##############ECHO OF PROBLEM################# ##############temp/cospostode.ode################# diff ( y , x , 1 ) = cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.0 x_end=5.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=false # 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(1.0 + sin(x)) 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 5.0 estimated_steps 5000000.0 step_error 1.1180339887498947e-21 est_needed_step_err 1.1180339887498947e-21 opt_iter 1 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 5.0 estimated_steps 5000000.0 step_error 1.1180339887498947e-21 est_needed_step_err 1.1180339887498947e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.6327300895765305e-266 estimated_step_error 3.6327300895765305e-266 Double H and LOOP opt_iter 2 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 5.0 estimated_steps 2500000.0 step_error 1.5811388300841896e-21 est_needed_step_err 1.5811388300841896e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.992786217576429e-255 estimated_step_error 4.992786217576429e-255 Double H and LOOP opt_iter 3 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 5.0 estimated_steps 1250000.0 step_error 2.2360679774997895e-21 est_needed_step_err 2.2360679774997895e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.862033126531284e-244 estimated_step_error 6.862033126531284e-244 Double H and LOOP opt_iter 4 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 5.0 estimated_steps 625000.0 step_error 3.1622776601683792e-21 est_needed_step_err 3.1622776601683792e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.431106516006481e-233 estimated_step_error 9.431106516006481e-233 Double H and LOOP opt_iter 5 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 5.0 estimated_steps 312500.0 step_error 4.472135954999579e-21 est_needed_step_err 4.472135954999579e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2962014096428488e-221 estimated_step_error 1.2962014096428488e-221 Double H and LOOP opt_iter 6 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 5.0 estimated_steps 156250.0 step_error 6.3245553203367584e-21 est_needed_step_err 6.3245553203367584e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.7814856523022124e-210 estimated_step_error 1.7814856523022124e-210 Double H and LOOP opt_iter 7 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 5.0 estimated_steps 78125.0 step_error 8.944271909999158e-21 est_needed_step_err 8.944271909999158e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.4484552367767244e-199 estimated_step_error 2.4484552367767244e-199 Double H and LOOP opt_iter 8 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 5.0 estimated_steps 39062.5 step_error 1.2649110640673517e-20 est_needed_step_err 1.2649110640673517e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.365131253649334e-188 estimated_step_error 3.365131253649334e-188 Double H and LOOP opt_iter 9 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 5.0 estimated_steps 19531.25 step_error 1.7888543819998316e-20 est_needed_step_err 1.7888543819998316e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.625001177936491e-177 estimated_step_error 4.625001177936491e-177 Double H and LOOP opt_iter 10 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 5.0 estimated_steps 9765.625 step_error 2.5298221281347034e-20 est_needed_step_err 2.5298221281347034e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.356553216812763e-166 estimated_step_error 6.356553216812763e-166 Double H and LOOP opt_iter 11 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 5.0 estimated_steps 4882.8125 step_error 3.577708763999663e-20 est_needed_step_err 3.577708763999663e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.736380216919211e-155 estimated_step_error 8.736380216919211e-155 Double H and LOOP opt_iter 12 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 5.0 estimated_steps 2441.40625 step_error 5.059644256269407e-20 est_needed_step_err 5.059644256269407e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2007189535096922e-143 estimated_step_error 1.2007189535096922e-143 Double H and LOOP opt_iter 13 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 5.0 estimated_steps 1220.703125 step_error 7.155417527999326e-20 est_needed_step_err 7.155417527999326e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6502555603407997e-132 estimated_step_error 1.6502555603407997e-132 Double H and LOOP opt_iter 14 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 5.0 estimated_steps 610.3515625 step_error 1.0119288512538813e-19 est_needed_step_err 1.0119288512538813e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.2680939524886466e-121 estimated_step_error 2.2680939524886466e-121 Double H and LOOP opt_iter 15 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.016384 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 5.0 estimated_steps 305.17578125 step_error 1.4310835055998653e-19 est_needed_step_err 1.4310835055998653e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.1172444861943306e-110 estimated_step_error 3.1172444861943306e-110 Double H and LOOP opt_iter 16 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.032768 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 5.0 estimated_steps 152.587890625 step_error 2.0238577025077627e-19 est_needed_step_err 2.0238577025077627e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.284307616974801e-99 estimated_step_error 4.284307616974801e-99 Double H and LOOP opt_iter 17 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.065536 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 5.0 estimated_steps 76.2939453125 