##############ECHO OF PROBLEM################# ##############temp/diff0postode.ode################# diff ( y , x , 1 ) = y ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-5.0 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(exp(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 10.0 estimated_steps 10000000.0 step_error 1.0540925533894597e-21 est_needed_step_err 1.0540925533894597e-21 opt_iter 1 min_size 0.006737946999085467 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 10.0 estimated_steps 10000000.0 step_error 1.0540925533894597e-21 est_needed_step_err 1.0540925533894597e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6707388510135127e-185 estimated_step_error 1.6707388510135127e-185 Double H and LOOP opt_iter 2 min_size 0.006737946999085467 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 10.0 estimated_steps 5000000.0 step_error 1.4907119849998596e-21 est_needed_step_err 1.4907119849998596e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1212138840850413e-177 estimated_step_error 1.1212138840850413e-177 Double H and LOOP opt_iter 3 min_size 0.006737946999085467 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 10.0 estimated_steps 2500000.0 step_error 2.1081851067789195e-21 est_needed_step_err 2.1081851067789195e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.524339284876721e-170 estimated_step_error 7.524339284876721e-170 Double H and LOOP opt_iter 4 min_size 0.006737946999085467 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 10.0 estimated_steps 1250000.0 step_error 2.9814239699997193e-21 est_needed_step_err 2.9814239699997193e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.049498991623479e-162 estimated_step_error 5.049498991623479e-162 Double H and LOOP opt_iter 5 min_size 0.006737946999085467 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 10.0 estimated_steps 625000.0 step_error 4.216370213557839e-21 est_needed_step_err 4.216370213557839e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.3886619129940254e-154 estimated_step_error 3.3886619129940254e-154 Double H and LOOP opt_iter 6 min_size 0.006737946999085467 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 10.0 estimated_steps 312500.0 step_error 5.9628479399994385e-21 est_needed_step_err 5.9628479399994385e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.274093188416526e-146 estimated_step_error 2.274093188416526e-146 Double H and LOOP opt_iter 7 min_size 0.006737946999085467 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 10.0 estimated_steps 156250.0 step_error 8.432740427115678e-21 est_needed_step_err 8.432740427115678e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.5261190094150094e-138 estimated_step_error 1.5261190094150094e-138 Double H and LOOP opt_iter 8 min_size 0.006737946999085467 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 10.0 estimated_steps 78125.0 step_error 1.1925695879998877e-20 est_needed_step_err 1.1925695879998877e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.024162344329788e-130 estimated_step_error 1.024162344329788e-130 Double H and LOOP opt_iter 9 min_size 0.006737946999085467 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 10.0 estimated_steps 39062.5 step_error 1.6865480854231356e-20 est_needed_step_err 1.6865480854231356e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.873053439671597e-123 estimated_step_error 6.873053439671597e-123 Double H and LOOP opt_iter 10 min_size 0.006737946999085467 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 10.0 estimated_steps 19531.25 step_error 2.3851391759997754e-20 est_needed_step_err 2.3851391759997754e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.612449951998493e-115 estimated_step_error 4.612449951998493e-115 Double H and LOOP opt_iter 11 min_size 0.006737946999085467 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 10.0 estimated_steps 9765.625 step_error 3.373096170846271e-20 est_needed_step_err 3.373096170846271e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.095392114506204e-107 estimated_step_error 3.095392114506204e-107 Double H and LOOP opt_iter 12 min_size 0.006737946999085467 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 10.0 estimated_steps 4882.8125 step_error 4.770278351999551e-20 est_needed_step_err 4.770278351999551e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.0773218772354795e-99 estimated_step_error 2.0773218772354795e-99 Double H and LOOP opt_iter 13 min_size 0.006737946999085467 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 10.0 estimated_steps 2441.40625 step_error 6.746192341692542e-20 est_needed_step_err 6.746192341692542e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3941199885180883e-91 estimated_step_error 1.3941199885180883e-91 Double H and LOOP opt_iter 14 min_size 0.006737946999085467 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 10.0 estimated_steps 1220.703125 step_error 9.540556703999102e-20 est_needed_step_err 9.540556703999102e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.356490626122458e-84 estimated_step_error 9.356490626122458e-84 Double H and LOOP opt_iter 15 min_size 0.006737946999085467 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 