##############ECHO OF PROBLEM################# ##############temp/sing3postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-1.0 x_end=-0.7 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=100 $glob_max_h=0.001 # ELIMINATED in preodein.rb ## Not Given = 0 ## No Pole = 3 ## Pole = 4 $glob_type_given_pole=4 ## Real Part $array_given_rad_poles[1][1]=0.0 ## Imag Part $array_given_rad_poles[1][2]=0.0 ## Order $array_given_ord_poles[1][1]=3.0 ## Not Used $array_given_ord_poles[1][2]=0.0 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(1.0/x/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 10 desired_abs_gbl_error 1.0e-10 range 0.30000000000000004 estimated_steps 300000.00000000006 step_error 3.3333333333333326e-16 est_needed_step_err 3.3333333333333326e-16 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.333337387389348e-217 estimated_step_error 8.333337387389348e-217 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.726628633188216e-206 estimated_step_error 5.726628633188216e-206 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.935313060297872e-195 estimated_step_error 3.935313060297872e-195 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.7043318054539415e-184 estimated_step_error 2.7043318054539415e-184 best_h 1.6e-05 opt_iter 5 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8584098986717968e-173 estimated_step_error 1.8584098986717968e-173 best_h 3.2e-05 opt_iter 6 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.277099498721197e-162 estimated_step_error 1.277099498721197e-162 best_h 6.4e-05 opt_iter 7 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.77629755692946e-152 estimated_step_error 8.77629755692946e-152 best_h 0.000128 opt_iter 8 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.03121354642344e-141 estimated_step_error 6.03121354642344e-141 best_h 0.000256 opt_iter 9 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.1448765086147165e-130 estimated_step_error 4.1448765086147165e-130 best_h 0.000512 opt_iter 10 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.8486922699966054e-119 estimated_step_error 2.8486922699966054e-119 best_h 0.001024 opt_iter 11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9580942675651462e-108 estimated_step_error 1.9580942675651462e-108 best_h 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] -1.0 y[1] (analytic) 1.0 y[1] (numeric) 1.0 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 1.03125 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9992498124531161 Order of pole (three term test) 1225.0262565641444 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.99 y[1] (analytic) 1.020304050607081 y[1] (numeric) 1.020304050607081 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.99 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 1.0209375 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9892573143285824 Order of pole (three term test) 1225.0262565641417 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.98 y[1] (analytic) 1.0412328196584757 y[1] (numeric) 1.0412328196584757 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.98 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 1.0106250000000003 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9792648162040576 Order of pole (three term test) 1225.0262565641497 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.97 y[1] (analytic) 1.0628122010840686 y[1] (numeric) 1.0628122010840684 absolute error 2.220446049250313e-16 relative error 2.0892176877396193e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.97 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 1.0003125 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9692723180795217 Order of pole (three term test) 1225.0262565641438 Radius of convergence (six term test) for eq 1 1.1258860538231157 Order of pole (six term test) 9.36282162911084e-11 TOP MAIN SOLVE Loop x[1] -0.96 y[1] (analytic) 1.0850694444444446 y[1] (numeric) 1.0850694444444442 absolute error 4.440892098500626e-16 relative error 4.092726157978176e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.96 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.9900000000000001 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9592798199549835 Order of pole (three term test) 1225.0262565641344 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.95 y[1] (analytic) 1.10803324099723 y[1] (numeric) 1.1080332409972296 absolute error 4.440892098500626e-16 relative error 4.007905118896815e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.95 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.9796874999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9492873218304676 Order of pole (three term test) 1225.0262565641542 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.94 y[1] (analytic) 1.1317338162064283 y[1] (numeric) 1.1317338162064279 absolute error 4.440892098500626e-16 relative error 3.923972258235153e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.94 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.9693750000000001 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9392948237059372 Order of pole (three term test) 1225.0262565641553 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9299999999999999 y[1] (analytic) 1.156203029251937 y[1] (numeric) 1.1562030292519363 absolute error 6.661338147750939e-16 relative error 5.761391363989785e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9299999999999999 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.9590624999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9293023255813996 Order of pole (three term test) 1225.0262565641467 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9199999999999999 y[1] (analytic) 1.181474480151229 y[1] (numeric) 1.1814744801512282 absolute error 6.661338147750939e-16 relative error 5.638156608256394e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9199999999999999 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.94875 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9193098274568696 Order of pole (three term test) 1225.0262565641488 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9099999999999999 y[1] (analytic) 1.207583625166043 y[1] (numeric) 1.2075836251660423 absolute error 6.661338147750939e-16 relative error 5.5162541201525517e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9099999999999999 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.9384374999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.9093173293323406 Order of pole (three term test) 1225.0262565641515 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8999999999999999 y[1] (analytic) 1.234567901234568 y[1] (numeric) 1.2345679012345674 absolute error 6.661338147750939e-16 relative error 5.39568389967826e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8999999999999999 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.9281249999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8993248312077989 Order of pole (three term test) 1225.026256564137 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8899999999999999 y[1] (analytic) 1.2624668602449187 y[1] (numeric) 1.262466860244918 absolute error 6.661338147750939e-16 relative error 5.276445946833518e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8899999999999999 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.9178124999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8893323330832618 Order of pole (three term test) 1225.0262565641287 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8799999999999999 y[1] (analytic) 1.291322314049587 y[1] (numeric) 1.2913223140495864 absolute error 6.661338147750939e-16 relative error 5.158540261618326e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8799999999999999 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.9074999999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8793398349587374 Order of pole (three term test) 1225.026256564138 Radius of convergence (six term test) for eq 1 0.6469036442928808 Order of pole (six term test) -1.971400820366398e-11 TOP MAIN SOLVE Loop x[1] -0.8699999999999999 y[1] (analytic) 1.3211784912141633 y[1] (numeric) 1.3211784912141626 absolute error 6.661338147750939e-16 