##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrtpostode.ode################# diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #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=0.5 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $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]=-2.0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=0.5 # 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(0.8 * (x + 2.0) * sqrt(sqrt(0.1 * x + 0.2))) 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 0.4 estimated_steps 400.0 step_error 1.2499999999999998e-19 est_needed_step_err 1.2499999999999998e-19 opt_iter 1 Radius of convergence (given) for eq 1 2.1 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1000000000000196 Order of pole (three term test) 1.2499999999997322 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.1372713678556832 $glob_desired_digits_correct 16 estimated_h 0.001 estimated_answer 1.1372713678556832 desired_abs_gbl_error 1.1372713678556832e-16 range 0.4 estimated_steps 400.0 step_error 1.421589209819604e-19 est_needed_step_err 1.421589209819604e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.387832209790197e-124 estimated_step_error 2.387832209790197e-124 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 2.1 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1000000000000196 Order of pole (three term test) 1.2499999999997322 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.1372713678556832 $glob_desired_digits_correct 16 estimated_h 0.002 estimated_answer 1.1372713678556832 desired_abs_gbl_error 1.1372713678556832e-16 range 0.4 estimated_steps 200.0 step_error 2.0104307406501352e-19 est_needed_step_err 2.0104307406501352e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.640539030783244e-113 estimated_step_error 1.640539030783244e-113 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 2.1 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1000000000000196 Order of pole (three term test) 1.2499999999997322 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.1372713678556832 $glob_desired_digits_correct 16 estimated_h 0.004 estimated_answer 1.1372713678556832 desired_abs_gbl_error 1.1372713678556832e-16 range 0.4 estimated_steps 100.0 step_error 2.843178419639208e-19 est_needed_step_err 2.843178419639208e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.126866092402042e-102 estimated_step_error 1.126866092402042e-102 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 2.1 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1000000000000196 Order of pole (three term test) 1.2499999999997322 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.1372713678556832 $glob_desired_digits_correct 16 estimated_h 0.008 estimated_answer 1.1372713678556832 desired_abs_gbl_error 1.1372713678556832e-16 range 0.4 estimated_steps 50.0 step_error 4.0208614813002704e-19 est_needed_step_err 4.0208614813002704e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.736850689019475e-92 estimated_step_error 7.736850689019475e-92 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 2.1 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1000000000000196 Order of pole (three term test) 1.2499999999997322 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.1372713678556832 $glob_desired_digits_correct 16 estimated_h 0.016 estimated_answer 1.1372713678556832 desired_abs_gbl_error 1.1372713678556832e-16 range 0.4 estimated_steps 25.0 step_error 5.686356839278416e-19 est_needed_step_err 5.686356839278416e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.307246047945901e-81 estimated_step_error 5.307246047945901e-81 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 2.1 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1000000000000196 Order of pole (three term test) 1.2499999999997322 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.1372713678556832 $glob_desired_digits_correct 16 estimated_h 0.032 estimated_answer 1.1372713678556832 desired_abs_gbl_error 1.1372713678556832e-16 range 0.4 estimated_steps 12.5 step_error 8.041722962600541e-19 est_needed_step_err 8.041722962600541e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.634155780754282e-70 estimated_step_error 3.634155780754282e-70 Double H and LOOP opt_iter 7 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 2.1 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3125000000000122 Order of pole (three term test) 1.2499999999997322 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 1.1372713678556832 y[1] (numeric) 1.1372713678556832 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.04 Radius of convergence (given) for eq 1 2.1 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0999999999999845 Order of pole (three term test) 1.2500000000001974 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.14 y[1] (closed_form) 1.164413424258851 y[1] (numeric) 1.1644134242588513 absolute error 2.220446049250313e-16 relative error 1.9069224065873567e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.04 Radius of convergence (given) for eq 1 2.14 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.140000000000014 Order of pole (three term test) 1.249999999999854 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000002 y[1] (closed_form) 1.191682615993191 y[1] (numeric) 1.1916826159931913 absolute error 2.220446049250313e-16 relative error 1.8632864316810677e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.04 Radius of convergence (given) for eq 1 2.18 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.180000000000023 Order of pole (three term test) 1.2499999999997058 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.22000000000000003 y[1] (closed_form) 1.2190771892719083 y[1] (numeric) 1.2190771892719083 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.04 Radius of convergence (given) for eq 1 2.22 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2200000000000206 Order of pole (three term test) 1.2499999999997964 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.26 y[1] (closed_form) 1.2465954457420954 y[1] (numeric) 1.2465954457420956 absolute error 2.220446049250313e-16 relative error 1.7812082154114453e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.04 Radius of convergence (given) for eq 1 2.26 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.259999999999995 Order of pole (three term test) 1.2500000000001088 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3 y[1] (closed_form) 1.2742357397800275 y[1] (numeric) 1.2742357397800277 absolute error 2.220446049250313e-16 relative error 1.742570844570433e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.04 Radius of convergence (given) for eq 1 2.3 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.300000000000018 Order of pole (three term test) 1.249999999999884 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.33999999999999997 y[1] (closed_form) 1.301996475963283 y[1] (numeric) 1.3019964759632832 absolute error 2.220446049250313e-16 relative error 1.7054163281106537e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.04 Radius of convergence (given) for eq 1 2.34 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3400000000000176 Order of pole (three term test) 1.2499999999998719 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.37999999999999995 y[1] (closed_form) 1.3298761067052998 y[1] (numeric) 1.3298761067053 absolute error 2.220446049250313e-16 relative error 1.6696638416576675e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.04 Radius of convergence (given) for eq 1 2.38 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.380000000000035 Order of pole (three term test) 1.2499999999996148 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.41999999999999993 y[1] (closed_form) 1.3578731300393683 y[1] (numeric) 1.3578731300393685 absolute error 2.220446049250313e-16 relative error 1.635238226700853e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.04 Radius of convergence (given) for eq 1 2.42 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4199999999999844 Order of pole (three term test) 1.25000000000028 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4599999999999999 y[1] (closed_form) 1.3859860875402967 y[1] (numeric) 1.3859860875402967 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.04 Radius of convergence (given) for eq 1 2.46 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4600000000000493 Order of pole (three term test) 1.249999999999351 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4999999999999999 y[1] (closed_form) 1.4142135623730951 y[1] (numeric) 1.4142135623730951 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.04 Radius of convergence (given) for eq 1 2.5 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.500000000000043 Order of pole (three term test) 1.24999999999949 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 11 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 120.0%