##############ECHO OF PROBLEM################# ##############temp/expt_sin_sinpostode.ode################# diff ( y , x , 1 ) = expt ( sin ( 0.1 * x ) , sin ( 0.2 * x ) ) ; ! #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=5.0 $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 #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(0.0) 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 4.9 estimated_steps 4900000.000000001 step_error 1.5058465048420852e-21 est_needed_step_err 1.5058465048420852e-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 0.0 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 4.9 estimated_steps 4900000.000000001 step_error 1.5058465048420852e-21 est_needed_step_err 1.5058465048420852e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.0761929802770158e-142 estimated_step_error 3.0761929802770158e-142 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 0.0 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 4.9 estimated_steps 2450000.0000000005 step_error 2.1295885499997994e-21 est_needed_step_err 2.1295885499997994e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.0643889904506183e-134 estimated_step_error 2.0643889904506183e-134 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 0.0 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 4.9 estimated_steps 1225000.0000000002 step_error 3.0116930096841704e-21 est_needed_step_err 3.0116930096841704e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3853756883232302e-126 estimated_step_error 1.3853756883232302e-126 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 0.0 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 4.9 estimated_steps 612500.0000000001 step_error 4.259177099999599e-21 est_needed_step_err 4.259177099999599e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.296933625119876e-119 estimated_step_error 9.296933625119876e-119 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 0.0 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 4.9 estimated_steps 306250.00000000006 step_error 6.023386019368341e-21 est_needed_step_err 6.023386019368341e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.23884477243261e-111 estimated_step_error 6.23884477243261e-111 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 0.0 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 4.9 estimated_steps 153125.00000000003 step_error 8.518354199999198e-21 est_needed_step_err 8.518354199999198e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.18652023043387e-103 estimated_step_error 4.18652023043387e-103 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 0.0 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 4.9 estimated_steps 76562.50000000001 step_error 1.2046772038736681e-20 est_needed_step_err 1.2046772038736681e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.8091267904108614e-95 estimated_step_error 2.8091267904108614e-95 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 0.0 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 4.9 estimated_steps 38281.25000000001 step_error 1.7036708399998395e-20 est_needed_step_err 1.7036708399998395e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8846372716930343e-87 estimated_step_error 1.8846372716930343e-87 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 0.0 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 4.9 estimated_steps 19140.625000000004 step_error 2.4093544077473363e-20 est_needed_step_err 2.4093544077473363e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2640401329350816e-79 estimated_step_error 1.2640401329350816e-79 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 0.0 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 4.9 estimated_steps 9570.312500000002 step_error 3.407341679999679e-20 est_needed_step_err 3.407341679999679e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.473202273554506e-72 estimated_step_error 8.473202273554506e-72 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 0.0 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 4.9 estimated_steps 4785.156250000001 step_error 4.8187088154946726e-20 est_needed_step_err 4.8187088154946726e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.673392116749606e-64 estimated_step_error 5.673392116749606e-64 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 0.0 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 4.9 estimated_steps 2392.5781250000005 step_error 6.814683359999358e-20 est_needed_step_err 6.814683359999358e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.7901822726025056e-56 estimated_step_error 3.7901822726025056e-56 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 0.0 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 4.9 estimated_steps 1196.2890625000002 step_error 9.637417630989345e-20 est_needed_step_err 9.637417630989345e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.520817456655616e-48 estimated_step_error 2.520817456655616e-48 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 0.0 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 4.9 estimated_steps 