##############ECHO OF PROBLEM################# ##############temp/sing2postode.ode################# diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=16; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-2.0 x_end=-1.5 $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=2 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=0.0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=1.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=1.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=0.0 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=16 $glob_max_minutes=3.0 $glob_subiter_method=3 $glob_max_iter=100000000 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(arctan(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 0.5 estimated_steps 500000.0 step_error 7.071067811865475e-21 est_needed_step_err 7.071067811865475e-21 opt_iter 1 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 500000.0 step_error 7.828723661341925e-21 est_needed_step_err 7.828723661341925e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.4505741605933443e-103 estimated_step_error 1.4505741605933443e-103 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 250000.0 step_error 1.1071487177940902e-20 est_needed_step_err 1.1071487177940902e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.506485024763502e-99 estimated_step_error 9.506485024763502e-99 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 125000.0 step_error 1.565744732268385e-20 est_needed_step_err 1.565744732268385e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.230172917146513e-94 estimated_step_error 6.230172917146513e-94 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 62500.0 step_error 2.2142974355881805e-20 est_needed_step_err 2.2142974355881805e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.083009912693051e-89 estimated_step_error 4.083009912693051e-89 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 31250.0 step_error 3.13148946453677e-20 est_needed_step_err 3.13148946453677e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.675846343644817e-84 estimated_step_error 2.675846343644817e-84 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 15625.0 step_error 4.428594871176361e-20 est_needed_step_err 4.428594871176361e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.7536491704902098e-79 estimated_step_error 1.7536491704902098e-79 Double H and LOOP opt_iter 7 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 7812.5 step_error 6.26297892907354e-20 est_needed_step_err 6.26297892907354e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1492800541785464e-74 estimated_step_error 1.1492800541785464e-74 Double H and LOOP opt_iter 8 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 3906.25 step_error 8.857189742352722e-20 est_needed_step_err 8.857189742352722e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.532033619367497e-70 estimated_step_error 7.532033619367497e-70 Double H and LOOP opt_iter 9 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 1953.125 step_error 1.252595785814708e-19 est_needed_step_err 1.252595785814708e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.93634017032486e-65 estimated_step_error 4.93634017032486e-65 Double H and LOOP opt_iter 10 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 976.5625 step_error 1.7714379484705444e-19 est_needed_step_err 1.7714379484705444e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.2352720823055137e-60 estimated_step_error 3.2352720823055137e-60 Double H and LOOP opt_iter 11 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 488.28125 step_error 2.505191571629416e-19 est_needed_step_err 2.505191571629416e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.1205198529185375e-55 estimated_step_error 2.1205198529185375e-55 Double H and LOOP opt_iter 12 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 244.140625 step_error 3.542875896941089e-19 est_needed_step_err 3.542875896941089e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3900342094792536e-50 estimated_step_error 1.3900342094792536e-50 Double H and LOOP opt_iter 13 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 122.0703125 step_error 5.010383143258832e-19 est_needed_step_err 5.010383143258832e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.114060226246165e-46 estimated_step_error 9.114060226246165e-46 Double H and LOOP opt_iter 14 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 61.03515625 step_error 7.085751793882178e-19 est_needed_step_err 7.085751793882178e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.978675092256558e-41 estimated_step_error 5.978675092256558e-41 Double H and LOOP opt_iter 15 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 0.016384 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 30.517578125 step_error 1.0020766286517665e-18 est_needed_step_err 1.0020766286517665e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.925652484578803e-36 estimated_step_error 3.925652484578803e-36 Double H and LOOP opt_iter 16 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.23606797749978 Order of pole (six term test) -2.5757174171303632e-14 min_size 1.1071487177940904 $glob_desired_digits_correct 16 estimated_h 0.032768 estimated_answer 1.1071487177940904 desired_abs_gbl_error 1.1071487177940904e-16 range 0.5 estimated_steps 15.2587890625 step_error 1.4171503587764355e-18 est_needed_step_err 1.4171503587764355e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.5825489903244456e-31 estimated_step_error 2.5825489903244456e-31 Double H and LOOP opt_iter 17 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.7059844799040071 Order of pole (six term test) -2.5757174171303632e-14 START of Soultion TOP MAIN SOLVE Loop x[1] -2.0 y[1] (closed_form) -1.1071487177940904 y[1] (numeric) -1.1071487177940904 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.236067977499785 Order of pole (six term test) -1.1546319456101628e-14 TOP MAIN SOLVE Loop x[1] -1.95 y[1] (closed_form) -1.0969449903001363 y[1] (numeric) -1.0969449903001363 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 2.191460700081113 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.1914607000810267 Order of pole (six term test) -2.1405099914773018e-13 TOP MAIN SOLVE Loop x[1] -1.9 y[1] (closed_form) -1.0863183977578734 y[1] (numeric) -1.0863183977578734 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 2.1470910553583886 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.1470910553583824 Order of pole (six term test) -1.3322676295501878e-14 TOP MAIN SOLVE Loop x[1] -1.8499999999999999 y[1] (closed_form) -1.075244653309068 y[1] (numeric) -1.075244653309068 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 2.1029740844813087 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.102974084481294 Order of pole (six term test) -3.6415315207705135e-14 TOP MAIN SOLVE Loop x[1] -1.7999999999999998 y[1] (closed_form) -1.0636978224025597 y[1] (numeric) -1.0636978224025597 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 2.0591260281974 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.0591260281973667 Order of pole (six term test) -6.661338147750939e-14 TOP MAIN SOLVE Loop x[1] -1.7499999999999998 y[1] (closed_form) -1.0516502125483735 y[1] (numeric) -1.0516502125483738 absolute error 2.220446049250313e-16 relative error 2.1113921936740706e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 2.0155644370746373 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 2.015564437074621 Order of pole (six term test) -2.1316282072803006e-14 TOP MAIN SOLVE Loop x[1] -1.6999999999999997 y[1] (closed_form) -1.039072259536091 y[1] (numeric) -1.039072259536091 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 1.9723082923316018 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.972308292331604 Order of pole (six term test) 1.1546319456101628e-14 TOP MAIN SOLVE Loop x[1] -1.6499999999999997 y[1] (closed_form) -1.0259324113433528 y[1] (numeric) -1.025932411343353 absolute error 2.220446049250313e-16 relative error 2.1643200124098506e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 1.9293781381574735 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9293781381574708 Order of pole (six term test) 1.5987211554602254e-14 TOP MAIN SOLVE Loop x[1] -1.5999999999999996 y[1] (closed_form) -1.0121970114513341 y[1] (numeric) -1.0121970114513343 absolute error 2.220446049250313e-16 relative error 2.1936895921738955e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 1.8867962264113205 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.8867962264113214 Order of pole (six term test) 7.105427357601002e-15 TOP MAIN SOLVE Loop x[1] -1.5499999999999996 y[1] (closed_form) -0.9978301839061904 y[1] (numeric) -0.9978301839061906 absolute error 2.220446049250313e-16 relative error 2.2252744856424038e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 1.8445866745696715 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.844586674569669 Order of pole (six term test) -8.881784197001252e-15 Finished! diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; 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%