step_error 2.8621670111997305e-19 est_needed_step_err 2.8621670111997305e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.88830435263384e-88 estimated_step_error 5.88830435263384e-88 Double H and LOOP opt_iter 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (closed_form) 1.0 y[1] (numeric) 1.0 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 1.0998334166468282 y[1] (numeric) 1.0998334166468282 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.1 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09933466539753069 Order of pole (three term test) 32.99003328892063 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19933466539753078 y[1] (closed_form) 1.1980172146637207 y[1] (numeric) 1.198017214663721 absolute error 2.220446049250313e-16 relative error 1.8534341761304194e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.00993346653975307 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.19409618520103575 Order of pole (three term test) 32.96078918269682 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3086027973348146 y[1] (closed_form) 1.3037277361104649 y[1] (numeric) 1.3037277361104649 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.00993346653975307 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.28937929431807075 Order of pole (three term test) 32.907749462317206 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4079374627323454 y[1] (closed_form) 1.3967168855958874 y[1] (numeric) 1.3967168855958876 absolute error 2.220446049250313e-16 relative error 1.589761011805191e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.00993346653975307 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3641627018554369 Order of pole (three term test) 32.842615712683106 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5072721281298761 y[1] (closed_form) 1.4857946983114445 y[1] (numeric) 1.4857946983114447 absolute error 2.220446049250313e-16 relative error 1.4944501092740304e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.00993346653975307 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.42462000203810024 Order of pole (three term test) 32.76400351109249 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6066067935274063 y[1] (closed_form) 1.570082932526311 y[1] (numeric) 1.5700829325263115 absolute error 4.440892098500626e-16 relative error 2.8284442856499918e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.00993346653975307 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.46837281353162064 Order of pole (three term test) 32.6750054500422 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7059414589249365 y[1] (closed_form) 1.6487505682317052 y[1] (numeric) 1.6487505682317063 absolute error 1.1102230246251565e-15 relative error 6.733723378278362e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.00993346653975307 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4936999071400034 Order of pole (three term test) 32.579122700219045 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8052761243224668 y[1] (closed_form) 1.7210220003870942 y[1] (numeric) 1.7210220003870955 absolute error 1.3322676295501878e-15 relative error 7.741142351756879e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.00993346653975307 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49960491871017126 Order of pole (three term test) 32.48012727495779 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.904610789719997 y[1] (closed_form) 1.7861846858155581 y[1] (numeric) 1.7861846858155594 absolute error 1.3322676295501878e-15 relative error 7.458733915535083e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.00993346653975307 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.48585554595181846 Order of pole (three term test) 32.38191363978909 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0039454551175273 y[1] (closed_form) 1.8435961683555537 y[1] (numeric) 1.843596168355555 absolute error 1.3322676295501878e-15 relative error 7.226461263143873e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.00993346653975307 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.45299268717548735 Order of pole (three term test) 32.28834550473584 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1032801205150575 y[1] (closed_form) 1.8926904130062412 y[1] (numeric) 1.892690413006243 absolute error 1.7763568394002505e-15 relative error 9.385353395322517e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.00993346653975307 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4023091624322516 Order of pole (three term test) 32.20310382652675 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2026147859125877 y[1] (closed_form) 1.9329833866163662 y[1] (numeric) 1.9329833866163684 absolute error 2.220446049250313e-15 relative error 1.1487145024754415e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.00993346653975307 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.33579885416225913 Order of pole (three term test) 32.12954200029785 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.301949451310118 y[1] (closed_form) 1.9640778300952002 y[1] (numeric) 1.9640778300952026 absolute error 2.4424906541753444e-15 relative error 1.2435813982264415e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.00993346653975307 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2560782681515658 Order of pole (three term test) 32.07055393751893 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4012841167076482 y[1] (closed_form) 1.9856671750950543 y[1] (numeric) 1.9856671750950572 absolute error 2.886579864025407e-15 relative error 1.4537078017050998e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.00993346653975307 