimated correct digits 13 Correct digits 10 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7999999999999999 y1[1] (closed_form) -0.6967067093471655 y1[1] (numeric) -0.6967067093117303 absolute error 3.5435210321566046e-11 relative error 5.086101489501927e-09% Desired digits 16 Estimated correct digits 13 Correct digits 11 h 0.1 y2[1] (closed_form) -0.7173560908995227 y2[1] (numeric) -0.7173560913011536 absolute error 4.0163095071932275e-10 relative error 5.59876685811228e-08% Desired digits 16 Estimated correct digits 13 Correct digits 10 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8999999999999999 y1[1] (closed_form) -0.6216099682706645 y1[1] (numeric) -0.6216099681781837 absolute error 9.24808007951583e-11 relative error 1.4877625121174031e-08% Desired digits 16 Estimated correct digits 13 Correct digits 10 h 0.1 y2[1] (closed_form) -0.7833269096274833 y2[1] (numeric) -0.7833269103760433 absolute error 7.48559991770037e-10 relative error 9.556163366403689e-08% Desired digits 16 Estimated correct digits 13 Correct digits 10 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9999999999999999 y1[1] (closed_form) -0.5403023058681398 y1[1] (numeric) -0.540302305679519 absolute error 1.8862078565717866e-10 relative error 3.4910231477563115e-08% Desired digits 16 Estimated correct digits 13 Correct digits 10 h 0.1 y2[1] (closed_form) -0.8414709848078964 y2[1] (numeric) -0.8414709859896337 absolute error 1.1817372636002688e-09 relative error 1.404370780378189e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0999999999999999 y1[1] (closed_form) -0.4535961214255775 y1[1] (numeric) -0.45359612109383624 absolute error 3.317412455849933e-10 relative error 7.313582059352392e-08% Desired digits 16 Estimated correct digits 13 Correct digits 10 h 0.1 y2[1] (closed_form) -0.8912073600614353 y2[1] (numeric) -0.8912073617475995 absolute error 1.6861642082588446e-09 relative error 1.8919998687427906e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2 y1[1] (closed_form) -0.3623577544766736 y1[1] (numeric) -0.36235775394852443 absolute error 5.28149191048044e-10 relative error 1.4575352245760842e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) -0.9320390859672263 y2[1] (numeric) -0.932039088212527 absolute error 2.245300723124899e-09 relative error 2.40901991872458e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.3 y1[1] (closed_form) -0.26749882862458735 y1[1] (numeric) -0.26749882784215473 absolute error 7.824326186955943e-10 relative error 2.9249945606067465e-07% Desired digits 16 Estimated correct digits 12 Correct digits 9 h 0.1 y2[1] (closed_form) -0.963558185417193 y2[1] (numeric) -0.9635581882585377 absolute error 2.8413447150654747e-09 relative error 2.948804501967107e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.4000000000000001 y1[1] (closed_form) -0.16996714290024081 y1[1] (numeric) -0.16996714180289169 absolute error 1.0973491282317838e-09 relative error 6.456242715545635e-07% Desired digits 16 Estimated correct digits 12 Correct digits 9 h 0.1 y2[1] (closed_form) -0.9854497299884603 y2[1] (numeric) -0.985449733443993 absolute error 3.455532748830592e-09 relative error 3.5065540571725125e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.5000000000000002 y1[1] (closed_form) -0.07073720166770268 y1[1] (numeric) -0.07073720019395752 absolute error 1.4737451675683744e-09 relative error 2.0834089175473555e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 h 0.1 y2[1] (closed_form) -0.9974949866040544 y2[1] (numeric) -0.9974949906725096 absolute error 4.068455128347637e-09 relative error 4.078672256989066e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.6000000000000003 y1[1] (closed_form) 0.029199522301289037 y1[1] (numeric) 0.029199524211797 absolute error 1.9105079636372313e-09 relative error 6.542942531470422e-06% Desired digits 16 Estimated correct digits 11 Correct digits 8 h 0.1 y2[1] (closed_form) -0.9995736030415051 y2[1] (numeric) -0.9995736077018873 absolute error 4.6603821912682974e-09 relative error 4.662370211745963e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.7000000000000004 y1[1] (closed_form) 0.12884449429552508 y1[1] (numeric) 0.12884449670007508 absolute error 2.4045500035541068e-09 relative error 1.8662419505787293e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 h 0.1 y2[1] (closed_form) -0.9916648104524686 y2[1] (numeric) -0.9916648156640663 absolute error 5.211597708942861e-09 relative error 5.255402484802255e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.8000000000000005 