##############ECHO OF PROBLEM################# ##############temp/sing4postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 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=-2.0 x_end=-1.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=0.1 # 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 # 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 # 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 * x + 1.0)) 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 2.5e-21 est_needed_step_err 2.5e-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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 2.5e-21 est_needed_step_err 2.5e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1633716769922073e-229 estimated_step_error 1.1633716769922073e-229 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 3.5355339059327375e-21 est_needed_step_err 3.5355339059327375e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.99463098764576e-219 estimated_step_error 7.99463098764576e-219 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 5.0e-21 est_needed_step_err 5.0e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.493870915958275e-208 estimated_step_error 5.493870915958275e-208 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 7.071067811865475e-21 est_needed_step_err 7.071067811865475e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.7753625542027424e-197 estimated_step_error 3.7753625542027424e-197 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 1.0e-20 est_needed_step_err 1.0e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.594413801466996e-186 estimated_step_error 2.594413801466996e-186 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 1.414213562373095e-20 est_needed_step_err 1.414213562373095e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.7828736488983694e-175 estimated_step_error 1.7828736488983694e-175 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 2.0e-20 est_needed_step_err 2.0e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2251897714783587e-164 estimated_step_error 1.2251897714783587e-164 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 2.82842712474619e-20 est_needed_step_err 2.82842712474619e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.4195544757987e-154 estimated_step_error 8.4195544757987e-154 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 4.0e-20 est_needed_step_err 4.0e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.786031118819402e-143 estimated_step_error 5.786031118819402e-143 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 5.65685424949238e-20 est_needed_step_err 5.65685424949238e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.976346568135108e-132 estimated_step_error 3.976346568135108e-132 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 8.0e-20 est_needed_step_err 8.0e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.7328218172109426e-121 estimated_step_error 2.7328218172109426e-121 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 1.131370849898476e-19 est_needed_step_err 1.131370849898476e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.878389510546474e-110 estimated_step_error 1.878389510546474e-110 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 1.6e-19 est_needed_step_err 1.6e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2913813816123636e-99 estimated_step_error 1.2913813816123636e-99 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 2.262741699796952e-19 est_needed_step_err 2.262741699796952e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.882036325997041e-89 estimated_step_error 8.882036325997041e-89 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 3.2e-19 est_needed_step_err 3.2e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.114335866490241e-78 estimated_step_error 6.114335866490241e-78 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 4.525483399593904e-19 est_needed_step_err 4.525483399593904e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.216432007036364e-67 estimated_step_error 4.216432007036364e-67 Double H and LOOP opt_iter 17 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 2.236067977499766 Order of pole (six term test) 0.9999999999997122 min_size 0.2 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 6.4e-19 est_needed_step_err 6.4e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.917866971552321e-56 estimated_step_error 2.917866971552321e-56 Double H and LOOP opt_iter 18 SETTING H FOR MAX H 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 1.7059844799039963 Order of pole (six term test) 0.9999999999997122 START of Soultion TOP MAIN SOLVE Loop x[1] -2.0 y[1] (closed_form) 0.2 y[1] (numeric) 0.2 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 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 2.236067977499802 Order of pole (six term test) 1.000000000000128 TOP MAIN SOLVE Loop x[1] -1.9 y[1] (closed_form) 0.2169197396963124 y[1] (numeric) 0.21691973969631237 absolute error 2.7755575615628914e-17 relative error 1.2795320358804928e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 2.147091055358361 Order of pole (six term test) 0.9999999999996163 TOP MAIN SOLVE Loop x[1] -1.7999999999999998 y[1] (closed_form) 0.23584905660377362 y[1] (numeric) 0.2358490566037736 absolute error 2.7755575615628914e-17 relative error 1.1768364061026658e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 2.0591260281974004 Order of pole (six term test) 1.0000000000000107 TOP MAIN SOLVE Loop x[1] -1.6999999999999997 y[1] (closed_form) 0.25706940874035994 y[1] (numeric) 0.2570694087403599 absolute error 5.551115123125783e-17 relative error 2.159383782895929e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 1.972308292331777 Order of pole (six term test) 1.0000000000026255 TOP MAIN SOLVE Loop x[1] -1.5999999999999996 y[1] (closed_form) 0.28089887640449446 y[1] (numeric) 0.2808988764044944 absolute error 5.551115123125783e-17 relative error 1.976196983832778e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 1.886796226411236 Order of pole (six term test) 0.9999999999987352 TOP MAIN SOLVE Loop x[1] -1.4999999999999996 y[1] (closed_form) 0.3076923076923078 y[1] (numeric) 0.3076923076923077 absolute error 1.1102230246251565e-16 relative error 3.6082248300317575e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.8027756377319943 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 1.802775637731992 Order of pole (six term test) 0.9999999999999822 TOP MAIN SOLVE Loop x[1] -1.3999999999999995 y[1] (closed_form) 0.33783783783783805 y[1] (numeric) 0.3378378378378379 absolute error 1.6653345369377348e-16 relative error 4.929390229335692e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.7204650534085248 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 1.720465053408544 Order of pole (six term test) 1.000000000000334 TOP MAIN SOLVE Loop x[1] -1.2999999999999994 y[1] (closed_form) 0.371747211895911 y[1] (numeric) 0.37174721189591087 absolute error 1.1102230246251565e-16 relative error 2.986499936241669e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.640121946685672 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 1.6401219466855825 Order of pole (six term test) 0.9999999999984261 TOP MAIN SOLVE Loop x[1] -1.1999999999999993 y[1] (closed_form) 0.4098360655737707 y[1] (numeric) 0.4098360655737706 absolute error 1.1102230246251565e-16 relative error 2.7089441800853804e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.5620499351813304 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 1.562049935181336 Order of pole (six term test) 1.0000000000001243 TOP MAIN SOLVE Loop x[1] -1.0999999999999992 y[1] (closed_form) 0.4524886877828058 y[1] (numeric) 0.4524886877828056 absolute error 2.220446049250313e-16 relative error 4.9071857688431875e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.48660687473185 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 1.4866068747318468 Order of pole (six term test) 0.9999999999999396 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 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 110.00000000000007%