##############ECHO OF PROBLEM################# ##############temp/mtest1postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ; diff ( y2 , x , 1 ) = y1 - 1.0 ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=10.0 $array_y1_init[0 + 1] = exact_soln_y1(x_start) $array_y2_init[0 + 1] = exact_soln_y2(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(1.0 + cos(x)) end def exact_soln_y2 (x) return(1.0 + sin(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 9.9 estimated_steps 9900000.0 step_error 7.945521577046603e-22 est_needed_step_err 7.945521577046603e-22 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 1.9950041652780257 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 9.9 estimated_steps 9900000.0 step_error 8.738750143124259e-22 est_needed_step_err 8.738750143124259e-22 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.674790358513323e-258 estimated_step_error 2.674790358513323e-258 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 1.9950041652780257 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 9.9 estimated_steps 4950000.0 step_error 1.2358458970596152e-21 est_needed_step_err 1.2358458970596152e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8381019356630983e-247 estimated_step_error 1.8381019356630983e-247 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 1.9950041652780257 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 9.9 estimated_steps 2475000.0 step_error 1.7477500286248517e-21 est_needed_step_err 1.7477500286248517e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2631340286366648e-236 estimated_step_error 1.2631340286366648e-236 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 1.9950041652780257 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 9.9 estimated_steps 1237500.0 step_error 2.4716917941192304e-21 est_needed_step_err 2.4716917941192304e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.68019090245767e-226 estimated_step_error 8.68019090245767e-226 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 1.9950041652780257 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 9.9 estimated_steps 618750.0 step_error 3.4955000572497034e-21 est_needed_step_err 3.4955000572497034e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.964981703152477e-215 estimated_step_error 5.964981703152477e-215 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 1.9950041652780257 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 9.9 estimated_steps 309375.0 step_error 4.943383588238461e-21 est_needed_step_err 4.943383588238461e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.099104124878063e-204 estimated_step_error 4.099104124878063e-204 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 1.9950041652780257 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 9.9 estimated_steps 154687.5 step_error 6.991000114499407e-21 est_needed_step_err 6.991000114499407e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.8168827832596326e-193 estimated_step_error 2.8168827832596326e-193 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 1.9950041652780257 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 9.9 estimated_steps 77343.75 step_error 9.886767176476921e-21 est_needed_step_err 9.886767176476921e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9357469409419875e-182 estimated_step_error 1.9357469409419875e-182 Double H and LOOP opt_iter 9 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09933466539749951 Order of pole (three term test) 32.00996671107996 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.09933466539752886 Order of pole (three term test) 32.99003328892069 NO COMPLEX POLE (six term test) for Equation 2 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y1[1] (closed_form) 1.9950041652780257 y1[1] (numeric) 1.9950041652780257 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.000128 y2[1] (closed_form) 1.0998334166468282 y2[1] (numeric) 1.0998334166468282 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.000128 NO POLE (given) for Equation 1 NO 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] 0.2000959999999943 y1[1] (closed_form) 1.980047501069369 y1[1] (numeric) 1.980047501069369 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 12 Correct digits 16 h 0.000128 y2[1] (closed_form) 1.1987634162709155 y2[1] (numeric) 1.1987634162709224 absolute error 6.8833827526759706e-15 relative error 5.742069418575212e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.000128 NO POLE (given) for Equation 1 NO 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] 0.3000639999999968 y1[1] (closed_form) 1.9553175738758646 y1[1] (numeric) 1.9553175738758632 absolute error 1.3322676295501878e-15 relative error 6.813561374121666e-14% Desired digits 16 Estimated correct digits 12 Correct digits 16 h 0.000128 y2[1] (closed_form) 1.2955813475913733 y2[1] (numeric) 1.2955813475913767 absolute error 3.3306690738754696e-15 relative error 2.570791158785626e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.000128 NO POLE (given) for Equation 1 NO 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] 0.40003200000001005 y1[1] (closed_form) 1.9210485321443462 y1[1] (numeric) 1.9210485321443478 absolute error 1.5543122344752192e-15 relative error 8.090957664355506e-14% Desired digits 16 Estimated correct digits 12 Correct digits 16 h 0.000128 y2[1] (closed_form) 1.3894478160610806 y2[1] (numeric) 1.3894478160610715 absolute error 9.103828801926284e-15 