598.1445312500001 step_error 1.3629366719998716e-19 est_needed_step_err 1.3629366719998716e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6619876615495682e-40 estimated_step_error 1.6619876615495682e-40 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 0.0 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 4.9 estimated_steps 299.07226562500006 step_error 1.927483526197869e-19 est_needed_step_err 1.927483526197869e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0774838323048502e-32 estimated_step_error 1.0774838323048502e-32 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 0.0 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 4.9 estimated_steps 149.53613281250003 step_error 2.7258733439997433e-19 est_needed_step_err 2.7258733439997433e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.768788302254761e-25 estimated_step_error 6.768788302254761e-25 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 0.0 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 4.9 estimated_steps 74.76806640625001 step_error 3.854967052395738e-19 est_needed_step_err 3.854967052395738e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.003073796656913e-17 estimated_step_error 4.003073796656913e-17 Found H for OPTIMAL START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 0.0 y[1] (numeric) 0.0 absolute error 0.0 relative error -1.0% Desired digits 16 Estimated correct digits -16 Correct digits -16 h 0.032768 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] 0.19830399999999998 y[1] (closed_form) 0.0 y[1] (numeric) 0.08725449375418594 absolute error 0.08725449375418594 relative error -1.0% Desired digits 16 Estimated correct digits 12 Correct digits -16 h 0.032768 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] 0.329376 y[1] (closed_form) 0.0 y[1] (numeric) 0.19602015013029225 absolute error 0.19602015013029225 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 0.42768000000000006 y[1] (closed_form) 0.0 y[1] (numeric) 0.27307326663429105 absolute error 0.27307326663429105 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 0.5259840000000001 y[1] (closed_form) 0.0 y[1] (numeric) 0.34691039682747493 absolute error 0.34691039682747493 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 0.6242880000000002 y[1] (closed_form) 0.0 y[1] (numeric) 0.41796712676133235 absolute error 0.41796712676133235 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 0.7225920000000002 y[1] (closed_form) 0.0 y[1] (numeric) 0.4865891220115807 absolute error 0.4865891220115807 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 0.8208960000000003 y[1] (closed_form) 0.0 y[1] (numeric) 0.553059417352412 absolute error 0.553059417352412 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 0.9192000000000004 y[1] (closed_form) 0.0 y[1] (numeric) 0.6176151169076496 absolute error 0.6176151169076496 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 1.0175040000000004 y[1] (closed_form) 0.0 y[1] (numeric) 0.6804583653458116 absolute error 0.6804583653458116 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 1.1158080000000001 y[1] (closed_form) 0.0 y[1] (numeric) 0.7417639377663704 absolute error 0.7417639377663704 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 1.2141119999999999 y[1] (closed_form) 0.0 y[1] (numeric) 0.8016847017715958 absolute error 0.8016847017715958 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 1.3124159999999996 y[1] (closed_form) 0.0 y[1] (numeric) 0.8603556727727687 absolute error 0.8603556727727687 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 1.4107199999999993 y[1] (closed_form) 0.0 y[1] (numeric) 0.9178971019814769 absolute error 0.9178971019814769 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 1.509023999999999 y[1] (closed_form) 0.0 y[1] (numeric) 0.9744168775998059 absolute error 0.9744168775998059 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 1.6073279999999988 y[1] (closed_form) 0.0 y[1] (numeric) 1.030012425195265 absolute error 1.030012425195265 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 1.7056319999999985 y[1] (closed_form) 0.0 y[1] (numeric) 1.0847722345462836 absolute error 1.0847722345462836 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 1.8039359999999982 y[1] (closed_form) 0.0 y[1] (numeric) 1.1387771024478275 absolute error 1.1387771024478275 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 1.902239999999998 y[1] (closed_form) 0.0 y[1] (numeric) 1.1921011558670445 absolute error 1.1921011558670445 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 2.000543999999998 y[1] (closed_form) 0.0 y[1] (numeric) 1.244812702720825 absolute error 1.244812702720825 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 2.0988479999999976 y[1] (closed_form) 0.0 y[1] (numeric) 1.2969749455982338 absolute error 1.2969749455982338 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 2.1971519999999973 y[1] (closed_form) 0.0 y[1] (numeric) 1.3486465852377998 absolute error 1.3486465852377998 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 2.328223999999997 y[1] (closed_form) 0.0 y[1] (numeric) 