10.0 estimated_steps 610.3515625 step_error 1.3492384683385085e-19 est_needed_step_err 1.3492384683385085e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.279987395861066e-76 estimated_step_error 6.279987395861066e-76 Double H and LOOP opt_iter 16 min_size 0.006737946999085467 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 10.0 estimated_steps 305.17578125 step_error 1.9081113407998203e-19 est_needed_step_err 1.9081113407998203e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.215707624202576e-68 estimated_step_error 4.215707624202576e-68 Double H and LOOP opt_iter 17 min_size 0.006737946999085467 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 10.0 estimated_steps 152.587890625 step_error 2.698476936677017e-19 est_needed_step_err 2.698476936677017e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.83083221819058e-60 estimated_step_error 2.83083221819058e-60 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] -5.0 y[1] (closed_form) 0.006737946999085467 y[1] (numeric) 0.006737946999085467 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] -4.9 y[1] (closed_form) 0.007446583070924338 y[1] (numeric) 0.007446583070924341 absolute error 2.6020852139652106e-18 relative error 3.4943345010481643e-14% 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] -4.800000000000001 y[1] (closed_form) 0.008229747049020023 y[1] (numeric) 0.008229747049020028 absolute error 5.204170427930421e-18 relative error 6.323609215364792e-14% 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] -4.700000000000001 y[1] (closed_form) 0.009095277101695807 y[1] (numeric) 0.009095277101695817 absolute error 1.0408340855860843e-17 relative error 1.1443676470198161e-13% Desired digits 16 Estimated correct digits 14 Correct digits 15 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] -4.600000000000001 y[1] (closed_form) 0.010051835744633567 y[1] (numeric) 0.010051835744633583 absolute error 1.5612511283791264e-17 relative error 1.5532000005199456e-13% Desired digits 16 Estimated correct digits 14 Correct digits 15 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] -4.500000000000002 y[1] (closed_form) 0.011108996538242287 y[1] (numeric) 0.011108996538242308 absolute error 2.0816681711721685e-17 relative error 1.8738579708852253e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -4.400000000000002 y[1] (closed_form) 0.012277339903068415 y[1] (numeric) 0.012277339903068443 absolute error 2.7755575615628914e-17 relative error 2.260715744189187e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -4.3000000000000025 y[1] (closed_form) 0.013568559012200897 y[1] (numeric) 0.013568559012200934 absolute error 3.642919299551295e-17 relative error 2.6848240084120715e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -4.200000000000003 y[1] (closed_form) 0.014995576820477663 y[1] (numeric) 0.014995576820477708 absolute error 4.5102810375396984e-17 relative error 3.007740943569805e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -4.100000000000003 y[1] (closed_form) 0.016572675401761196 y[1] (numeric) 0.01657267540176125 absolute error 5.551115123125783e-17 relative error 3.3495588301547617e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -4.0000000000000036 y[1] (closed_form) 0.018315638888734116 y[1] (numeric) 0.018315638888734186 absolute error 6.938893903907228e-17 relative error 3.7885077042959815e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -3.9000000000000035 y[1] (closed_form) 0.02024191144580432 y[1] (numeric) 0.020241911445804395 absolute error 7.632783294297951e-17 relative error 3.7707818823009676e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -3.8000000000000034 y[1] (closed_form) 0.02237077185616552 y[1] (numeric) 0.0223707718561656 absolute error 7.979727989493313e-17 relative error 3.567032930646982e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -3.7000000000000033 y[1] (closed_form) 0.02472352647033931 y[1] (numeric) 0.0247235264703394 absolute error 9.020562075079397e-17 relative error 3.6485741974961864e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -3.600000000000003 y[1] (closed_form) 0.027323722447292472 y[1] (numeric) 0.02732372244729257 absolute error 9.71445146547012e-17 relative error 3.555317722250078e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -3.500000000000003 y[1] (closed_form) 0.030197383422318407 y[1] (numeric) 0.03019738342231851 absolute error 1.0408340855860843e-16 relative error 3.446769115819552e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -3.400000000000003 y[1] (closed_form) 0.033373269960325976 y[1] (numeric) 0.033373269960326093 absolute error 1.1796119636642288e-16 relative error 3.5346010896341515e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -3.300000000000003 y[1] (closed_form) 0.0368831674012399 y[1] (numeric) 0.03688316740124002 absolute error 1.249000902703301e-16 relative error 3.3863710486570457e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -3.200000000000003 y[1] (closed_form) 0.0407622039783661 y[1] (numeric) 0.04076220397836623 absolute error 1.3183898417423734e-16 relative error 3.234343860410708e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -3.1000000000000028 