##############ECHO OF PROBLEM################# ##############temp/tan_sqrtpostode.ode################# diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=1.4 x_end=2.1 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=0.0001 # 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 # 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 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb #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(tan(sqrt(2.0*x + 1.0))) 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 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.7000000000000002 estimated_steps 700000.0000000002 step_error 2.988071523335984e-21 est_needed_step_err 2.988071523335984e-21 opt_iter 1 Radius of convergence (given) for eq 1 3.4 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.514161640922489 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 2.514161640922489 desired_abs_gbl_error 2.514161640922489e-16 range 0.7000000000000002 estimated_steps 700000.0000000002 step_error 7.512494804304158e-21 est_needed_step_err 7.512494804304158e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.7841030978274847e-224 estimated_step_error 2.7841030978274847e-224 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 3.4 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.514161640922489 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 2.514161640922489 desired_abs_gbl_error 2.514161640922489e-16 range 0.7000000000000002 estimated_steps 350000.0000000001 step_error 1.062427203950435e-20 est_needed_step_err 1.062427203950435e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9132204946031803e-213 estimated_step_error 1.9132204946031803e-213 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 3.4 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.514161640922489 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 2.514161640922489 desired_abs_gbl_error 2.514161640922489e-16 range 0.7000000000000002 estimated_steps 175000.00000000006 step_error 1.5024989608608316e-20 est_needed_step_err 1.5024989608608316e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3147543072855777e-202 estimated_step_error 1.3147543072855777e-202 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 3.4 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.514161640922489 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 2.514161640922489 desired_abs_gbl_error 2.514161640922489e-16 range 0.7000000000000002 estimated_steps 87500.00000000003 step_error 2.12485440790087e-20 est_needed_step_err 2.12485440790087e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.03491173383377e-192 estimated_step_error 9.03491173383377e-192 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 3.4 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.514161640922489 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 2.514161640922489 desired_abs_gbl_error 2.514161640922489e-16 range 0.7000000000000002 estimated_steps 43750.000000000015 step_error 3.004997921721663e-20 est_needed_step_err 3.004997921721663e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.208728853338198e-181 estimated_step_error 6.208728853338198e-181 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 3.4 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.514161640922489 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 2.514161640922489 desired_abs_gbl_error 2.514161640922489e-16 range 0.7000000000000002 estimated_steps 21875.000000000007 step_error 4.24970881580174e-20 est_needed_step_err 4.24970881580174e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.2665850705584534e-170 estimated_step_error 4.2665850705584534e-170 Double H and LOOP opt_iter 7 Radius of convergence (given) for eq 1 3.4 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.514161640922489 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 2.514161640922489 desired_abs_gbl_error 2.514161640922489e-16 range 0.7000000000000002 estimated_steps 10937.500000000004 step_error 6.009995843443327e-20 est_needed_step_err 6.009995843443327e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.931946197728727e-159 estimated_step_error 2.931946197728727e-159 Double H and LOOP opt_iter 8 SETTING H FOR MAX H Radius of convergence (given) for eq 1 3.4 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] 1.4 y[1] (closed_form) -2.514161640922489 y[1] (numeric) -2.514161640922489 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.0001 Radius of convergence (given) for eq 1 3.4 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4699999999999922 y[1] (closed_form) -2.274947836382328 y[1] (numeric) -2.2749187028168585 absolute error 2.913356546940804e-05 relative error 0.0012806256479153772% Desired digits 16 Estimated correct digits 12 Correct digits 5 h 0.0001 Radius of convergence (given) for eq 1 3.469999999999992 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5399999999999845 y[1] (closed_form) -2.074898511298209 y[1] (numeric) -2.0748476397455407 absolute error 5.087155266814136e-05 relative error 0.002451761008605302% Desired digits 16 Estimated correct digits 12 Correct digits 5 h 0.0001 Radius of convergence (given) for eq 1 3.5399999999999845 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6099999999999768 y[1] (closed_form) -1.9046668929605788 y[1] (numeric) -1.9045993869100692 absolute error 6.750605050953595e-05 relative error 0.0035442444429012888% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 Radius of convergence (given) for eq 1 3.609999999999977 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.679999999999969 y[1] (closed_form) -1.7576673782460641 y[1] (numeric) -1.757586870970808 absolute error 8.050727525610313e-05 relative error 0.004580347581829703% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 Radius of convergence (given) for eq 1 3.679999999999969 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7499999999999614 y[1] (closed_form) -1.629125005006734 y[1] (numeric) -1.6290341521195129 absolute error 9.085288722121554e-05 relative error 0.005576790420747363% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 Radius of convergence (given) for eq 1 3.7499999999999614 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8199999999999537 y[1] (closed_form) -1.5154923783358651 y[1] (numeric) -1.5153931651381496 absolute error 9.921319771555304e-05 relative error 0.0065465982629683206% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 Radius of convergence (given) for eq 1 3.8199999999999537 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.889999999999946 y[1] (closed_form) -1.414078344665924 y[1] (numeric) -1.413972284636747 absolute error 0.00010606002917690205 relative error 0.0075002937126484835% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 Radius of convergence (given) for eq 1 3.889999999999946 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9599999999999382 y[1] (closed_form) -1.3228038102193087 y[1] (numeric) -1.3226920770585044 absolute error 0.00011173316080426154 relative error 0.008446691787630791% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 Radius of convergence (given) for eq 1 3.9599999999999382 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.029999999999997 y[1] (closed_form) -1.2400366479213394 y[1] (numeric) -1.2399201656900705 absolute error 0.00011648223126892177 relative error 0.009393450706814167% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 Radius of convergence (given) for eq 1 4.029999999999998 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; Iterations 7000 Total Elapsed Time 15 Seconds Elapsed Time(since restart) 14 Seconds Time to Timeout 2 Minutes 45.0 Seconds Percent Done 100.01428571430642%