##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrt_tonepostode.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=0.5 x_end=1.5 $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 1.0 estimated_steps 1000.0 step_error 7.905694150420949e-20 est_needed_step_err 7.905694150420949e-20 opt_iter 1 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 2.5000000000000244 Order of pole (three term test) 1.249999999999909 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.4142135623730951 $glob_desired_digits_correct 16 estimated_h 0.001 estimated_answer 1.4142135623730951 desired_abs_gbl_error 1.414213562373095e-16 range 1.0 estimated_steps 1000.0 step_error 1.118033988749895e-19 est_needed_step_err 1.118033988749895e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.581160759120225e-127 estimated_step_error 5.581160759120225e-127 Double H and LOOP opt_iter 2 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 2.5000000000000244 Order of pole (three term test) 1.249999999999909 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.4142135623730951 $glob_desired_digits_correct 16 estimated_h 0.002 estimated_answer 1.4142135623730951 desired_abs_gbl_error 1.414213562373095e-16 range 1.0 estimated_steps 500.0 step_error 1.5811388300841898e-19 est_needed_step_err 1.5811388300841898e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.834624317884502e-116 estimated_step_error 3.834624317884502e-116 Double H and LOOP opt_iter 3 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 2.5000000000000244 Order of pole (three term test) 1.249999999999909 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.4142135623730951 $glob_desired_digits_correct 16 estimated_h 0.004 estimated_answer 1.4142135623730951 desired_abs_gbl_error 1.414213562373095e-16 range 1.0 estimated_steps 250.0 step_error 2.23606797749979e-19 est_needed_step_err 2.23606797749979e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.634144555525965e-105 estimated_step_error 2.634144555525965e-105 Double H and LOOP opt_iter 4 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 2.5000000000000244 Order of pole (three term test) 1.249999999999909 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.4142135623730951 $glob_desired_digits_correct 16 estimated_h 0.008 estimated_answer 1.4142135623730951 desired_abs_gbl_error 1.414213562373095e-16 range 1.0 estimated_steps 125.0 step_error 3.1622776601683796e-19 est_needed_step_err 3.1622776601683796e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.808812326998184e-94 estimated_step_error 1.808812326998184e-94 Double H and LOOP opt_iter 5 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 2.5000000000000244 Order of pole (three term test) 1.249999999999909 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.4142135623730951 $glob_desired_digits_correct 16 estimated_h 0.016 estimated_answer 1.4142135623730951 desired_abs_gbl_error 1.414213562373095e-16 range 1.0 estimated_steps 62.5 step_error 4.47213595499958e-19 est_needed_step_err 4.47213595499958e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2411441082389687e-83 estimated_step_error 1.2411441082389687e-83 Double H and LOOP opt_iter 6 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 2.5000000000000244 Order of pole (three term test) 1.249999999999909 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.4142135623730951 $glob_desired_digits_correct 16 estimated_h 0.032 estimated_answer 1.4142135623730951 desired_abs_gbl_error 1.414213562373095e-16 range 1.0 estimated_steps 31.25 step_error 6.324555320336759e-19 est_needed_step_err 6.324555320336759e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.503597565314252e-73 estimated_step_error 8.503597565314252e-73 Double H and LOOP opt_iter 7 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 2.5000000000000244 Order of pole (three term test) 1.249999999999909 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.4142135623730951 $glob_desired_digits_correct 16 estimated_h 0.064 estimated_answer 1.4142135623730951 desired_abs_gbl_error 1.414213562373095e-16 range 1.0 estimated_steps 15.625 step_error 8.94427190999916e-19 est_needed_step_err 8.94427190999916e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.808920981709633e-62 estimated_step_error 5.808920981709633e-62 Double H and LOOP opt_iter 8 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL 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 1.953125000000019 Order of pole (three term test) 1.249999999999909 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.5 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 14 Correct digits 16 h 0.1 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 2.5000000000000204 Order of pole (three term test) 1.249999999999518 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6 y[1] (closed_form) 1.4852743188922317 y[1] (numeric) 1.4852743188922317 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 2.6 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.600000000000011 Order of pole (three term test) 1.2499999999999711 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7 y[1] (closed_form) 1.5570217963593211 y[1] (numeric) 1.557021796359321 absolute error 2.220446049250313e-16 relative error 1.4260853987029803e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 2.7 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.700000000000005 Order of pole (three term test) 1.2500000000000404 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7999999999999999 y[1] (closed_form) 1.62943682162873 y[1] (numeric) 1.6294368216287303 absolute error 2.220446049250313e-16 relative error 1.3627076667083233e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 2.8 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.799999999999985 Order of pole (three term test) 1.2500000000003 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8999999999999999 y[1] (closed_form) 1.7025014260763707 y[1] (numeric) 1.7025014260763707 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 2.9 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.899999999999976 Order of pole (three term test) 1.2500000000002913 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9999999999999999 y[1] (closed_form) 1.7761987307814848 y[1] (numeric) 1.7761987307814848 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 3.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.000000000000039 Order of pole (three term test) 1.2499999999993008 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0999999999999999 y[1] (closed_form) 1.8505128461361668 y[1] (numeric) 1.850512846136167 absolute error 2.220446049250313e-16 relative error 1.1999084761213948e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 3.0999999999999996 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.100000000000055 Order of pole (three term test) 1.2499999999994191 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2 y[1] (closed_form) 1.925428783660234 y[1] (numeric) 1.9254287836602337 absolute error 2.220446049250313e-16 relative error 1.1532215930776999e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 3.2 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2000000000000104 Order of pole (three term test) 1.2500000000000235 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3 y[1] (closed_form) 2.000932378200509 y[1] (numeric) 2.0009323782005093 absolute error 4.440892098500626e-16 relative error 2.2194113838541796e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 3.3 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.300000000000045 Order of pole (three term test) 1.2499999999994293 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4000000000000001 y[1] (closed_form) 2.077010219012499 y[1] (numeric) 2.077010219012499 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 3.4000000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.400000000000027 Order of pole (three term test) 1.249999999999592 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 10 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 110.00000000000003%