##############ECHO OF PROBLEM################# ##############temp/lin_arccospostode.ode################# diff ( y , x , 1 ) = arccos ( 0.1 * x + 0.2 ) ; ! #BEGIN FIRST INPUT BLOCK max_terms=30 # Digits:=32; ELIMINATED in preodein.rb ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-0.8 x_end=0.8 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # 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=0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=0.0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=1.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=1.0 # 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(0.1 * x + 0.2 ) - 10.0 * sqrt(1.0 - expt((0.1 * x + 0.2) , 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 1.6 estimated_steps 1600000.0000000002 step_error 2.6352313834736493e-21 est_needed_step_err 2.6352313834736493e-21 opt_iter 1 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 1600000.0000000002 step_error 2.1574985035408045e-20 est_needed_step_err 2.1574985035408045e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 2 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 800000.0000000001 step_error 3.0511636445070626e-20 est_needed_step_err 3.0511636445070626e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 3 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 400000.00000000006 step_error 4.314997007081609e-20 est_needed_step_err 4.314997007081609e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 4 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 200000.00000000003 step_error 6.102327289014125e-20 est_needed_step_err 6.102327289014125e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 5 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 100000.00000000001 step_error 8.629994014163218e-20 est_needed_step_err 8.629994014163218e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 6 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 50000.00000000001 step_error 1.220465457802825e-19 est_needed_step_err 1.220465457802825e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 7 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 25000.000000000004 step_error 1.7259988028326436e-19 est_needed_step_err 1.7259988028326436e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 8 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 12500.000000000002 step_error 2.44093091560565e-19 est_needed_step_err 2.44093091560565e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 9 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 6250.000000000001 step_error 3.451997605665287e-19 est_needed_step_err 3.451997605665287e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 10 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 3125.0000000000005 step_error 4.8818618312113e-19 est_needed_step_err 4.8818618312113e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 11 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 1562.5000000000002 step_error 6.903995211330574e-19 est_needed_step_err 6.903995211330574e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 12 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 781.2500000000001 step_error 9.7637236624226e-19 est_needed_step_err 9.7637236624226e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 13 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 390.62500000000006 step_error 1.3807990422661149e-18 est_needed_step_err 1.3807990422661149e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 14 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 195.31250000000003 step_error 1.95274473248452e-18 est_needed_step_err 1.95274473248452e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 15 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 0.016384 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 97.65625000000001 step_error 2.7615980845322298e-18 est_needed_step_err 2.7615980845322298e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 16 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 0.032768 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 48.82812500000001 step_error 3.90548946496904e-18 est_needed_step_err 3.90548946496904e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 17 NO INFO (given) for Equation 1 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 8.187131183512555 $glob_desired_digits_correct 16 estimated_h 0.065536 estimated_answer 8.187131183512555 desired_abs_gbl_error 8.187131183512555e-16 range 1.6 estimated_steps 24.414062500000004 step_error 5.5231961690644595e-18 est_needed_step_err 5.5231961690644595e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 Double H and LOOP opt_iter 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL NO INFO (given) for Equation 1 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] -0.8 y[1] (closed_form) -8.187131183512555 y[1] (numeric) -8.187131183512555 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.1 NO INFO (given) for Equation 1 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] -0.7000000000000001 y[1] (closed_form) -8.042584387278817 y[1] (numeric) -8.042584178425061 absolute error 2.08853755623295e-07 relative error 2.596848793450584e-06% Desired digits 16 Estimated correct digits 14 Correct digits 8 h 0.1 NO INFO (given) for Equation 1 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] -0.6000000000000001 y[1] (closed_form) -7.899046158670194 y[1] (numeric) -7.899045723033275 absolute error 4.356369185387621e-07 relative error 5.515057258661489e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.1 NO INFO (given) for Equation 1 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] -0.5000000000000001 y[1] (closed_form) -7.7565178856152786 y[1] (numeric) -7.7565172050518 absolute error 6.80563478461238e-07 relative error 8.774085079122498e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.1 NO INFO (given) for Equation 1 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] -0.40000000000000013 y[1] (closed_form) -7.615001065253676 y[1] (numeric) -7.6150001213874035 absolute error 9.438662722516256e-07 relative error 1.239482784261676e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 NO INFO (given) for Equation 1 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] -0.30000000000000016 y[1] (closed_form) -7.4744973053622585 y[1] (numeric) -7.47449607956465 absolute error 1.2257976083063227e-06 relative error 1.6399733095454147e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 NO INFO (given) for Equation 1 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] -0.20000000000000015 y[1] (closed_form) -7.335008325899322 y[1] (numeric) -7.335006799269361 absolute error 1.5266299611127465e-06 relative error 2.081292744716239e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 NO INFO (given) for Equation 1 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] -0.10000000000000014 y[1] (closed_form) -7.196535960670852 y[1] (numeric) -7.196534114014128 absolute error 1.8466567244246335e-06 relative error 2.5660355683854465e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 NO INFO (given) for Equation 1 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] -1.3877787807814457e-16 y[1] (closed_form) -7.05908215912358 y[1] (numeric) -7.059079972930538 absolute error 2.18619304259704e-06 relative error 3.096993338959051e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 NO INFO (given) for Equation 1 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] 0.09999999999999987 y[1] (closed_form) -6.9226489882698665 y[1] (numeric) -6.922646442693161 absolute error 2.5455767058701895e-06 relative error 3.6771714269834574e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 NO INFO (given) for Equation 1 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] 0.19999999999999987 y[1] (closed_form) -6.787238634749933 y[1] (numeric) -6.787235709580811 absolute error 2.925169122036664e-06 relative error 4.309807389208495e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 NO INFO (given) for Equation 1 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] 0.2999999999999999 y[1] (closed_form) -6.652853407037465 y[1] (numeric) -6.652850081681066 absolute error 3.3253563991308965e-06 relative error 4.9983912100232e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 NO INFO (given) for Equation 1 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] 0.3999999999999999 y[1] (closed_form) -6.5194957377950375 y[1] (numeric) -6.519491991244562 absolute error 3.746550475192123e-06 relative error 5.746687513686827e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 NO INFO (given) for Equation 1 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] 0.4999999999999999 y[1] (closed_form) -6.387168186386497 y[1] (numeric) -6.387163997196113 absolute error 4.189190383918628e-06 relative error 6.558760097859014e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 NO INFO (given) for Equation 1 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] 0.5999999999999999 y[1] (closed_form) -6.255873441553938 y[1] (numeric) -6.255868787810326 absolute error 4.653743611804373e-06 relative error 7.438998974775293e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 NO INFO (given) for Equation 1 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] 0.6999999999999998 y[1] (closed_form) -6.12561432426758 y[1] (numeric) -6.125609183560018 absolute error 5.1407075618570275e-06 relative error 8.392150223188734e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 NO INFO (given) for Equation 1 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] 0.7999999999999998 y[1] (closed_form) -5.996393790757606 y[1] (numeric) -5.996388140146445 absolute error 5.6506111612009136e-06 relative error 9.423349030062609e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 NO INFO (given) for Equation 1 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 ) = arccos ( 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 112.49999999999997%