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.16628360057773117 Order of pole (three term test) 32.028460219940136 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] 1.505055086899326 y[1] (closed_form) 1.9978398228643586 y[1] (numeric) 1.9978398228643612 absolute error 2.6645352591003757e-15 relative error 1.3337081524784892e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.007275776712777524 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.06555198504945058 Order of pole (three term test) 32.00431568790602 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] 1.600101216846044 y[1] (closed_form) 1.9995706424377162 y[1] (numeric) 1.999570642437718 absolute error 1.7763568394002505e-15 relative error 8.883691337029527e-14% Desired digits 16 Estimated correct digits 12 Correct digits 16 h 0.00018315543846663006 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] 1.7001040862488004 y[1] (closed_form) 1.991651394140581 y[1] (numeric) 1.9916513941405787 absolute error 2.220446049250313e-15 relative error 1.1148768583612794e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.00018315543846663006 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] 1.8001069556515568 y[1] (closed_form) 1.9738233247599979 y[1] (numeric) 1.9738233247599901 absolute error 7.771561172376096e-15 relative error 3.937313474254875e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.00018315543846663006 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.22136860849656576 Order of pole (three term test) 32.052047824980924 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9001098250543131 y[1] (closed_form) 1.946264576686327 y[1] (numeric) 1.9462645766863083 absolute error 1.865174681370263e-14 relative error 9.583356259537302e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.00018315543846663006 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3059978633565651 Order of pole (three term test) 32.107493513761 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0001126944570697 y[1] (closed_form) 1.9092505236099178 y[1] (numeric) 1.9092505236098907 absolute error 2.708944180085382e-14 relative error 1.4188521341680411e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.00018315543846663006 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] 2.1001155638599474 y[1] (closed_form) 1.8631510189203937 y[1] (numeric) 1.863151018920414 absolute error 2.020605904817785e-14 relative error 1.084509996397731e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.00018315543846663006 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] 2.200118433262825 y[1] (closed_form) 1.8084267000420982 y[1] (numeric) 1.8084267000421703 absolute error 7.216449660063518e-14 relative error 3.990457373746764e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.00018315543846663006 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] 2.3001213026657026 y[1] (closed_form) 1.7456243856331648 y[1] (numeric) 1.7456243856333 absolute error 1.3522516439934407e-13 relative error 7.746521274122544e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.00018315543846663006 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] 2.40012417206858 y[1] (closed_form) 1.6753716116409865 y[1] (numeric) 1.6753716116411923 absolute error 2.0583534876550402e-13 relative error 1.2285951805276992e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.00018315543846663006 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] 2.500127041471458 y[1] (closed_form) 1.598370360810931 y[1] (numeric) 1.5983703608112128 absolute error 2.8177460364986473e-13 relative error 1.7628868162126502e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.00018315543846663006 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] 2.6001299108743354 y[1] (closed_form) 1.515390048304603 y[1] (numeric) 1.5153900483049654 absolute error 3.623767952376511e-13 relative error 2.391310380077216e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.00018315543846663006 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.44164631664631665 Order of pole (three term test) 32.735347985347985 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.700132780277213 y[1] (closed_form) 1.4272598335170628 y[1] (numeric) 1.4272598335175124 absolute error 4.496403249731884e-13 relative error 3.150374685912528e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.00018315543846663006 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] 2.8001356496800907 y[1] (closed_form) 1.33486033491518 y[1] (numeric) 1.3348603349157193 absolute error 5.39346345362901e-13 relative error 4.040470236889407e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.00018315543846663006 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] 2.9001385190829683 y[1] (closed_form) 1.2391148306844728 y[1] (numeric) 1.2391148306851056 absolute error 6.328271240363392e-13 relative error 5.107090225744234e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.00018315543846663006 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] 3.000141388485846 y[1] (closed_form) 1.1409800331096962 y[1] (numeric) 1.1409800331104254 absolute error 7.291944825738028e-13 relative error 6.390948670560096e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.00018315543846663006 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] 3.1001442578887235 y[1] (closed_form) 1.0414365288738088 y[1] (numeric) 1.041436528874634 absolute error 8.251177519014163e-13 relative error 7.922880838390452e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.00018315543846663006 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] 3.200147127291601 