1.4168729908641595 absolute error 1.4168729908641595 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 2.4265279999999967 y[1] (closed_form) 0.0 y[1] (numeric) 1.4676065853762241 absolute error 1.4676065853762241 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 2.5248319999999964 y[1] (closed_form) 0.0 y[1] (numeric) 1.5180188044933647 absolute error 1.5180188044933647 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 2.623135999999996 y[1] (closed_form) 0.0 y[1] (numeric) 1.5681539246714347 absolute error 1.5681539246714347 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 2.721439999999996 y[1] (closed_form) 0.0 y[1] (numeric) 1.6180537560027055 absolute error 1.6180537560027055 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 2.8197439999999956 y[1] (closed_form) 0.0 y[1] (numeric) 1.6677578814007306 absolute error 1.6677578814007306 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 2.9180479999999953 y[1] (closed_form) 0.0 y[1] (numeric) 1.717303866637573 absolute error 1.717303866637573 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 3.016351999999995 y[1] (closed_form) 0.0 y[1] (numeric) 1.766727445379194 absolute error 1.766727445379194 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 3.1146559999999948 y[1] (closed_form) 0.0 y[1] (numeric) 1.81606268266011 absolute error 1.81606268266011 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 3.2129599999999945 y[1] (closed_form) 0.0 y[1] (numeric) 1.8653421196708186 absolute error 1.8653421196708186 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 3.311263999999994 y[1] (closed_form) 0.0 y[1] (numeric) 1.9145969022710445 absolute error 1.9145969022710445 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 3.409567999999994 y[1] (closed_form) 0.0 y[1] (numeric) 1.9638568952659257 absolute error 1.9638568952659257 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 3.5078719999999937 y[1] (closed_form) 0.0 y[1] (numeric) 2.013150784173429 absolute error 2.013150784173429 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 3.6061759999999934 y[1] (closed_form) 0.0 y[1] (numeric) 2.062506165956155 absolute error 2.062506165956155 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 3.704479999999993 y[1] (closed_form) 0.0 y[1] (numeric) 2.1119496299788327 absolute error 2.1119496299788327 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 3.802783999999993 y[1] (closed_form) 0.0 y[1] (numeric) 2.161506830275984 absolute error 2.161506830275984 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 3.9010879999999926 y[1] (closed_form) 0.0 y[1] (numeric) 2.2112025500660253 absolute error 2.2112025500660253 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 3.9993919999999923 y[1] (closed_form) 0.0 y[1] (numeric) 2.2610607593233003 absolute error 2.2610607593233003 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 4.097695999999992 y[1] (closed_form) 0.0 y[1] (numeric) 2.3111046661140975 absolute error 2.3111046661140975 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 4.228767999999992 y[1] (closed_form) 0.0 y[1] (numeric) 2.3781575148267615 absolute error 2.3781575148267615 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 4.327071999999991 y[1] (closed_form) 0.0 y[1] (numeric) 2.428721021913697 absolute error 2.428721021913697 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.032768 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] 4.425375999999991 y[1] (closed_form) 0.0 y[1] (numeric) 2.4795426339694027 absolute error 2.4795426339694027 relative error -1.0% Desired digits 16 Estimated correct digits 12 Correct digits -16 h 0.032768 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] 4.523679999999991 y[1] (closed_form) 0.0 y[1] (numeric) 2.530642723982006 absolute error 2.530642723982006 relative error -1.0% Desired digits 16 Estimated correct digits 12 Correct digits -16 h 0.032768 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] 4.6219839999999905 y[1] (closed_form) 0.0 y[1] (numeric) 2.58204109387103 absolute error 2.58204109387103 relative error -1.0% Desired digits 16 Estimated correct digits 12 Correct digits -16 h 0.032768 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] 4.72028799999999 y[1] (closed_form) 0.0 y[1] (numeric) 2.6337569979564384 absolute error 2.6337569979564384 relative error -1.0% Desired digits 16 Estimated correct digits 12 Correct digits -16 h 0.032768 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] 4.81859199999999 y[1] (closed_form) 0.0 y[1] (numeric) 2.685809163336385 absolute error 2.685809163336385 relative error -1.0% Desired digits 16 Estimated correct digits 12 Correct digits -16 h 0.032768 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] 4.91689599999999 y[1] (closed_form) 0.0 y[1] (numeric) 2.738215807430312 absolute error 2.738215807430312 relative error -1.0% Desired digits 16 Estimated correct digits 12 Correct digits -16 h 0.032768 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 ( 0.1 * x ) , sin ( 0.2 * x ) ) ; Iterations 150 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.97893877550999%