y[1] (closed_form) 0.04504920239355768 y[1] (numeric) 0.04504920239355782 absolute error 1.3877787807814457e-16 relative error 3.0805845765205086e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -3.0000000000000027 y[1] (closed_form) 0.04978706836786381 y[1] (numeric) 0.04978706836786396 absolute error 1.457167719820518e-16 relative error 2.9267996039732274e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -2.9000000000000026 y[1] (closed_form) 0.055023220056407085 y[1] (numeric) 0.055023220056407245 absolute error 1.5959455978986625e-16 relative error 2.900494729793309e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -2.8000000000000025 y[1] (closed_form) 0.06081006262521781 y[1] (numeric) 0.06081006262521798 absolute error 1.6653345369377348e-16 relative error 2.7385838215649587e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -2.7000000000000024 y[1] (closed_form) 0.0672055127397496 y[1] (numeric) 0.06720551273974978 absolute error 1.8041124150158794e-16 relative error 2.684470873694879e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -2.6000000000000023 y[1] (closed_form) 0.07427357821433371 y[1] (numeric) 0.0742735782143339 absolute error 1.942890293094024e-16 relative error 2.615856593696565e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -2.500000000000002 y[1] (closed_form) 0.08208499862389862 y[1] (numeric) 0.08208499862389883 absolute error 2.0816681711721685e-16 relative error 2.5359909923493643e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -2.400000000000002 y[1] (closed_form) 0.0907179532894123 y[1] (numeric) 0.09071795328941254 absolute error 2.3592239273284576e-16 relative error 2.600614147237163e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -2.300000000000002 y[1] (closed_form) 0.10025884372280353 y[1] (numeric) 0.10025884372280378 absolute error 2.498001805406602e-16 relative error 2.491552577958208e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -2.200000000000002 y[1] (closed_form) 0.11080315836233366 y[1] (numeric) 0.11080315836233393 absolute error 2.636779683484747e-16 relative error 2.3796972238483516e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -2.100000000000002 y[1] (closed_form) 0.12245642825298168 y[1] (numeric) 0.12245642825298196 absolute error 2.7755575615628914e-16 relative error 2.2665674649834558e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -2.0000000000000018 y[1] (closed_form) 0.13533528323661245 y[1] (numeric) 0.13533528323661276 absolute error 3.0531133177191805e-16 relative error 2.2559625581019344e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -1.9000000000000017 y[1] (closed_form) 0.1495686192226348 y[1] (numeric) 0.14956861922263512 absolute error 3.0531133177191805e-16 relative error 2.0412793362587522e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -1.8000000000000016 y[1] (closed_form) 0.16529888822158628 y[1] (numeric) 0.16529888822158662 absolute error 3.3306690738754696e-16 relative error 2.0149373717569382e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -1.7000000000000015 y[1] (closed_form) 0.1826835240527344 y[1] (numeric) 0.18268352405273475 absolute error 3.608224830031759e-16 relative error 1.9751232897117693e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -1.6000000000000014 y[1] (closed_form) 0.20189651799465513 y[1] (numeric) 0.20189651799465552 absolute error 3.885780586188048e-16 relative error 1.9246397237474484e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -1.5000000000000013 y[1] (closed_form) 0.22313016014842954 y[1] (numeric) 0.22313016014842996 absolute error 4.163336342344337e-16 relative error 1.8658778981625894e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -1.4000000000000012 y[1] (closed_form) 0.24659696394160616 y[1] (numeric) 0.24659696394160663 absolute error 4.718447854656915e-16 relative error 1.9134249583763074e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -1.3000000000000012 y[1] (closed_form) 0.2725317930340123 y[1] (numeric) 0.27253179303401276 absolute error 4.440892098500626e-16 relative error 1.6294950578284997e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -1.200000000000001 y[1] (closed_form) 0.30119421191220175 y[1] (numeric) 0.30119421191220225 absolute error 4.996003610813204e-16 relative error 1.6587316134313835e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -1.100000000000001 y[1] (closed_form) 0.3328710836980792 y[1] (numeric) 0.3328710836980797 absolute error 4.996003610813204e-16 relative error 1.5008824303118743e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -1.0000000000000009 y[1] (closed_form) 0.367879441171442 y[1] (numeric) 0.3678794411714425 absolute error 4.996003610813204e-16 relative error 1.358054583018932e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -0.9000000000000009 y[1] (closed_form) 0.4065696597405987 y[1] (numeric) 0.40656965974059933 absolute error 6.106226635438361e-16 relative error 1.501889402995364e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -0.8000000000000009 y[1] (closed_form) 0.4493289641172212 y[1] (numeric) 0.44932896411722184 absolute error 6.661338147750939e-16 relative error 1.4825080686347934e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -0.700000000000001 