##############ECHO OF PROBLEM################# ##############temp/cosh_sqrtpostode.ode################# diff ( y , x , 1 ) = cosh ( 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=-1.9 x_end=-1.8 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=0.01 $glob_upper_ratio_limit=1.001 $glob_lower_ratio_limit=0.999 # 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 #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(20.0 * sqrt(0.1 * x + 0.2) * sinh( sqrt(0.1 * x + 0.2)) - 20.0 * cosh( 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 0.09999999999999987 estimated_steps 99999.99999999987 step_error 1.0540925533894603e-20 est_needed_step_err 1.0540925533894603e-20 opt_iter 1 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0996766451942949 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 min_size 19.899749861076383 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 19.899749861076383 desired_abs_gbl_error 1.989974986107638e-15 range 0.09999999999999987 estimated_steps 99999.99999999987 step_error 2.0976178142873565e-19 est_needed_step_err 2.0976178142873565e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.689350542413945e-138 estimated_step_error 4.689350542413945e-138 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0996766451942949 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 min_size 19.899749861076383 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 19.899749861076383 desired_abs_gbl_error 1.989974986107638e-15 range 0.09999999999999987 estimated_steps 49999.999999999935 step_error 2.9664795616405875e-19 est_needed_step_err 2.9664795616405875e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.146955635139175e-130 estimated_step_error 3.146955635139175e-130 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0996766451942949 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 min_size 19.899749861076383 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 19.899749861076383 desired_abs_gbl_error 1.989974986107638e-15 range 0.09999999999999987 estimated_steps 24999.999999999967 step_error 4.195235628574713e-19 est_needed_step_err 4.195235628574713e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.1118670611531895e-122 estimated_step_error 2.1118670611531895e-122 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0996766451942949 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 min_size 19.899749861076383 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 19.899749861076383 desired_abs_gbl_error 1.989974986107638e-15 range 0.09999999999999987 estimated_steps 12499.999999999984 step_error 5.932959123281175e-19 est_needed_step_err 5.932959123281175e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.4172243373368017e-114 estimated_step_error 1.4172243373368017e-114 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0996766451942949 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 min_size 19.899749861076383 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 19.899749861076383 desired_abs_gbl_error 1.989974986107638e-15 range 0.09999999999999987 estimated_steps 6249.999999999992 step_error 8.390471257149426e-19 est_needed_step_err 8.390471257149426e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.510487192989343e-107 estimated_step_error 9.510487192989343e-107 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0996766451942949 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 min_size 19.899749861076383 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 19.899749861076383 desired_abs_gbl_error 1.989974986107638e-15 range 0.09999999999999987 estimated_steps 3124.999999999996 step_error 1.186591824656235e-18 est_needed_step_err 1.186591824656235e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.38191780356733e-99 estimated_step_error 6.38191780356733e-99 Double H and LOOP opt_iter 7 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0996766451942949 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 min_size 19.899749861076383 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 19.899749861076383 desired_abs_gbl_error 1.989974986107638e-15 range 0.09999999999999987 estimated_steps 1562.499999999998 step_error 1.6780942514298852e-18 est_needed_step_err 1.6780942514298852e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.2822124376916545e-91 estimated_step_error 4.2822124376916545e-91 Double H and LOOP opt_iter 8 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0996766451942949 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 min_size 19.899749861076383 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 19.899749861076383 desired_abs_gbl_error 1.989974986107638e-15 range 0.09999999999999987 estimated_steps 781.249999999999 step_error 2.37318364931247e-18 est_needed_step_err 2.37318364931247e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.8729121973867996e-83 estimated_step_error 2.8729121973867996e-83 Double H and LOOP opt_iter 9 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0996766451942949 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 min_size 19.899749861076383 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 19.899749861076383 desired_abs_gbl_error 1.989974986107638e-15 range 0.09999999999999987 estimated_steps 390.6249999999995 step_error 3.3561885028597704e-18 est_needed_step_err 3.3561885028597704e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9268631232788424e-75 estimated_step_error 1.9268631232788424e-75 Double H and LOOP opt_iter 10 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0996766451942949 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 min_size 19.899749861076383 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 19.899749861076383 desired_abs_gbl_error 1.989974986107638e-15 range 0.09999999999999987 estimated_steps 195.31249999999974 step_error 4.74636729862494e-18 est_needed_step_err 4.74636729862494e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2916012044598128e-67 estimated_step_error 1.2916012044598128e-67 Double H and LOOP opt_iter 11 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0996766451942949 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 min_size 19.899749861076383 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 19.899749861076383 desired_abs_gbl_error 1.989974986107638e-15 range 0.09999999999999987 estimated_steps 97.65624999999987 step_error 6.712377005719541e-18 est_needed_step_err 6.712377005719541e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.647796455898528e-60 estimated_step_error 8.647796455898528e-60 Double H and LOOP opt_iter 