relative error 6.552119983702991e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.000128 NO POLE (given) for Equation 1 NO 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] 0.5000000000000233 y1[1] (closed_form) 1.8775825618903617 y1[1] (numeric) 1.8775825618903677 absolute error 5.995204332975845e-15 relative error 3.1930443191482546e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.000128 y2[1] (closed_form) 1.4794255386042234 y2[1] (numeric) 1.4794255386042041 absolute error 1.9317880628477724e-14 relative error 1.3057690383460152e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO 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] 0.6000960000000366 y1[1] (closed_form) 1.8252814054291484 y1[1] (numeric) 1.8252814054291644 absolute error 1.5987211554602254e-14 relative error 8.758765364644387e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.000128 y2[1] (closed_form) 1.5647217030121028 y2[1] (numeric) 1.5647217030120721 absolute error 3.064215547965432e-14 relative error 1.958313444535722e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO 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] 0.7000640000000499 y1[1] (closed_form) 1.7648009557861044 y1[1] (numeric) 1.764800955786132 absolute error 2.7533531010703882e-14 relative error 1.560149370977617e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.000128 y2[1] (closed_form) 1.6442666358183242 y2[1] (numeric) 1.6442666358182867 absolute error 3.752553823233029e-14 relative error 2.2822051737159074e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO 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] 0.8000320000000631 y1[1] (closed_form) 1.6966837535955013 y1[1] (numeric) 1.6966837535955408 absolute error 3.952393967665557e-14 relative error 2.329481825525766e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 y2[1] (closed_form) 1.7173783851469757 y2[1] (numeric) 1.7173783851469304 absolute error 4.529709940470639e-14 relative error 2.637572464895661e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO 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] 0.9000000000000764 y1[1] (closed_form) 1.6216099682706044 y1[1] (numeric) 1.6216099682706575 absolute error 5.306866057708248e-14 relative error 3.2725909198547e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 y2[1] (closed_form) 1.7833269096275308 y2[1] (numeric) 1.783326909627479 absolute error 5.1736392947532295e-14 relative error 2.9011165966389225e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO 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] 1.0000960000000896 y1[1] (closed_form) 1.5402215221639337 y1[1] (numeric) 1.5402215221640028 absolute error 6.905587213168474e-14 relative error 4.483502609070461e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 y2[1] (closed_form) 1.8415228499517302 y2[1] (numeric) 1.8415228499516765 absolute error 5.3734794391857577e-14 relative error 2.917954256894834e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO 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] 1.1000640000000161 y1[1] (closed_form) 1.4535390832255932 y1[1] (numeric) 1.4535390832256037 absolute error 1.0436096431476471e-14 relative error 7.179783847516098e-13% Desired digits 16 Estimated correct digits 11 Correct digits 15 h 0.000128 y2[1] (closed_form) 1.8912363883880015 y2[1] (numeric) 1.8912363883879881 absolute error 1.3322676295501878e-14 relative error 7.044426797888277e-13% Desired digits 16 Estimated correct digits 11 Correct digits 15 h 0.000128 NO POLE (given) for Equation 1 NO 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] 1.2000319999999427 y1[1] (closed_form) 1.362327929040454 y1[1] (numeric) 1.362327929040397 absolute error 5.706546346573305e-14 relative error 4.188819905199088e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 y2[1] (closed_form) 1.9320506809381428 y2[1] (numeric) 1.9320506809381561 absolute error 1.3322676295501878e-14 relative error 6.895614295704089e-13% Desired digits 16 Estimated correct digits 11 Correct digits 15 h 0.000128 NO POLE (given) for Equation 1 NO 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] 1.2999999999998693 y1[1] (closed_form) 1.2674988286247133 y1[1] (numeric) 1.2674988286245856 absolute error 1.27675647831893e-13 relative error 1.007303872386424e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 y2[1] (closed_form) 1.963558185417158 y2[1] (numeric) 1.9635581854171884 absolute error 3.042011087472929e-14 relative error 1.5492339926899868e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO 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] 1.4000959999997957 y1[1] (closed_form) 1.1698725389433 y1[1] (numeric) 1.169872538943099 absolute error 2.0095036745715333e-13 relative error 1.717711637531589e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 y2[1] (closed_form) 1.9854660422931665 y2[1] (numeric) 1.9854660422931967 absolute error 3.019806626980426e-14 relative error 1.5209560690812018e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO 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] 1.5000639999997223 y1[1] (closed_form) 1.070673361844011 y1[1] (numeric) 1.070673361843734 absolute error 2.7688962234151404e-13 relative error 2.5861260045232616e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 y2[1] (closed_form) 1.9974995117420686 y2[1] (numeric) 1.9974995117420804 absolute error 1.176836406102666e-14 relative error 5.891547903690439e-13% Desired digits 16 Estimated