y1[1] (closed_form) 0.22720209469308753 y1[1] (numeric) 0.2272020976439148 absolute error 2.9508272769707133e-09 relative error 1.298767637224821e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 h 0.1 y2[1] (closed_form) -0.973847630878195 y2[1] (numeric) -0.9738476365809292 absolute error 5.702734173773649e-09 relative error 5.855879290511848e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.9000000000000006 y1[1] (closed_form) 0.32328956686350396 y1[1] (numeric) 0.32328957040589457 absolute error 3.5423906030729313e-09 relative error 1.095733041260983e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 h 0.1 y2[1] (closed_form) -0.9463000876874142 y2[1] (numeric) -0.946300093802518 absolute error 6.115103756698659e-09 relative error 6.462118979237192e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 2.0000000000000004 y1[1] (closed_form) 0.4161468365471428 y1[1] (numeric) 0.4161468407176131 absolute error 4.170470302433671e-09 relative error 1.0021631636171823e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.1 y2[1] (closed_form) -0.9092974268256815 y2[1] (numeric) -0.9092974332567051 absolute error 6.431023602537778e-09 relative error 7.072519302059621e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 2.1000000000000005 y1[1] (closed_form) 0.5048461045998579 y1[1] (numeric) 0.5048461094244494 absolute error 4.824591504082321e-09 relative error 9.556558840651653e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) -0.8632093666488735 y2[1] (numeric) -0.8632093732830015 absolute error 6.634128024707309e-09 relative error 7.685421730839331e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 2.2000000000000006 y1[1] (closed_form) 0.5885011172553463 y1[1] (numeric) 0.5885011227480681 absolute error 5.492721832922598e-09 relative error 9.333409354496343e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) -0.8084964038195899 y2[1] (numeric) -0.8084964105292531 absolute error 6.709663269433008e-09 relative error 8.298940153270269e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 2.3000000000000007 y1[1] (closed_form) 0.6662760212798248 y1[1] (numeric) 0.6662760274412709 absolute error 6.16144613108105e-09 relative error 9.247587988001966e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) -0.7457052121767197 y2[1] (numeric) -0.7457052188214827 absolute error 6.6447629620824955e-09 relative error 8.910710095060724e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 2.400000000000001 y1[1] (closed_form) 0.737393715541246 y1[1] (numeric) 0.7373937223574138 absolute error 6.816167852363719e-09 relative error 9.243593630792827e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) -0.6754631805511503 y2[1] (numeric) -0.6754631869798472 absolute error 6.428696908145071e-09 relative error 9.517464597995581e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 2.500000000000001 y1[1] (closed_form) 0.8011436155469343 y1[1] (numeric) 0.8011436229882678 absolute error 7.441333549351725e-09 relative error 9.288389004100828e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) -0.5984721441039558 y2[1] (numeric) -0.5984721501570481 absolute error 6.053092360680523e-09 relative error 1.011424244271775e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 2.600000000000001 y1[1] (closed_form) 0.8568887533689478 y1[1] (numeric) 0.8568887613896268 absolute error 8.020679009845821e-09 relative error 9.360233727320709e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) -0.5155013718214634 y2[1] (numeric) -0.5155013773335865 absolute error 5.512123091300225e-09 relative error 1.0692741848239486e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 2.700000000000001 y1[1] (closed_form) 0.9040721420170617 y1[1] (numeric) 0.9040721505545533 absolute error 8.537491602567115e-09 relative error 9.443374268251699e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) -0.42737988023382895 y2[1] (numeric) -0.42737988503649194 absolute error 4.802662989522588e-09 relative error 1.1237456912793707e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 2.800000000000001 y1[1] (closed_form) 0.9422223406686585 y1[1] (numeric) 0.9422223496435449 absolute error 8.974886389623293e-09 relative error 9.525231999120468e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) -0.33498815015590383 y2[1] (numeric) -0.33498815408030647 absolute error 3.924402636190649e-09 relative error 1.1715049127451905e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 2.9000000000000012 y1[1] (closed_form) 0.9709581651495908 y1[1] (numeric) 0.9709581744656823 absolute error 9.31609156484825e-09 