##############ECHO OF PROBLEM################# ##############temp/cos_sqrt_linpostode.ode################# diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-1.4 x_end=-1.3 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=0.0001 $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 # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=-1.5 # 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(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0))) 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 0.09999999999999987 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 0.09967108794652511 Order of pole (three term test) 1.6398183324573619 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.0950552785699608 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0950552785699608 desired_abs_gbl_error 1.0950552785699608e-16 range 0.09999999999999987 estimated_steps 99999.99999999987 step_error 1.1542896146904169e-20 est_needed_step_err 1.1542896146904169e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.307033538337183e-137 estimated_step_error 9.307033538337183e-137 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 0.09967108794652511 Order of pole (three term test) 1.6398183324573619 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.0950552785699608 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.0950552785699608 desired_abs_gbl_error 1.0950552785699608e-16 range 0.09999999999999987 estimated_steps 49999.999999999935 step_error 1.6324120280016016e-20 est_needed_step_err 1.6324120280016016e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.245816212876361e-129 estimated_step_error 6.245816212876361e-129 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 0.09967108794652511 Order of pole (three term test) 1.6398183324573619 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.0950552785699608 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.0950552785699608 desired_abs_gbl_error 1.0950552785699608e-16 range 0.09999999999999987 estimated_steps 24999.999999999967 step_error 2.3085792293808337e-20 est_needed_step_err 2.3085792293808337e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.191458369448505e-121 estimated_step_error 4.191458369448505e-121 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 0.09967108794652511 Order of pole (three term test) 1.6398183324573619 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.0950552785699608 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.0950552785699608 desired_abs_gbl_error 1.0950552785699608e-16 range 0.09999999999999987 estimated_steps 12499.999999999984 step_error 3.264824056003203e-20 est_needed_step_err 3.264824056003203e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.8127891779104904e-113 estimated_step_error 2.8127891779104904e-113 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 0.09967108794652511 Order of pole (three term test) 1.6398183324573619 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.0950552785699608 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.0950552785699608 desired_abs_gbl_error 1.0950552785699608e-16 range 0.09999999999999987 estimated_steps 6249.999999999992 step_error 4.6171584587616675e-20 est_needed_step_err 4.6171584587616675e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.887562525600106e-105 estimated_step_error 1.887562525600106e-105 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 0.09967108794652511 Order of pole (three term test) 1.6398183324573619 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.0950552785699608 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.0950552785699608 desired_abs_gbl_error 1.0950552785699608e-16 range 0.09999999999999987 estimated_steps 3124.999999999996 step_error 6.529648112006406e-20 est_needed_step_err 6.529648112006406e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2666300559573402e-97 estimated_step_error 1.2666300559573402e-97 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 0.09967108794652511 Order of pole (three term test) 1.6398183324573619 NO COMPLEX POLE (six term test) for Equation 1 min_size 1.0950552785699608 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.0950552785699608 desired_abs_gbl_error 1.0950552785699608e-16 range 0.09999999999999987 estimated_steps 1562.499999999998 step_error 9.234316917523335e-20 est_needed_step_err 9.234316917523335e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.498979743554776e-90 estimated_step_error 8.498979743554776e-90 Double H and LOOP opt_iter 8 SETTING H FOR MAX H 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 0.07786803745822275 Order of pole (three term test) 1.6398183324573619 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] -1.4 y[1] (closed_form) 1.0950552785699608 y[1] (numeric) 1.0950552785699608 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.0001 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 0.09967108794652436 Order of pole (three term test) 1.6398183324574496 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.390000000000001 y[1] (closed_form) 1.1040235390255817 y[1] (numeric) 1.1040240217879598 absolute error 4.827623780734314e-07 relative error 4.372754393439116e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.0001 Radius of convergence (given) for eq 1 0.10999999999999899 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10963762766783595 Order of pole (three term test) 1.6400424855938187 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3800000000000021 y[1] (closed_form) 1.1128954259704735 y[1] (numeric) 1.112896389858023 absolute error 9.63887549554343e-07 relative error 8.661079262805023e-05% Desired digits 16 Estimated correct digits 12 Correct digits 7 h 0.0001 Radius of convergence (given) for eq 1 0.11999999999999789 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11960406642296906 Order of pole (three term test) 1.6402659744016141 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3700000000000032 y[1] (closed_form) 1.1216712651341294 y[1] (numeric) 1.1216727085140303 absolute error 1.4433799009339054e-06 relative error 0.00012868118724261926% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 0.12999999999999678 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1295704048409041 Order of pole (three term test) 1.6404887980103002 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3600000000000043 y[1] (closed_form) 1.1303513815907278 y[1] (numeric) 1.1303533028342965 absolute error 1.9212435686810636e-06 relative error 0.0001699687017657575% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 0.13999999999999568 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.13953664355173856 Order of pole (three term test) 1.6407109555457815 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3500000000000054 y[1] (closed_form) 1.1389360997600726 y[1] (numeric) 1.1389384972425778 absolute error 2.3974825051897852e-06 relative error 0.00021050193296136957% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 0.14999999999999458 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.14950278318666343 Order of pole (three term test) 1.6409324461330002 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3400000000000065 y[1] (closed_form) 1.1474257434085307 y[1] (numeric) 1.1474286155090585 absolute error 2.872100527850918e-06 relative error 0.0002503081828475529% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 0.15999999999999348 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.15946882437800214 Order of pole (three term test) 1.6411532688934687 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3300000000000076 y[1] (closed_form) 1.1558206356499694 y[1] (numeric) 1.1558239807513158 absolute error 3.345101346363677e-06 relative error 0.00028941353382937114% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 0.16999999999999238 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1694347677591742 Order of pole (three term test) 1.6413734229477608 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3200000000000087 y[1] (closed_form) 1.1641210989466924 y[1] (numeric) 1.1641249154352813 absolute error 3.816488588936906e-06 relative error 0.00032784291878139657% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 0.17999999999999128 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.17940061396472456 Order of pole (three term test) 1.6415929074140372 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3100000000000098 y[1] (closed_form) 1.1723274551103748 y[1] (numeric) 1.1723317413761942 absolute error 4.286265819386514e-06 relative error 0.00036562018578528997% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 0.18999999999999018 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.18936636363032494 Order of pole (three term test) 1.6418117214075363 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.300000000000011 y[1] (closed_form) 1.180440025302998 y[1] (numeric) 1.180444779739545 absolute error 4.754436546905438e-06 relative error 0.0004027681580591152% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 Radius of convergence (given) for eq 1 0.19999999999998908 Order of pole (given) 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1993320173927918 Order of pole (three term test) 1.6420298640397009 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations 1001 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.1999999999891%