##############ECHO OF PROBLEM################# ##############temp/sing7postode.ode################# diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=64; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=2.0 x_end=3.0 $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=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=6.0 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=16 $glob_max_minutes=3.0 $glob_subiter_method=3 $glob_max_iter=100000000 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(1.0/ ( x - 6.0 ) / ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )) 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 1.0 estimated_steps 1000000.0 step_error 3.3333333333333333e-21 est_needed_step_err 3.3333333333333333e-21 opt_iter 1 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 1000000.0 step_error 3.3333333333333333e-21 est_needed_step_err 3.3333333333333333e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.254211160650322e-174 estimated_step_error 5.254211160650322e-174 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 500000.0 step_error 4.7140452079103165e-21 est_needed_step_err 4.7140452079103165e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.5260418465046603e-166 estimated_step_error 3.5260418465046603e-166 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 250000.0 step_error 6.6666666666666666e-21 est_needed_step_err 6.6666666666666666e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.3662871970157716e-158 estimated_step_error 2.3662871970157716e-158 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 125000.0 step_error 9.428090415820633e-21 est_needed_step_err 9.428090415820633e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.587989221482499e-150 estimated_step_error 1.587989221482499e-150 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 62500.0 step_error 1.3333333333333333e-20 est_needed_step_err 1.3333333333333333e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.06568255319317e-142 estimated_step_error 1.06568255319317e-142 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 31250.0 step_error 1.8856180831641266e-20 est_needed_step_err 1.8856180831641266e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.15168832658992e-135 estimated_step_error 7.15168832658992e-135 Double H and LOOP opt_iter 7 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 15625.0 step_error 2.6666666666666666e-20 est_needed_step_err 2.6666666666666666e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.799435279580277e-127 estimated_step_error 4.799435279580277e-127 Double H and LOOP opt_iter 8 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 7812.5 step_error 3.771236166328253e-20 est_needed_step_err 3.771236166328253e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.220871307371706e-119 estimated_step_error 3.220871307371706e-119 Double H and LOOP opt_iter 9 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 3906.25 step_error 5.333333333333333e-20 est_needed_step_err 5.333333333333333e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.161523449266746e-111 estimated_step_error 2.161523449266746e-111 Double H and LOOP opt_iter 10 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 1953.125 step_error 7.542472332656506e-20 est_needed_step_err 7.542472332656506e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.4506185338211745e-103 estimated_step_error 1.4506185338211745e-103 Double H and LOOP opt_iter 11 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 976.5625 step_error 1.0666666666666666e-19 est_needed_step_err 1.0666666666666666e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.735536224832558e-96 estimated_step_error 9.735536224832558e-96 Double H and LOOP opt_iter 12 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 488.28125 step_error 1.5084944665313013e-19 est_needed_step_err 1.5084944665313013e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.534213266775494e-88 estimated_step_error 6.534213266775494e-88 Double H and LOOP opt_iter 13 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 244.140625 step_error 2.1333333333333333e-19 est_needed_step_err 2.1333333333333333e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.3861178216530524e-80 estimated_step_error 4.3861178216530524e-80 Double H and LOOP opt_iter 14 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 122.0703125 step_error 3.0169889330626025e-19 est_needed_step_err 3.0169889330626025e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.944926520833646e-72 estimated_step_error 2.944926520833646e-72 Double H and LOOP opt_iter 15 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 61.03515625 step_error 4.2666666666666666e-19 est_needed_step_err 4.2666666666666666e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.97825937741948e-64 estimated_step_error 1.97825937741948e-64 Double H and LOOP opt_iter 16 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 30.517578125 step_error 6.033977866125205e-19 est_needed_step_err 6.033977866125205e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3302159832359724e-56 estimated_step_error 1.3302159832359724e-56 Double H and LOOP opt_iter 17 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.9999999999999645 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0009765625 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 1.0 estimated_steps 15.2587890625 step_error 8.533333333333333e-19 est_needed_step_err 8.533333333333333e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.962419322997394e-49 estimated_step_error 8.962419322997394e-49 Double H and LOOP opt_iter 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.051757812499973 Order of pole (three term test) 1.339595059443141e-13 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] 2.0 y[1] (closed_form) -0.0009765625 y[1] (numeric) -0.0009765625 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.999999999999985 Order of pole (three term test) 1.2998409788388275e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1 y[1] (closed_form) -0.0011083501001765614 y[1] (numeric) -0.0011083500736475795 absolute error 2.652898191922437e-11 relative error 2.3935561439475013e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.1 Radius of convergence (given) for eq 1 3.9 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.899999999999958 Order of pole (three term test) 1.259530518312036e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2 y[1] (closed_form) -0.001262065854394352 y[1] (numeric) -0.0012620657927638612 absolute error 6.163049085829153e-11 relative error 4.883302297079192e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.1 Radius of convergence (given) for eq 1 3.8 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7999999999999803 Order of pole (three term test) 1.1763379369547133e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3000000000000003 y[1] (closed_form) -0.0014420867271822983 y[1] (numeric) -0.0014420866187666653 absolute error 1.0841563302492474e-10 relative error 7.517968994608159e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.1 Radius of convergence (given) for eq 1 3.6999999999999997 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.699999999999989 Order of pole (three term test) 1.056835107315319e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4000000000000004 y[1] (closed_form) -0.0016538171687920209 y[1] (numeric) -0.001653816997536185 absolute error 1.712558359012739e-10 relative error 1.0355185514633544e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 Radius of convergence (given) for eq 1 3.5999999999999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.599999999999983 Order of pole (three term test) 9.114035552040825e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5000000000000004 y[1] (closed_form) -0.0019039685845183567 y[1] (numeric) -0.0019039683281684597 absolute error 2.563498970389877e-10 relative error 1.3463977248544573e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 Radius of convergence (given) for eq 1 3.4999999999999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.500000000000022 Order of pole (three term test) 7.527333367546456e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6000000000000005 y[1] (closed_form) -0.0022009258678866972 y[1] (numeric) -0.0022009254953134828 absolute error 3.7257321446743097e-10 relative error 1.6928021970370647e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 Radius of convergence (given) for eq 1 3.3999999999999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.3999999999999777 Order of pole (three term test) 2.3755818785633563e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7000000000000006 y[1] (closed_form) -0.0025552317821364435 y[1] (numeric) -0.002555231249372466 absolute error 5.327639774656279e-10 relative error 2.084992763436047e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 Radius of convergence (given) for eq 1 3.2999999999999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2999999999999656 Order of pole (three term test) 1.78562917785641e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8000000000000007 y[1] (closed_form) -0.0029802322387695347 y[1] (numeric) -0.0029802314830751323 absolute error 7.556944024537937e-10 relative error 2.5356896439916424e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 Radius of convergence (given) for eq 1 3.1999999999999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.199999999999996 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.900000000000001 y[1] (closed_form) -0.003492943259127737 y[1] (numeric) -0.003492942189997632 absolute error 1.0691301051933555e-09 relative error 3.0608287220226426e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 Radius of convergence (given) for eq 1 3.099999999999999 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.1000000000000005 Order of pole (three term test) 8.617583060923643e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; Iterations 10 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 110.0000000000001%