relative error 9.594740431904154e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) -0.23924932921398112 y2[1] (numeric) -0.23924933209390759 absolute error 2.879926463972282e-09 relative error 1.2037343943382669e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 3.0000000000000013 y1[1] (closed_form) 0.9899924966004456 y1[1] (numeric) 0.9899925061451863 absolute error 9.544740664502172e-09 relative error 9.641225259058065e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) -0.1411200080598659 y2[1] (numeric) -0.14112000973461444 absolute error 1.6747485342971657e-09 relative error 1.1867548459795326e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 3.1000000000000014 y1[1] (closed_form) 0.9991351502732795 y1[1] (numeric) 0.9991351599184447 absolute error 9.645165222060825e-09 relative error 9.653514061058425e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) -0.04158066243328916 y2[1] (numeric) -0.041580662750595965 absolute error 3.173068058304196e-10 relative error 7.631114736074676e-07% Desired digits 16 Estimated correct digits 11 Correct digits 9 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 3.2000000000000015 y1[1] (closed_form) 0.998294775794753 y1[1] (numeric) 0.9982947853974378 absolute error 9.602684758469593e-09 relative error 9.619087459237471e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) 0.05837414342758142 y2[1] (numeric) 0.05837414460866666 absolute error 1.1810852434956942e-09 relative error 2.0233020548917192e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 3.3000000000000016 y1[1] (closed_form) 0.9874797699088647 y1[1] (numeric) 0.9874797793127553 absolute error 9.403890666170867e-09 relative error 9.52312234916849e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) 0.15774569414324996 y2[1] (numeric) 0.15774569694957907 absolute error 2.8063291135360657e-09 relative error 1.779021055869594e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 3.4000000000000017 y1[1] (closed_form) 0.9667981925794605 y1[1] (numeric) 0.9667982016163786 absolute error 9.03691810272278e-09 relative error 9.347264167521746e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) 0.25554110202683294 y2[1] (numeric) 0.2555411065685064 absolute error 4.5416734817393944e-09 relative error 1.7772770977807314e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 3.5000000000000018 y1[1] (closed_form) 0.9364566872907957 y1[1] (numeric) 0.9364566957824983 absolute error 8.4917026743625e-09 relative error 9.067907560070199e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) 0.3507832276896215 y2[1] (numeric) 0.3507832340575082 absolute error 6.367886717928428e-09 relative error 1.8153338629869825e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 3.600000000000002 y1[1] (closed_form) 0.8967584163341462 y1[1] (numeric) 0.8967584240943649 absolute error 7.760218689867315e-09 relative error 8.65363351881354e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) 0.44252044329485407 y2[1] (numeric) 0.442520451558322 absolute error 8.263467909941369e-09 relative error 1.867364103772121e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 3.700000000000002 y1[1] (closed_form) 0.8481000317104072 y1[1] (numeric) 0.8481000385471011 absolute error 6.8366939887098965e-09 relative error 8.061188224367806e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) 0.5298361409084948 y2[1] (numeric) 0.5298361511133891 absolute error 1.0204894262955122e-08 relative error 1.9260472200814922e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 3.800000000000002 y1[1] (closed_form) 0.7909677119144155 y1[1] (numeric) 0.7909677176322132 absolute error 5.717797679771763e-09 relative error 7.228863572613747e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) 0.6118578909427207 y2[1] (numeric) 0.6118579031096223 absolute error 1.2166901597332469e-08 relative error 1.9885175589688486e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 3.900000000000002 y1[1] (closed_form) 0.7259323042001387 y1[1] (numeric) 0.7259323086029382 absolute error 4.40279956936962e-09 relative error 6.06502774968914e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) 0.6877661591839753 y2[1] (numeric) 0.6877661733067715 absolute error 1.4122796154758532e-08 relative error 2.0534299290786607e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 4.000000000000002 y1[1] (closed_form) 0.6536436208636106 y1[1] (numeric) 0.6536436237573062 absolute error 2.893695616457137e-09 relative error 4.427023417797473e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h 0.1 y2[1] (closed_form) 