##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrt_tzeropostode.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=0.0 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 0.5 estimated_steps 500.0 step_error 1.1180339887498947e-19 est_needed_step_err 1.1180339887498947e-19 opt_iter 1 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9999999999999978 Order of pole (three term test) 1.2500000000002283 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.0699844879622753 $glob_desired_digits_correct 16 estimated_h 0.001 estimated_answer 1.0699844879622753 desired_abs_gbl_error 1.0699844879622753e-16 range 0.5 estimated_steps 500.0 step_error 1.1962790249769764e-19 est_needed_step_err 1.1962790249769764e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3011491854610612e-123 estimated_step_error 1.3011491854610612e-123 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9999999999999978 Order of pole (three term test) 1.2500000000002283 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.0699844879622753 $glob_desired_digits_correct 16 estimated_h 0.002 estimated_answer 1.0699844879622753 desired_abs_gbl_error 1.0699844879622753e-16 range 0.5 estimated_steps 250.0 step_error 1.6917940215049027e-19 est_needed_step_err 1.6917940215049027e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.939330682575976e-113 estimated_step_error 8.939330682575976e-113 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9999999999999978 Order of pole (three term test) 1.2500000000002283 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.0699844879622753 $glob_desired_digits_correct 16 estimated_h 0.004 estimated_answer 1.0699844879622753 desired_abs_gbl_error 1.0699844879622753e-16 range 0.5 estimated_steps 125.0 step_error 2.392558049953953e-19 est_needed_step_err 2.392558049953953e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.140179234085203e-102 estimated_step_error 6.140179234085203e-102 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9999999999999978 Order of pole (three term test) 1.2500000000002283 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.0699844879622753 $glob_desired_digits_correct 16 estimated_h 0.008 estimated_answer 1.0699844879622753 desired_abs_gbl_error 1.0699844879622753e-16 range 0.5 estimated_steps 62.5 step_error 3.3835880430098053e-19 est_needed_step_err 3.3835880430098053e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.2155435811945216e-91 estimated_step_error 4.2155435811945216e-91 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9999999999999978 Order of pole (three term test) 1.2500000000002283 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.0699844879622753 $glob_desired_digits_correct 16 estimated_h 0.016 estimated_answer 1.0699844879622753 desired_abs_gbl_error 1.0699844879622753e-16 range 0.5 estimated_steps 31.25 step_error 4.785116099907906e-19 est_needed_step_err 4.785116099907906e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.8914784341508644e-80 estimated_step_error 2.8914784341508644e-80 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9999999999999978 Order of pole (three term test) 1.2500000000002283 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.0699844879622753 $glob_desired_digits_correct 16 estimated_h 0.032 estimated_answer 1.0699844879622753 desired_abs_gbl_error 1.0699844879622753e-16 range 0.5 estimated_steps 15.625 step_error 6.767176086019611e-19 est_needed_step_err 6.767176086019611e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9795999433152496e-69 estimated_step_error 1.9795999433152496e-69 Double H and LOOP opt_iter 7 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5624999999999984 Order of pole (three term test) 1.2500000000002283 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (closed_form) 1.0699844879622753 y[1] (numeric) 1.0699844879622753 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0000000000000173 Order of pole (three term test) 1.2499999999998 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.05 y[1] (closed_form) 1.1035253478632558 y[1] (numeric) 1.1035253478632558 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 2.05 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0499999999999554 Order of pole (three term test) 1.2500000000005953 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 1.1372713678556832 y[1] (numeric) 1.137271367855683 absolute error 2.220446049250313e-16 relative error 1.952432912680241e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 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 2.099999999999981 Order of pole (three term test) 1.2500000000001812 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15000000000000002 y[1] (closed_form) 1.171218872736315 y[1] (numeric) 1.1712188727363149 absolute error 2.220446049250313e-16 relative error 1.8958421017095565e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 2.15 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.1500000000000097 Order of pole (three term test) 1.2499999999998945 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2 y[1] (closed_form) 1.2053643373531946 y[1] (numeric) 1.2053643373531944 absolute error 2.220446049250313e-16 relative error 1.8421368381663678e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 2.2 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.200000000000034 Order of pole (three term test) 1.249999999999241 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.25 y[1] (closed_form) 1.2397043771971739 y[1] (numeric) 1.2397043771971736 absolute error 2.220446049250313e-16 relative error 1.7911093080678485e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 2.25 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.2499999999999956 Order of pole (three term test) 1.2500000000001408 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) 1.2742357397800275 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 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 2.299999999999996 Order of pole (three term test) 1.2500000000000508 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.35 y[1] (closed_form) 1.3089552967176639 y[1] (numeric) 1.3089552967176636 absolute error 2.220446049250313e-16 relative error 1.6963497949993428e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 2.35 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.349999999999992 Order of pole (three term test) 1.2500000000001308 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.39999999999999997 y[1] (closed_form) 1.343860036446944 y[1] (numeric) 1.3438600364469437 absolute error 2.220446049250313e-16 relative error 1.652289664867921e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 2.4 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.399999999999993 Order of pole (three term test) 1.2500000000001144 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.44999999999999996 y[1] (closed_form) 1.3789470575132206 y[1] (numeric) 1.37894705751322 absolute error 4.440892098500626e-16 relative error 3.220494996022028e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 2.45 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4499999999999935 Order of pole (three term test) 1.249999999999927 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.49999999999999994 y[1] (closed_form) 1.4142135623730951 y[1] (numeric) 1.4142135623730947 absolute error 4.440892098500626e-16 relative error 3.1401849173675496e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 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 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%