##############ECHO OF PROBLEM################# ##############temp/sqrt_tonepostode.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=0.5 x_end=0.6 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=0.01 $glob_min_h=0.001 # 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 0.09999999999999998 estimated_steps 99.99999999999997 step_error 2.5000000000000007e-19 est_needed_step_err 2.5000000000000007e-19 opt_iter 1 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4999999999999888 Order of pole (three term test) 1.5000000000006768 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.23570226039551587 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 0.09999999999999998 estimated_steps 99.99999999999997 step_error 2.5000000000000007e-19 est_needed_step_err 2.5000000000000007e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.285783216869341e-103 estimated_step_error 9.285783216869341e-103 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4999999999999888 Order of pole (three term test) 1.5000000000006768 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.23570226039551587 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 0.09999999999999998 estimated_steps 49.999999999999986 step_error 3.535533905932738e-19 est_needed_step_err 3.535533905932738e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.375202760816313e-92 estimated_step_error 6.375202760816313e-92 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4999999999999888 Order of pole (three term test) 1.5000000000006768 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.23570226039551587 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 0.09999999999999998 estimated_steps 24.999999999999993 step_error 5.000000000000001e-19 est_needed_step_err 5.000000000000001e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.372866438037111e-81 estimated_step_error 4.372866438037111e-81 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4999999999999888 Order of pole (three term test) 1.5000000000006768 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.23570226039551587 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 0.09999999999999998 estimated_steps 12.499999999999996 step_error 7.071067811865476e-19 est_needed_step_err 7.071067811865476e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.9938862671211814e-70 estimated_step_error 2.9938862671211814e-70 Double H and LOOP opt_iter 5 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 0.5 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.31249999999999295 Order of pole (three term test) 1.5000000000006768 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.5 y[1] (closed_form) 0.23570226039551587 y[1] (numeric) 0.23570226039551587 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5000000000000004 Order of pole (three term test) 1.5000000000000409 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.51 y[1] (closed_form) 0.2428085665704569 y[1] (numeric) 0.24280856657045694 absolute error 2.7755575615628914e-17 relative error 1.1431052869205481e-14% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.51 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5100000000000056 Order of pole (three term test) 1.499999999999582 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.52 y[1] (closed_form) 0.24998488843216993 y[1] (numeric) 0.24998488843216995 absolute error 2.7755575615628914e-17 relative error 1.1102901375240535e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.52 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5199999999999974 Order of pole (three term test) 1.5000000000001374 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.53 y[1] (closed_form) 0.257230549421245 y[1] (numeric) 0.257230549421245 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.53 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5299999999999966 Order of pole (three term test) 1.5000000000003717 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.54 y[1] (closed_form) 0.26454489222058325 y[1] (numeric) 0.26454489222058325 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.54 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5399999999999973 Order of pole (three term test) 1.5000000000003018 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.55 y[1] (closed_form) 0.27192727786017434 y[1] (numeric) 0.27192727786017434 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.55 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5499999999999935 Order of pole (three term test) 1.5000000000005176 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.56 y[1] (closed_form) 0.279377084879121 y[1] (numeric) 0.279377084879121 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.56 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5600000000000053 Order of pole (three term test) 1.4999999999997755 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5700000000000001 y[1] (closed_form) 0.28689370854028856 y[1] (numeric) 0.2868937085402885 absolute error 5.551115123125783e-17 relative error 1.9349030522034742e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.5700000000000001 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.570000000000003 Order of pole (three term test) 1.5000000000000733 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5800000000000001 y[1] (closed_form) 0.2944765600934045 y[1] (numeric) 0.29447656009340445 absolute error 5.551115123125783e-17 relative error 1.885078772098205e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.5800000000000001 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5799999999999913 Order of pole (three term test) 1.5000000000004414 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5900000000000001 y[1] (closed_form) 0.302125066082832 y[1] (numeric) 0.3021250660828319 absolute error 1.1102230246251565e-16 relative error 3.674713386147089e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.5900000000000001 Order of pole (given) 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5900000000000019 Order of pole (three term test) 1.5000000000001534 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sqrt ( x ) ; Iterations 10 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 110.00000000000013%