##############ECHO OF PROBLEM################# ##############temp/lin_coshpostode.ode################# diff ( y , x , 1 ) = cosh ( 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=0.1 x_end=2.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_min_h=0.000000001 # 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=3 #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(sinh(2.0*x+3.0)/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-09 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 1.9 estimated_steps 1899999999.9999998 step_error 7.647191129018727e-23 est_needed_step_err 7.647191129018727e-23 opt_iter 1 NO POLE (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 6.122941998282746 $glob_desired_digits_correct 16 estimated_h 1.0e-09 estimated_answer 6.122941998282746 desired_abs_gbl_error 6.122941998282746e-16 range 1.9 estimated_steps 1899999999.9999998 step_error 4.682330773276401e-22 est_needed_step_err 4.682330773276401e-22 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0188752340044735e-252 estimated_step_error 1.0188752340044735e-252 Double H and LOOP opt_iter 2 NO POLE (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 6.122941998282746 $glob_desired_digits_correct 16 estimated_h 2.0e-09 estimated_answer 6.122941998282746 desired_abs_gbl_error 6.122941998282746e-16 range 1.9 estimated_steps 949999999.9999999 step_error 6.621815683084387e-22 est_needed_step_err 6.621815683084387e-22 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.837555950923353e-245 estimated_step_error 6.837555950923353e-245 Double H and LOOP opt_iter 3 NO POLE (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 6.122941998282746 $glob_desired_digits_correct 16 estimated_h 4.0e-09 estimated_answer 6.122941998282746 desired_abs_gbl_error 6.122941998282746e-16 range 1.9 estimated_steps 474999999.99999994 step_error 9.364661546552803e-22 est_needed_step_err 9.364661546552803e-22 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.588606123688032e-237 estimated_step_error 4.588606123688032e-237 Double H and LOOP opt_iter 4 NO POLE (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 6.122941998282746 $glob_desired_digits_correct 16 estimated_h 8.0e-09 estimated_answer 6.122941998282746 desired_abs_gbl_error 6.122941998282746e-16 range 1.9 estimated_steps 237499999.99999997 step_error 1.3243631366168775e-21 est_needed_step_err 1.3243631366168775e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.0793614425837528e-229 estimated_step_error 3.0793614425837528e-229 Double H and LOOP opt_iter 5 NO POLE (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 6.122941998282746 $glob_desired_digits_correct 16 estimated_h 1.6e-08 estimated_answer 6.122941998282746 desired_abs_gbl_error 6.122941998282746e-16 range 1.9 estimated_steps 118749999.99999999 step_error 1.8729323093105605e-21 est_needed_step_err 1.8729323093105605e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.066524481957627e-221 estimated_step_error 2.066524481957627e-221 Double H and LOOP opt_iter 6 NO POLE (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 6.122941998282746 $glob_desired_digits_correct 16 estimated_h 3.2e-08 estimated_answer 6.122941998282746 desired_abs_gbl_error 6.122941998282746e-16 range 1.9 estimated_steps 59374999.99999999 step_error 2.648726273233755e-21 est_needed_step_err 2.648726273233755e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.386821103299093e-213 estimated_step_error 1.386821103299093e-213 Double H and LOOP opt_iter 7 NO POLE (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 6.122941998282746 $glob_desired_digits_correct 16 estimated_h 6.4e-08 estimated_answer 6.122941998282746 desired_abs_gbl_error 6.122941998282746e-16 range 1.9 estimated_steps 29687499.999999996 step_error 3.745864618621121e-21 est_needed_step_err 3.745864618621121e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.306798870295882e-206 estimated_step_error 9.306798870295882e-206 Double H and LOOP opt_iter 8 NO POLE (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 6.122941998282746 $glob_desired_digits_correct 16 estimated_h 1.28e-07 estimated_answer 6.122941998282746 desired_abs_gbl_error 6.122941998282746e-16 range 1.9 estimated_steps 14843749.999999998 step_error 5.29745254646751e-21 est_needed_step_err 5.29745254646751e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.245686981766529e-198 estimated_step_error 6.245686981766529e-198 Double H and LOOP opt_iter 9 NO POLE (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 6.122941998282746 $glob_desired_digits_correct 16 estimated_h 2.56e-07 estimated_answer 6.122941998282746 desired_abs_gbl_error 6.122941998282746e-16 range 1.9 estimated_steps 7421874.999999999 step_error 7.491729237242242e-21 est_needed_step_err 7.491729237242242e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.191409562522877e-190 estimated_step_error 4.191409562522877e-190 Double H and LOOP opt_iter 10 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24999599384911617 Order of pole (three term test) 22.501694441577822 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 6.122941998282746 y[1] (numeric) 6.122941998282746 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 2.56e-07 NO POLE (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] 0.20000000000157453 y[1] (closed_form) 7.482681694382786 y[1] (numeric) 7.482681694361508 absolute error 2.12780904007559e-11 relative error 2.843645001862001e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 2.56e-07 NO POLE (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] 0.29999999999772803 y[1] (closed_form) 9.142727680266068 y[1] (numeric) 9.14272768031297 absolute error 4.690114963068481e-11 relative error 5.129885879890925e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 2.56e-07 NO POLE (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] 0.39999999998846053 y[1] (closed_form) 11.169703430103121 y[1] (numeric) 11.169703430338172 absolute error 2.3505108970311994e-10 relative error 2.104362852371183e-09% Desired digits 16 Estimated correct digits 11 Correct digits 11 h 2.56e-07 NO POLE (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! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = cosh ( 2.0 * x + 3.0 ) ; Iterations 1409483 Total Elapsed Time 3 Minutes 0 Seconds Elapsed Time(since restart) 3 Minutes 0 Seconds Expected Time Remaining 12 Minutes 47.82026618506882 Seconds Optimized Time Remaining 12 Minutes 47.82026618506882 Seconds Expected Total Time 15 Minutes 47.82026618506882 Seconds Time to Timeout 0.0 Seconds Percent Done 18.990942314885437%