0.7568024953079294 y2[1] (numeric) 0.7568025113527208 absolute error 1.6044791384395296e-08 relative error 2.1200764378910984e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 4.100000000000001 y1[1] (closed_form) 0.5748239465332677 y1[1] (numeric) 0.5748239477285687 absolute error 1.1953009693144168e-09 relative error 2.0794209714525856e-07% Desired digits 16 Estimated correct digits 12 Correct digits 9 h 0.1 y2[1] (closed_form) 0.8182771110644114 y2[1] (numeric) 0.8182771289687795 absolute error 1.7904368099230794e-08 relative error 2.18805681561114e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 4.200000000000001 y1[1] (closed_form) 0.49026082134069865 y1[1] (numeric) 0.4902608206560012 absolute error 6.846974653917925e-10 relative error 1.3965983729219377e-07% Desired digits 16 Estimated correct digits 12 Correct digits 9 h 0.1 y2[1] (closed_form) 0.8715757724135886 y2[1] (numeric) 0.8715757920862414 absolute error 1.96726527290636e-08 relative error 2.257136252719097e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 4.300000000000001 y1[1] (closed_form) 0.4007991720799746 y1[1] (numeric) 0.40079916934425075 absolute error 2.7357238696623654e-09 relative error 6.82567245701916e-07% Desired digits 16 Estimated correct digits 12 Correct digits 9 h 0.1 y2[1] (closed_form) 0.9161659367494552 y2[1] (numeric) 0.9161659580702639 absolute error 2.1320808674119007e-08 relative error 2.3271776234952544e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 4.4 y1[1] (closed_form) 0.30733286997841935 y1[1] (numeric) 0.3073328650340815 absolute error 4.944337828050038e-09 relative error 1.6087891374577752e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 h 0.1 y2[1] (closed_form) 0.951602073889516 y2[1] (numeric) 0.9516020967099517 absolute error 2.2820435652270987e-08 relative error 2.3981069691237885e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 4.5 y1[1] (closed_form) 0.2107957994307797 y1[1] (numeric) 0.21079579213648197 absolute error 7.294297721394116e-09 relative error 3.460361990652185e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 h 0.1 y2[1] (closed_form) 0.977530117665097 y2[1] (numeric) 0.9775301418090703 absolute error 2.414397326511164e-08 relative error 2.4698955897933156e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 4.6 y1[1] (closed_form) 0.11215252693505487 y1[1] (numeric) 0.11215251716838982 absolute error 9.766665046151424e-09 relative error 8.708377165507016e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 h 0.1 y2[1] (closed_form) 0.9936910036334644 y2[1] (numeric) 0.993691028898566 absolute error 2.526510156641848e-08 relative error 2.5425511023080404e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 4.699999999999999 y1[1] (closed_form) 0.012388663462891447 y1[1] (numeric) 0.012388651122943309 absolute error 1.2339948137971013e-08 relative error 9.960677497563515e-05% Desired digits 16 Estimated correct digits 11 Correct digits 7 h 0.1 y2[1] (closed_form) 0.9999232575641008 y2[1] (numeric) 0.999923283723236 absolute error 2.6159135191328176e-08 relative error 2.616114286115725e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 4.799999999999999 y1[1] (closed_form) -0.08749898343944551 y1[1] (numeric) -0.0874989984297304 absolute error 1.4990284888383165e-08 relative error 1.713195319435606e-05% Desired digits 16 Estimated correct digits 12 Correct digits 7 h 0.1 y2[1] (closed_form) 0.9961646088358408 y2[1] (numeric) 0.9961646356392452 absolute error 2.6803404384878604e-08 relative error 2.690660172740143e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 4.899999999999999 y1[1] (closed_form) -0.18651236942257401 y1[1] (numeric) -0.18651238711423668 absolute error 1.7691662662633334e-08 relative error 9.485517082542662e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 h 0.1 y2[1] (closed_form) 0.9824526126243328 y2[1] (numeric) 0.982452639801952 absolute error 2.7177619155160926e-08 relative error 2.7663033113183873e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 4.999999999999998 y1[1] (closed_form) -0.2836621854632246 y1[1] (numeric) -0.2836622058793981 absolute error 2.0416173529547166e-08 relative error 7.19735466192198e-06% Desired digits 16 Estimated correct digits 12 Correct digits 8 h 0.1 y2[1] (closed_form) 0.958924274663139 y2[1] (numeric) 0.9589243019273491 absolute error 2.7264210111788145e-08 relative error 2.8432078352970886e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; Iterations 46 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 104.4444444444444%