##############ECHO OF PROBLEM################# ##############temp/sqrtpostode.ode################# diff ( y , x , 1 ) = sqrt ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=0.2 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_min_h=0.001 $glob_max_h=0.01 # 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]=0.0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=1.5 # 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(2.0*expt(x,1.5)/3.0) 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 0.001 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 100.0 step_error 2.4999999999999997e-19 est_needed_step_err 2.4999999999999997e-19 opt_iter 1 Radius of convergence (given) for eq 1 0.1 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10000000000000069 Order of pole (three term test) 1.499999999999913 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0210818510677892 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.001 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 100.0 step_error 2.4999999999999997e-19 est_needed_step_err 2.4999999999999997e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2041162643241813e-78 estimated_step_error 1.2041162643241813e-78 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 0.1 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10000000000000069 Order of pole (three term test) 1.499999999999913 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0210818510677892 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.002 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 50.0 step_error 3.535533905932737e-19 est_needed_step_err 3.535533905932737e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.236403653689294e-68 estimated_step_error 8.236403653689294e-68 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 0.1 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10000000000000069 Order of pole (three term test) 1.499999999999913 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0210818510677892 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.004 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 25.0 step_error 4.999999999999999e-19 est_needed_step_err 4.999999999999999e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.608205902107171e-57 estimated_step_error 5.608205902107171e-57 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 0.1 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10000000000000069 Order of pole (three term test) 1.499999999999913 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0210818510677892 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.008 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 12.5 step_error 7.071067811865474e-19 est_needed_step_err 7.071067811865474e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.784643348666978e-46 estimated_step_error 3.784643348666978e-46 Double H and LOOP opt_iter 5 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL SETTING H FOR POLE Radius of convergence (given) for eq 1 0.1 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.06250000000000043 Order of pole (three term test) 1.499999999999913 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 0.0210818510677892 y[1] (numeric) 0.0210818510677892 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.006250000000000044 Radius of convergence (given) for eq 1 0.1 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09999999999999959 Order of pole (three term test) 1.499999999999992 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1125000000000001 y[1] (closed_form) 0.02515576474687267 y[1] (numeric) 0.025155764746872665 absolute error 3.469446951953614e-18 relative error 1.3791856406929276e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.006250000000000044 Radius of convergence (given) for eq 1 0.1125000000000001 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11249999999999968 Order of pole (three term test) 1.500000000000107 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1250000000000002 y[1] (closed_form) 0.029462782549439546 y[1] (numeric) 0.029462782549439546 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.006250000000000044 Radius of convergence (given) for eq 1 0.1250000000000002 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.12500000000000086 Order of pole (three term test) 1.4999999999998628 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.13125000000000023 y[1] (closed_form) 0.03169988663228948 y[1] (numeric) 0.03169988663228948 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.006250000000000044 Radius of convergence (given) for eq 1 0.13125000000000023 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.13124999999999867 Order of pole (three term test) 1.5000000000004252 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1437500000000003 y[1] (closed_form) 0.036334611502747124 y[1] (numeric) 0.03633461150274713 absolute error 6.938893903907228e-18 relative error 1.909720131005833e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.006250000000000044 Radius of convergence (given) for eq 1 0.1437500000000003 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1437500000000014 Order of pole (three term test) 1.4999999999998166 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15000000000000033 y[1] (closed_form) 0.038729833462074294 y[1] (numeric) 0.03872983346207431 absolute error 1.3877787807814457e-17 relative error 3.58322940412437e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.006250000000000044 Radius of convergence (given) for eq 1 0.15000000000000033 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.15000000000000244 Order of pole (three term test) 1.4999999999995663 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1625000000000004 y[1] (closed_form) 0.04367056280328397 y[1] (numeric) 0.04367056280328399 absolute error 2.0816681711721685e-17 relative error 4.7667537067226205e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.006250000000000044 Radius of convergence (given) for eq 1 0.1625000000000004 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1625000000000015 Order of pole (three term test) 1.4999999999996712 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17500000000000046 y[1] (closed_form) 0.04880516821448794 y[1] (numeric) 0.048805168214487965 absolute error 2.7755575615628914e-17 relative error 5.68701566474462e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.006250000000000044 Radius of convergence (given) for eq 1 0.17500000000000046 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.17500000000000135 Order of pole (three term test) 1.4999999999998732 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1812500000000005 y[1] (closed_form) 0.051442937980402885 y[1] (numeric) 0.05144293798040292 absolute error 3.469446951953614e-17 relative error 6.744262843765446e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.006250000000000044 Radius of convergence (given) for eq 1 0.1812500000000005 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.18125000000000185 Order of pole (three term test) 1.4999999999998546 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19375000000000056 y[1] (closed_form) 0.056855346115774134 y[1] (numeric) 0.05685534611577418 absolute error 4.85722573273506e-17 relative error 8.543129300179311e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.006250000000000044 Radius of convergence (given) for eq 1 0.19375000000000056 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.19375000000000595 Order of pole (three term test) 1.4999999999991989 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sqrt ( x ) ; Iterations 16 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 106.25000000000061%