12 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0996766451942949 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 min_size 19.899749861076383 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 19.899749861076383 desired_abs_gbl_error 1.989974986107638e-15 range 0.09999999999999987 estimated_steps 48.828124999999936 step_error 9.49273459724988e-18 est_needed_step_err 9.49273459724988e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.776789965708514e-52 estimated_step_error 5.776789965708514e-52 Double H and LOOP opt_iter 13 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0996766451942949 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 min_size 19.899749861076383 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 19.899749861076383 desired_abs_gbl_error 1.989974986107638e-15 range 0.09999999999999987 estimated_steps 24.414062499999968 step_error 1.3424754011439081e-17 est_needed_step_err 1.3424754011439081e-17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.8414614196340635e-44 estimated_step_error 3.8414614196340635e-44 Double H and LOOP opt_iter 14 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0996766451942949 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 min_size 19.899749861076383 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 19.899749861076383 desired_abs_gbl_error 1.989974986107638e-15 range 0.09999999999999987 estimated_steps 12.207031249999984 step_error 1.898546919449976e-17 est_needed_step_err 1.898546919449976e-17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.5318834762992195e-36 estimated_step_error 2.5318834762992195e-36 Double H and LOOP opt_iter 15 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL SETTING H FOR POLE Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.06083779613909593 Order of pole (three term test) 1.637424832937546 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] -1.9 y[1] (closed_form) -19.899749861076383 y[1] (numeric) -19.899749861076383 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.006083779613909593 Radius of convergence (given) for eq 1 0.10000000000000009 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09967664519429255 Order of pole (three term test) 1.6374248329380672 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.887832440772181 y[1] (closed_form) -19.887517705677656 y[1] (numeric) -19.887519577400983 absolute error 1.8717233274401224e-06 relative error 9.411548264295282e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.006083779613909593 Radius of convergence (given) for eq 1 0.11216755922781907 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11180489689496803 Order of pole (three term test) 1.6374107536228577 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.875664881544362 y[1] (closed_form) -19.875278133957643 y[1] (numeric) -19.87528187593071 absolute error 3.7419730674059792e-06 relative error 1.8827273974157276e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.006083779613909593 Radius of convergence (given) for eq 1 0.12433511845563805 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.12393315660207535 Order of pole (three term test) 1.6373966718844712 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8695811019304525 y[1] (closed_form) -19.86915556650749 y[1] (numeric) -19.86916024316542 absolute error 4.6766579302470745e-06 relative error 2.3537275726655936e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.006083779613909593 Radius of convergence (given) for eq 1 0.13041889806954754 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.12999728945890837 Order of pole (three term test) 1.6373896301066793 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8574135427026335 y[1] (closed_form) -19.85690486748748 y[1] (numeric) -19.856911412807577 absolute error 6.545320097472995e-06 relative error 3.296243871415185e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.006083779613909593 Radius of convergence (given) for eq 1 0.14258645729736652 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.14212556118084607 Order of pole (three term test) 1.6373755447368763 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8452459834748145 y[1] (closed_form) -19.844646748388485 y[1] (numeric) -19.844655161607804 absolute error 8.413219319436394e-06 relative error 4.239540983575131e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.006083779613909593 Radius of convergence (given) for eq 1 0.1547540165251855 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.15425384091616032 Order of pole (three term test) 1.6373614569429311 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.839162203860905 y[1] (closed_form) -19.838514905839567 y[1] (numeric) -19.838524252778136 absolute error 9.346938568910446e-06 relative error 4.711511226154901e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.006083779613909593 Radius of convergence (given) for eq 1 0.160837796139095 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.16031798378968917 Order of pole (three term test) 1.6373544121387487 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.826994644633086 y[1] (closed_form) -19.82624565380316 y[1] (numeric) -19.826256867809693 absolute error 1.1214006534032706e-05 relative error 5.6561422317904066e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.006083779613909593 Radius of convergence (given) for eq 1 0.17300535536691397 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.17244627555023342 Order of pole (three term test) 1.637340320713972 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.814827085405267 y[1] (closed_form) -19.813968977928926 y[1] (numeric) -19.81398205860811 absolute error 1.3080679185151212e-05 relative error 6.601746071027957e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.006083779613909593 Radius of convergence (given) for eq 1 0.18517291459473295 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.18457457533107444 Order of pole (three term test) 1.6373262268675108 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8087433057913576 y[1] (closed_form) -19.80782785558268 y[1] (numeric) -19.80784186948152 absolute error 1.401389884136961e-05 relative error 7.074929640717724e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.006083779613909593 Radius of convergence (given) for eq 1 0.19125669420864244 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.19063872822997058 Order of pole (three term test) 1.6373191790363772 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 17 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 109.50803305037097%