##############ECHO OF PROBLEM################# ##############temp/arccos_sqrtpostode.ode################# diff ( y , x , 1 ) = arccos ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #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_max_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 # 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 #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(10.0 * (0.1 * x + 0.2) * arccos(sqrt ( 0.1 * x + 0.2)) - 5.0 * sqrt( 0.1 * x + 0.2) * sqrt( 0.8 - 0.1 * x) + 5.0 * arcsin(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 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.5 estimated_steps 500000.0 step_error 4.7140452079103165e-21 est_needed_step_err 4.7140452079103165e-21 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 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.532535480592211 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 2.532535480592211 desired_abs_gbl_error 2.532535480592211e-16 range 0.5 estimated_steps 500000.0 step_error 1.1938486746148563e-20 est_needed_step_err 1.1938486746148563e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2587599705259397e-168 estimated_step_error 1.2587599705259397e-168 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 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.532535480592211 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 2.532535480592211 desired_abs_gbl_error 2.532535480592211e-16 range 0.5 estimated_steps 250000.0 step_error 1.688356987061474e-20 est_needed_step_err 1.688356987061474e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.44739325058823e-161 estimated_step_error 8.44739325058823e-161 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 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.532535480592211 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 2.532535480592211 desired_abs_gbl_error 2.532535480592211e-16 range 0.5 estimated_steps 125000.0 step_error 2.3876973492297126e-20 est_needed_step_err 2.3876973492297126e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.668947075830024e-153 estimated_step_error 5.668947075830024e-153 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 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.532535480592211 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 2.532535480592211 desired_abs_gbl_error 2.532535480592211e-16 range 0.5 estimated_steps 62500.0 step_error 3.376713974122948e-20 est_needed_step_err 3.376713974122948e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.804362530936719e-145 estimated_step_error 3.804362530936719e-145 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 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.532535480592211 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 2.532535480592211 desired_abs_gbl_error 2.532535480592211e-16 range 0.5 estimated_steps 31250.0 step_error 4.775394698459425e-20 est_needed_step_err 4.775394698459425e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.553059843214273e-137 estimated_step_error 2.553059843214273e-137 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 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.532535480592211 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 2.532535480592211 desired_abs_gbl_error 2.532535480592211e-16 range 0.5 estimated_steps 15625.0 step_error 6.753427948245897e-20 est_needed_step_err 6.753427948245897e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.7133232387560482e-129 estimated_step_error 1.7133232387560482e-129 Double H and LOOP opt_iter 7 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 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.532535480592211 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 2.532535480592211 desired_abs_gbl_error 2.532535480592211e-16 range 0.5 estimated_steps 7812.5 step_error 9.55078939691885e-20 est_needed_step_err 9.55078939691885e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.14978341491193e-121 estimated_step_error 1.14978341491193e-121 Double H and LOOP opt_iter 8 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 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.532535480592211 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 2.532535480592211 desired_abs_gbl_error 2.532535480592211e-16 range 0.5 estimated_steps 3906.25 step_error 1.3506855896491793e-19 est_needed_step_err 1.3506855896491793e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.71595384942909e-114 estimated_step_error 7.71595384942909e-114 Double H and LOOP opt_iter 9 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 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.532535480592211 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 2.532535480592211 desired_abs_gbl_error 2.532535480592211e-16 range 0.5 estimated_steps 1953.125 step_error 1.91015787938377e-19 est_needed_step_err 1.91015787938377e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.177938614013485e-106 estimated_step_error 5.177938614013485e-106 Double H and LOOP opt_iter 10 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 2.0002204141583957 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.532535480592211 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 2.532535480592211 desired_abs_gbl_error 2.532535480592211e-16 range 0.5 estimated_steps 976.5625 step_error 2.7013711792983586e-19 est_needed_step_err 2.7013711792983586e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.474653988869495e-98 estimated_step_error 3.474653988869495e-98 Double H and LOOP opt_iter 11 SETTING H FOR MAX H 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 1.9533402482015583 Order of pole (three term test) 1.4951455387821966 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (closed_form) 2.532535480592211 y[1] (numeric) 2.532535480592211 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.001 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 2.0002204141583833 Order of pole (three term test) 1.4951455387824641 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.05000000000000004 y[1] (closed_form) 2.587737149360984 y[1] (numeric) 2.587737149425986 absolute error 6.500178173496352e-11 relative error 2.5119159320727397e-09% Desired digits 16 Estimated correct digits 13 Correct digits 11 h 0.001 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 2.0502322851721595 Order of pole (three term test) 1.4950080683235587 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10000000000000007 y[1] (closed_form) 2.6426291732054885 y[1] (numeric) 2.642629173335314 absolute error 1.2982548369677716e-10 relative error 4.912739366276648e-09% Desired digits 16 Estimated correct digits 13 Correct digits 11 h 0.001 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 2.1002445062508537 Order of pole (three term test) 1.4948697094387589 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1500000000000001 y[1] (closed_form) 2.6972142944484596 y[1] (numeric) 2.6972142946429534 absolute error 1.9449375443514327e-10 relative error 7.210912193200962e-09% Desired digits 16 Estimated correct digits 13 Correct digits 11 h 0.001 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 2.1502570805794377 Order of pole (three term test) 1.4947304538002055 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20000000000000015 y[1] (closed_form) 2.751495138739343 y[1] (numeric) 2.7514951389983695 absolute error 2.590265779645051e-10 relative error 9.41403000563482e-09% Desired digits 16 Estimated correct digits 12 Correct digits 11 h 0.001 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 2.2002700113785827 Order of pole (three term test) 1.4945902929758543 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.25000000000000017 y[1] (closed_form) 2.8054742215007202 y[1] (numeric) 2.805474221824166 absolute error 3.2344571465614536e-10 relative error 1.1529092378654113e-08% Desired digits 16 Estimated correct digits 12 Correct digits 10 h 0.001 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 2.2502833019052306 Order of pole (three term test) 1.494449218426984 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3000000000000002 y[1] (closed_form) 2.8591539538613966 y[1] (numeric) 2.859153954249172 absolute error 3.8777558941660573e-10 relative error 1.356259913506581e-08% Desired digits 16 Estimated correct digits 12 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.3000000000000003 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.3002969554532497 Order of pole (three term test) 1.4943072215044015 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.35000000000000026 y[1] (closed_form) 2.9125366481266495 y[1] (numeric) 2.9125366485786794 absolute error 4.520299690113916e-10 relative error 1.5520146992901817e-08% Desired digits 16 Estimated correct digits 12 Correct digits 10 h 0.001 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 2.350310975353532 Order of pole (three term test) 1.4941642934517245 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4000000000000003 y[1] (closed_form) 2.965624522830128 y[1] (numeric) 2.9656245233463614 absolute error 5.162332783470447e-10 relative error 1.7407236633395436e-08% Desired digits 16 Estimated correct digits 12 Correct digits 10 h 0.001 Radius of convergence (given) for eq 1 2.4000000000000004 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.4003253649748313 Order of pole (three term test) 1.49402042539943 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.45000000000000034 y[1] (closed_form) 3.018419707406812 y[1] (numeric) 3.0184197079872113 absolute error 5.803992841890704e-10 relative error 1.92285811931603e-08% Desired digits 16 Estimated correct digits 12 Correct digits 10 h 0.001 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 2.45034012772395 Order of pole (three term test) 1.4938756083668867 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arccos ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 500 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.20000000000007%