relative error 5.041966844032685e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8699999999999999 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.8971874999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8693473368342116 Order of pole (three term test) 1225.0262565641453 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8599999999999999 y[1] (analytic) 1.3520822065981615 y[1] (numeric) 1.3520822065981608 absolute error 6.661338147750939e-16 relative error 4.926725694076593e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8599999999999999 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.8868749999999997 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8593548387096794 Order of pole (three term test) 1225.0262565641442 Radius of convergence (six term test) for eq 1 0.1977844771715892 Order of pole (six term test) 4.462918923309189e-11 TOP MAIN SOLVE Loop x[1] -0.8499999999999999 y[1] (analytic) 1.3840830449826995 y[1] (numeric) 1.3840830449826984 absolute error 1.1102230246251565e-15 relative error 8.021361352916752e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8499999999999999 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.8765625 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.849362340585151 Order of pole (three term test) 1225.0262565641485 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8399999999999999 y[1] (analytic) 1.4172335600907033 y[1] (numeric) 1.4172335600907024 absolute error 8.881784197001252e-16 relative error 6.266986929404081e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8399999999999999 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.86625 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8393698424606224 Order of pole (three term test) 1225.026256564152 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8299999999999998 y[1] (analytic) 1.4515894904920894 y[1] (numeric) 1.4515894904920883 absolute error 1.1102230246251565e-15 relative error 7.6483264166427e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8299999999999998 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.8559374999999999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8293773443360866 Order of pole (three term test) 1225.0262565641453 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8199999999999998 y[1] (analytic) 1.4872099940511605 y[1] (numeric) 1.4872099940511592 absolute error 1.3322676295501878e-15 relative error 8.95816754109546e-14% Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8199999999999998 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.845625 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8193848462115533 Order of pole (three term test) 1225.026256564142 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8099999999999998 y[1] (analytic) 1.5241579027587262 y[1] (numeric) 1.5241579027587246 absolute error 1.5543122344752192e-15 relative error 1.019784257039191e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.8099999999999998 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.8353124999999998 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.8093923480870265 Order of pole (three term test) 1225.026256564149 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7999999999999998 y[1] (analytic) 1.5625000000000007 y[1] (numeric) 1.5624999999999984 absolute error 2.220446049250313e-15 relative error 1.4210854715201999e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7999999999999998 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.8249999999999998 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7993998499624996 Order of pole (three term test) 1225.0262565641551 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7899999999999998 y[1] (analytic) 1.6023073225444648 y[1] (numeric) 1.6023073225444624 absolute error 2.4424906541753444e-15 relative error 1.5243584172708317e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7899999999999998 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.8146874999999997 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7894073518379614 Order of pole (three term test) 1225.0262565641444 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7799999999999998 y[1] (analytic) 1.6436554898093367 y[1] (numeric) 1.643655489809334 absolute error 2.6645352591003757e-15 relative error 1.621103251636668e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7799999999999998 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.8043749999999997 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7794148537134397 Order of pole (three term test) 1225.0262565641594 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7699999999999998 y[1] (analytic) 1.686625063248441 y[1] (numeric) 1.6866250632484379 absolute error 3.1086244689504383e-15 relative error 1.8431034476407137e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7699999999999998 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.7940624999999998 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7694223555888905 Order of pole (three term test) 1225.0262565641303 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7599999999999998 y[1] (analytic) 1.7313019390581728 y[1] (numeric) 1.7313019390581696 absolute error 3.1086244689504383e-15 relative error 1.7955414932657721e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7599999999999998 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.7837499999999997 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7594298574643721 Order of pole (three term test) 1225.026256564151 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7499999999999998 y[1] (analytic) 1.7777777777777788 y[1] (numeric) 1.7777777777777752 absolute error 3.552713678800501e-15 relative error 1.9984014443252805e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7499999999999998 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.7734374999999997 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.749437359339841 Order of pole (three term test) 1225.0262565641515 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7399999999999998 y[1] (analytic) 1.8261504747991246 y[1] (numeric) 1.826150474799121 absolute error 3.552713678800501e-15 relative error 1.945466010511153e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7399999999999998 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.7631249999999998 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7394448612153036 Order of pole (three term test) 1225.026256564141 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7299999999999998 y[1] (analytic) 1.8765246762994945 y[1] (numeric) 1.8765246762994905 absolute error 3.9968028886505635e-15 relative error 2.129896259361884e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7299999999999998 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.7528124999999998 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7294523630907652 Order of pole (three term test) 1225.0262565641287 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7199999999999998 y[1] (analytic) 1.9290123456790136 y[1] (numeric) 1.9290123456790094 absolute error 4.218847493575595e-15 relative error 2.187050540669587e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7199999999999998 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.7424999999999996 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.7194598649662436 Order of pole (three term test) 1225.026256564145 Radius of convergence (six term test) for eq 1 0.8043266153554095 Order of pole (six term test) 5.8111737644139794e-11 TOP MAIN SOLVE Loop x[1] -0.7099999999999997 y[1] (analytic) 1.9837333862328919 y[1] (numeric) 1.9837333862328872 absolute error 4.6629367034256575e-15 relative error 2.350586392196872e-13% Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7099999999999997 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 0.7321874999999998 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 0.70946736684171 Order of pole (three term test) 1225.0262565641408 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; Iterations 300 Total Elapsed Time 1.0 Seconds Elapsed Time(since restart) 1.0 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.3333333333334%