##############ECHO OF PROBLEM################# ##############temp/expt_sin_cpostode.ode################# diff ( y , x , 1 ) = expt ( sin ( 0.2 * x + 0.3 ) , 2.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=0.2 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true #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(-2.5000000000000000000000000000000*sin(0.20000000000000000000000000000000*x+0.30000000000000000000000000000000)*cos(0.20000000000000000000000000000000*x+0.30000000000000000000000000000000)+0.50000000000000000000000000000000*x+0.75000000000000000000000000000000) 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 0.1 estimated_steps 100000.00000000001 step_error 7.905694150420948e-21 est_needed_step_err 7.905694150420948e-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 0.05350569829701002 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 0.1 estimated_steps 100000.00000000001 step_error 7.905694150420948e-21 est_needed_step_err 7.905694150420948e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.224391489014967e-229 estimated_step_error 4.224391489014967e-229 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 0.05350569829701002 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 50000.00000000001 step_error 1.1180339887498948e-20 est_needed_step_err 1.1180339887498948e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.9029788708715777e-218 estimated_step_error 2.9029788708715777e-218 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 0.05350569829701002 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 25000.000000000004 step_error 1.5811388300841896e-20 est_needed_step_err 1.5811388300841896e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9949107138109944e-207 estimated_step_error 1.9949107138109944e-207 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 0.05350569829701002 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 12500.000000000002 step_error 2.2360679774997895e-20 est_needed_step_err 2.2360679774997895e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3708905875902756e-196 estimated_step_error 1.3708905875902756e-196 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 0.05350569829701002 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 6250.000000000001 step_error 3.162277660168379e-20 est_needed_step_err 3.162277660168379e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.420666170094891e-186 estimated_step_error 9.420666170094891e-186 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 0.05350569829701002 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 3125.0000000000005 step_error 4.472135954999579e-20 est_needed_step_err 4.472135954999579e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.473801966584477e-175 estimated_step_error 6.473801966584477e-175 Double H and LOOP opt_iter 7 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6000279006041924 Order of pole (three term test) 1.1007208010899692 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) 0.05350569829701002 y[1] (numeric) 0.05350569829701002 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 3.2e-05 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] 0.11001600000000133 y[1] (closed_form) 0.05450280455948553 y[1] (numeric) 0.05450280455936239 absolute error 1.2313761121873767e-13 relative error 2.259289447836444e-10% Desired digits 16 Estimated correct digits 12 Correct digits 12 h 3.2e-05 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] 0.12000000000000266 y[1] (closed_form) 0.055508713965027434 y[1] (numeric) 0.05550871396478144 absolute error 2.4599072778741515e-13 relative error 4.431569571984653e-10% Desired digits 16 Estimated correct digits 12 Correct digits 12 h 3.2e-05 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] 0.130016000000004 y[1] (closed_form) 0.05652993866675293 y[1] (numeric) 0.05652993866638405 absolute error 3.688854777195161e-13 relative error 6.525488730743475e-10% Desired digits 16 Estimated correct digits 12 Correct digits 12 h 3.2e-05 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] 0.14000000000000531 y[1] (closed_form) 0.05756001681781853 y[1] (numeric) 0.05756001681732739 absolute error 4.911349105185536e-13 relative error 8.532570657041847e-10% Desired digits 16 Estimated correct digits 12 Correct digits 12 h 3.2e-05 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] 0.15001600000000664 y[1] (closed_form) 0.05860561511105222 y[1] (numeric) 0.05860561511043841 absolute error 6.138145547396334e-13 relative error 1.0473647509313084e-09% Desired digits 16 Estimated correct digits 12 Correct digits 11 h 3.2e-05 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] 0.16000000000000797 y[1] (closed_form) 0.059660115569287964 y[1] (numeric) 0.059660115568552 absolute error 7.359668430240163e-13 relative error 1.2335994256821047e-09% Desired digits 16 Estimated correct digits 12 Correct digits 11 h 3.2e-05 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] 0.1700160000000093 y[1] (closed_form) 0.06073034104638664 y[1] (numeric) 0.06073034104552828 absolute error 8.58355053701132e-13 relative error 1.4133875076471396e-09% Desired digits 16 Estimated correct digits 12 Correct digits 11 h 3.2e-05 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] 0.18000000000001062 y[1] (closed_form) 0.061809515810418714 y[1] (numeric) 0.06180951580943883 absolute error 9.798828415341632e-13 relative error 1.5853268363072866e-09% Desired digits 16 Estimated correct digits 12 Correct digits 11 h 3.2e-05 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] 0.19001600000001195 y[1] (closed_form) 0.06290462048760748 y[1] (numeric) 0.06290462048650568 absolute error 1.1017992074258132e-12 relative error 1.751539392313595e-09% Desired digits 16 Estimated correct digits 12 Correct digits 11 h 3.2e-05 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 ) = expt ( sin ( 0.2 * x + 0.3 ) , 2.0 ) ; Iterations 3125 Total Elapsed Time 2 Seconds Elapsed Time(since restart) 2 Seconds Time to Timeout 2 Minutes 58.0 Seconds Percent Done 100.03200000001328%