correct digits 11 Correct digits 15 h 0.000128 NO POLE (given) for Equation 1 NO 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] 1.6000319999996488 y1[1] (closed_form) 0.9707684913587206 y1[1] (numeric) 0.9707684913583713 absolute error 3.4927616354707425e-13 relative error 3.597934694586301e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 y2[1] (closed_form) 1.9995726681450203 y2[1] (numeric) 1.9995726681450023 absolute error 1.7985612998927536e-14 relative error 8.994728366442703e-13% Desired digits 16 Estimated correct digits 11 Correct digits 15 h 0.000128 NO POLE (given) for Equation 1 NO 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] 1.6999999999995754 y1[1] (closed_form) 0.8711555057048963 y1[1] (numeric) 0.8711555057044799 absolute error 4.164446565368962e-13 relative error 4.780371056714262e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 y2[1] (closed_form) 1.9916648104525234 y2[1] (numeric) 1.9916648104524606 absolute error 6.283862319378386e-14 relative error 3.1550802556734627e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO 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] 1.8000959999995019 y1[1] (closed_form) 0.7727044169819246 y1[1] (numeric) 0.7727044169814439 absolute error 4.807265696626928e-13 relative error 6.2213513873823e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 y2[1] (closed_form) 1.9738258149897616 y2[1] (numeric) 1.9738258149896417 absolute error 1.199040866595169e-13 relative error 6.074704553407559e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO 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] 1.9000639999994284 y1[1] (closed_form) 0.6766498705935637 y1[1] (numeric) 0.6766498705930278 absolute error 5.359046539865631e-13 relative error 7.919969799395105e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 y2[1] (closed_form) 1.9462793952173116 y2[1] (numeric) 1.9462793952171205 absolute error 1.9118040484045196e-13 relative error 9.822865376381675e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO 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] 2.000031999999355 y1[1] (closed_form) 0.5838240661488576 y1[1] (numeric) 0.5838240661482764 absolute error 5.812017533912694e-13 relative error 9.955083853002395e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 y2[1] (closed_form) 1.9092841096616224 y2[1] (numeric) 1.9092841096613458 absolute error 2.76667577736589e-13 relative error 1.4490644757192375e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO 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] 2.099999999999455 y1[1] (closed_form) 0.49515389540061283 y1[1] (numeric) 0.4951538954001461 absolute error 4.667377595524158e-13 relative error 9.426115070240809e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 y2[1] (closed_form) 1.8632093666491487 y2[1] (numeric) 1.8632093666488685 absolute error 2.802202914153895e-13 relative error 1.5039656650038533e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO 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] 2.2000959999995553 y1[1] (closed_form) 0.4114212698021795 y1[1] (numeric) 0.41142126980182386 absolute error 3.556599459386689e-13 relative error 8.64466599185983e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 y2[1] (closed_form) 1.8084399039871308 y2[1] (numeric) 1.8084399039868655 absolute error 2.653433028854124e-13 relative error 1.467249767605773e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO 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] 2.3000639999996553 y1[1] (closed_form) 0.3336762549514194 y1[1] (numeric) 0.3336762549511675 absolute error 2.51909604287448e-13 relative error 7.549521446293026e-11% Desired digits 16 Estimated correct digits 10 Correct digits 13 h 0.000128 y2[1] (closed_form) 1.7456625689844127 y2[1] (numeric) 1.745662568984179 absolute error 2.3381296898605797e-13 relative error 1.3393938389942399e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO 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] 2.4000319999997553 y1[1] (closed_form) 0.26258467001469143 y1[1] (numeric) 0.2625846700145319 absolute error 1.59539048638635e-13 relative error 6.075718305631052e-11% Desired digits 16 Estimated correct digits 10 Correct digits 13 h 0.000128 y2[1] (closed_form) 1.675439583606601 y2[1] (numeric) 1.6754395836064155 absolute error 1.8540724511240114e-13 relative error 1.106618507325033e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO 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] 2.4999999999998552 y1[1] (closed_form) 0.1988563844531529 y1[1] (numeric) 0.19885638445307285 absolute error 8.004708007547379e-14 relative error 4.02537139029255e-11% Desired digits 16 Estimated correct digits 10 Correct digits 13 h 0.000128 y2[1] (closed_form) 1.5984721441040723 y2[1] (numeric) 1.5984721441039524 absolute error 1.199040866595169e-13 relative error 7.501168356407107e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO 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! Maximum Time Reached before Solution Completed! diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ; diff ( y2 , x , 1 ) = y1 - 1.0 ; Iterations 19128 Total Elapsed Time 3 Minutes 0 Seconds Elapsed Time(since restart) 3 Minutes 0 Seconds Expected Time Remaining 9 Minutes 7.788959171966553 Seconds Optimized Time Remaining 9 Minutes 7.788959171966553 Seconds Expected Total Time 12 Minutes 7.788959171966553 Seconds Time to Timeout 0.0 Seconds Percent Done 24.73244444444347%