y[1] (closed_form) 0.941478980798164 y[1] (numeric) 0.9414789807990865 absolute error 9.22595333463505e-13 relative error 9.799425715073854e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.00018315543846663006 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] 3.3001499966944787 y[1] (closed_form) 0.8421061889305169 y[1] (numeric) 0.8421061889315354 absolute error 1.0185186027911186e-12 relative error 1.2094895111561253e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.00018315543846663006 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.15592875318066157 Order of pole (three term test) 32.9723155216285 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.4001528660973563 y[1] (closed_form) 0.7443111102928612 y[1] (numeric) 0.7443111102939742 absolute error 1.1129985821867194e-12 relative error 1.4953405461713345e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.00018315543846663006 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] 3.500155735500234 y[1] (closed_form) 0.6490709370141956 y[1] (numeric) 0.6490709370154012 absolute error 1.2055911824404575e-12 relative error 1.8574105135354264e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.00018315543846663006 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] 3.6001586049031116 y[1] (closed_form) 0.5573373319899216 y[1] (numeric) 0.5573373319912172 absolute error 1.2955192474350952e-12 relative error 2.3244795800948107e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.00018315543846663006 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] 3.700161474305989 y[1] (closed_form) 0.470026919635533 y[1] (numeric) 0.4700269196369127 absolute error 1.379674152701682e-12 relative error 2.9353087984226634e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.00018315543846663006 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] 3.800164343708867 y[1] (closed_form) 0.38801212675328656 y[1] (numeric) 0.38801212675474583 absolute error 1.4592771435673058e-12 relative error 3.7609060205872684e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.00018315543846663006 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] 3.8999840576732776 y[1] (closed_form) 0.3122454139533981 y[1] (numeric) 0.31224541395493105 absolute error 1.5329404412511849e-12 relative error 4.909408986483858e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.00018315543846663006 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] 3.999986927076155 y[1] (closed_form) 0.24320604979001792 y[1] (numeric) 0.24320604979161825 absolute error 1.6003309788459319e-12 relative error 6.580144614937187e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.00018315543846663006 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] 4.09998979647879 y[1] (closed_form) 0.1817287542065158 y[1] (numeric) 0.18172875420802725 absolute error 1.5114576257246881e-12 relative error 8.317107726425472e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.00018315543846663006 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] 4.1999926658814255 y[1] (closed_form) 0.12842782324084878 y[1] (numeric) 0.12842782324228275 absolute error 1.4339640586058522e-12 relative error 1.1165524902782546e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.00018315543846663006 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] 4.299995535284061 y[1] (closed_form) 0.08383585271412841 y[1] (numeric) 0.08383585271549775 absolute error 1.3693352007848603e-12 relative error 1.6333527440272502e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.00018315543846663006 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] 4.399998404686696 y[1] (closed_form) 0.04839841640391129 y[1] (numeric) 0.04839841640522933 absolute error 1.3180359581532741e-12 relative error 2.723303893155392e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.00018315543846663006 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] 4.500001274089331 y[1] (closed_form) 0.02246961376301726 y[1] (numeric) 0.022469613764297736 absolute error 1.2804757254514243e-12 relative error 5.698699314355636e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.00018315543846663006 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] 4.600004143491966 y[1] (closed_form) 0.006308531671971318 y[1] (numeric) 0.006308531673228393 absolute error 1.2570751731222352e-12 relative error 1.9926588919373986e-08% Desired digits 16 Estimated correct digits 9 Correct digits 10 h 0.00018315543846663006 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] 4.700007012894601 y[1] (closed_form) 7.665558009650741e-05 y[1] (numeric) 7.665558134451521e-05 absolute error 1.2480078006183587e-12 relative error 1.6280716929506616e-06% Desired digits 16 Estimated correct digits 7 Correct digits 8 h 0.00018315543846663006 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] 4.800009882297236 y[1] (closed_form) 0.0038362559037641297 y[1] (numeric) 0.0038362559050176726 absolute error 1.2535428424442774e-12 relative error 3.26762049740817e-08% Desired digits 16 Estimated correct digits 9 Correct digits 10 h 0.00018315543846663006 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] 4.9000127516998715 y[1] (closed_form) 0.017549765805300876 y[1] (numeric) 0.017549765806574292 absolute error 1.2734154009041987e-12 relative error 7.256025037778942e-09% Desired digits 16 Estimated correct digits 9 Correct digits 11 h 0.00018315543846663006 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! diff ( y , x , 1 ) = cos ( x ) ; Iterations 18910 Total Elapsed Time 3 Seconds Elapsed Time(since restart) 3 Seconds Time to Timeout 2 Minutes 57.0 Seconds Percent Done 100.00397553081946%