##############ECHO OF PROBLEM################# ##############temp/sing1postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; 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 $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 $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]=0.001 # 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(1.0 / (x * x + 0.000001)) 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 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.484894657593405e-101 estimated_step_error 6.484894657593405e-101 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 250000.0 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 4.249941687783492e-96 estimated_step_error 4.249941687783492e-96 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 125000.0 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 2.785243259044777e-91 estimated_step_error 2.785243259044777e-91 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 62500.0 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 1.825338954958387e-86 estimated_step_error 1.825338954958387e-86 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 31250.0 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 1.1962566707722527e-81 estimated_step_error 1.1962566707722527e-81 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 15625.0 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 7.839820921607223e-77 estimated_step_error 7.839820921607223e-77 Double H and LOOP opt_iter 7 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 7812.5 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 5.137948560927475e-72 estimated_step_error 5.137948560927475e-72 Double H and LOOP opt_iter 8 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 3906.25 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 3.3672630151535505e-67 estimated_step_error 3.3672630151535505e-67 Double H and LOOP opt_iter 9 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 1953.125 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 2.2068442650790195e-62 estimated_step_error 2.2068442650790195e-62 Double H and LOOP opt_iter 10 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 976.5625 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 1.4463754771965563e-57 estimated_step_error 1.4463754771965563e-57 Double H and LOOP opt_iter 11 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 488.28125 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 9.480251350755155e-53 estimated_step_error 9.480251350755155e-53 Double H and LOOP opt_iter 12 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 244.140625 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 6.214662514172606e-48 estimated_step_error 6.214662514172606e-48 Double H and LOOP opt_iter 13 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 122.0703125 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 4.075051566311024e-43 estimated_step_error 4.075051566311024e-43 Double H and LOOP opt_iter 14 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 61.03515625 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 2.673527639981127e-38 estimated_step_error 2.673527639981127e-38 Double H and LOOP opt_iter 15 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 30.517578125 step_error 9.050966799187808e-19 est_needed_step_err 9.050966799187808e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.7559389673284363e-33 estimated_step_error 1.7559389673284363e-33 Double H and LOOP opt_iter 16 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.00000500003826 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 2.0000000070382833 Order of pole (six term test) 1.0000000000092788 min_size 0.24999993750001562 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 0.5 estimated_steps 15.2587890625 step_error 1.28e-18 est_needed_step_err 1.28e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1558064421947916e-28 estimated_step_error 1.1558064421947916e-28 Double H and LOOP opt_iter 17 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5258827209764558 Order of pole (three term test) 2.0000175001899367 Radius of convergence (six term test) for eq 1 1.5258789116197842 Order of pole (six term test) 1.0000000000092788 START of Soultion TOP MAIN SOLVE Loop x[1] -2.0 y[1] (closed_form) 0.24999993750001562 y[1] (numeric) 0.24999993750001562 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 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000005000038268 Order of pole (three term test) 2.000017500190013 Radius of convergence (six term test) for eq 1 1.999999951753324 Order of pole (six term test) 1.0000000000101137 TOP MAIN SOLVE Loop x[1] -1.95 y[1] (closed_form) 0.2629848092084657 y[1] (numeric) 0.2629848092084657 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 1.9500002564102394 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9500051282463953 Order of pole (three term test) 2.000018409151581 Radius of convergence (six term test) for eq 1 1.9500001021090683 Order of pole (six term test) 1.0000000000059988 TOP MAIN SOLVE Loop x[1] -1.9 y[1] (closed_form) 0.2770082335157248 y[1] (numeric) 0.2770082335157248 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 1.9000002631578765 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9000052632025228 Order of pole (three term test) 2.0000193908149084 Radius of convergence (six term test) for eq 1 1.900000368344054 Order of pole (six term test) 0.9999999999963638 TOP MAIN SOLVE Loop x[1] -1.8499999999999999 y[1] (closed_form) 0.2921839905963505 y[1] (numeric) 0.2921839905963505 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 1.8500002702702505 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8500054054537387 Order of pole (three term test) 2.000020453144693 Radius of convergence (six term test) for eq 1 1.8500000743258753 Order of pole (six term test) 1.0000000000086002 TOP MAIN SOLVE Loop x[1] -1.7999999999999998 y[1] (closed_form) 0.3086418800488025 y[1] (numeric) 0.3086418800488025 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 1.8000002777777562 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8000055556080257 Order of pole (three term test) 2.0000216052276887 Radius of convergence (six term test) for eq 1 1.8000005230422955 Order of pole (six term test) 0.9999999999888383 TOP MAIN SOLVE Loop x[1] -1.7499999999999998 y[1] (closed_form) 0.32653050562269215 y[1] (numeric) 0.3265305056226921 absolute error 5.551115123125783e-17 relative error 1.7000295615687828e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 1.7500002857142622 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7500057143428127 Order of pole (three term test) 2.000022857466804 Radius of convergence (six term test) for eq 1 1.7500002928822143 Order of pole (six term test) 0.9999999999998046 TOP MAIN SOLVE Loop x[1] -1.6999999999999997 y[1] (closed_form) 0.34602064151534906 y[1] (numeric) 0.346020641515349 absolute error 5.551115123125783e-17 relative error 1.604272825694863e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 1.7000002941176213 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7000058824152355 Order of pole (three term test) 2.000024221817112 Radius of convergence (six term test) for eq 1 1.7000000413482195 Order of pole (six term test) 1.0000000000136913 TOP MAIN SOLVE Loop x[1] -1.6499999999999997 y[1] (closed_form) 0.3673093233023607 y[1] (numeric) 0.36730932330236066 absolute error 5.551115123125783e-17 relative error 1.5112916473825062e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 1.6500003030302748 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6500060606741882 Order of pole (three term test) 2.0000257120720146 Radius of convergence (six term test) for eq 1 1.6500000285702006 Order of pole (six term test) 1.0000000000171188 TOP MAIN SOLVE Loop x[1] -1.5999999999999996 y[1] (closed_form) 0.39062484741216913 y[1] (numeric) 0.3906248474121691 absolute error 5.551115123125783e-17 relative error 1.4210860266317122e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 1.600000312499969 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6000062500747159 Order of pole (three term test) 2.0000273442136445 Radius of convergence (six term test) for eq 1 1.6000003569981887 Order of pole (six term test) 0.999999999997506 TOP MAIN SOLVE Loop x[1] -1.5499999999999996 y[1] (closed_form) 0.4162329172807838 y[1] (numeric) 0.41623291728078377 absolute error 5.551115123125783e-17 relative error 1.333655963442481e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 1.5500003225806114 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5500064516950824 Order of pole (three term test) 2.000029136842705 Radius of convergence (six term test) for eq 1 1.5500003509810494 Order of pole (six term test) 0.9999999999978764 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; 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%