y[1] (closed_form) 0.496585303791409 y[1] (numeric) 0.4965853037914098 absolute error 7.771561172376096e-16 relative error 1.5650002352144808e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -0.600000000000001 y[1] (closed_form) 0.548811636094026 y[1] (numeric) 0.5488116360940267 absolute error 7.771561172376096e-16 relative error 1.4160707720571403e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -0.500000000000001 y[1] (closed_form) 0.6065306597126329 y[1] (numeric) 0.6065306597126338 absolute error 8.881784197001252e-16 relative error 1.4643586527364235e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -0.400000000000001 y[1] (closed_form) 0.6703200460356387 y[1] (numeric) 0.6703200460356397 absolute error 9.992007221626409e-16 relative error 1.490632315223222e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -0.30000000000000104 y[1] (closed_form) 0.7408182206817171 y[1] (numeric) 0.7408182206817182 absolute error 1.1102230246251565e-15 relative error 1.4986443281639388e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -0.20000000000000104 y[1] (closed_form) 0.818730753077981 y[1] (numeric) 0.8187307530779823 absolute error 1.2212453270876722e-15 relative error 1.491632410895103e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -0.10000000000000103 y[1] (closed_form) 0.9048374180359586 y[1] (numeric) 0.9048374180359601 absolute error 1.4432899320127035e-15 relative error 1.5950820592118202e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] -1.0269562977782698e-15 y[1] (closed_form) 0.999999999999999 y[1] (numeric) 1.0000000000000004 absolute error 1.4432899320127035e-15 relative error 1.443289932012705e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 0.09999999999999898 y[1] (closed_form) 1.1051709180756466 y[1] (numeric) 1.1051709180756482 absolute error 1.5543122344752192e-15 relative error 1.4063998690642616e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 0.19999999999999898 y[1] (closed_form) 1.2214027581601685 y[1] (numeric) 1.2214027581601705 absolute error 1.9984014443252818e-15 relative error 1.6361527194645662e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 0.299999999999999 y[1] (closed_form) 1.3498588075760019 y[1] (numeric) 1.3498588075760038 absolute error 1.9984014443252818e-15 relative error 1.4804522021928317e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 0.399999999999999 y[1] (closed_form) 1.4918246976412688 y[1] (numeric) 1.4918246976412712 absolute error 2.4424906541753444e-15 relative error 1.6372504477484373e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 0.499999999999999 y[1] (closed_form) 1.6487212707001264 y[1] (numeric) 1.648721270700129 absolute error 2.6645352591003757e-15 relative error 1.616122328529725e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 0.599999999999999 y[1] (closed_form) 1.822118800390507 y[1] (numeric) 1.82211880039051 absolute error 2.886579864025407e-15 relative error 1.5841886178918576e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 0.699999999999999 y[1] (closed_form) 2.0137527074704744 y[1] (numeric) 2.0137527074704775 absolute error 3.1086244689504383e-15 relative error 1.543697226287164e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 0.7999999999999989 y[1] (closed_form) 2.225540928492465 y[1] (numeric) 2.2255409284924688 absolute error 3.552713678800501e-15 relative error 1.5963371571005142e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 0.8999999999999989 y[1] (closed_form) 2.459603111156947 y[1] (numeric) 2.4596031111569507 absolute error 3.552713678800501e-15 relative error 1.4444255915456932e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 0.9999999999999989 y[1] (closed_form) 2.7182818284590424 y[1] (numeric) 2.7182818284590464 absolute error 3.9968028886505635e-15 relative error 1.4703416131491772e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 1.099999999999999 y[1] (closed_form) 3.00416602394643 y[1] (numeric) 3.0041660239464343 absolute error 4.440892098500626e-15 relative error 1.4782445654141437e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 1.199999999999999 y[1] (closed_form) 3.3201169227365446 y[1] (numeric) 3.320116922736549 absolute error 4.440892098500626e-15 relative error 1.3375709957950227e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 1.2999999999999992 y[1] (closed_form) 3.6692966676192413 y[1] (numeric) 3.6692966676192458 absolute error 4.440892098500626e-15 relative error 1.2102842862749555e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 1.3999999999999992 y[1] (closed_form) 4.055199966844672 y[1] (numeric) 4.055199966844676 absolute error 4.440892098500626e-15 relative error 1.0951105086825248e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 1.4999999999999993 y[1] (closed_form) 4.481689070338062 y[1] (numeric) 4.481689070338067 absolute error 5.329070518200751e-15 relative error 1.1890763581684103e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 1.5999999999999994 y[1] (closed_form) 4.953032424395112 y[1] (numeric) 4.953032424395118 absolute error 5.329070518200751e-15 relative error 1.0759207817727062e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 1.6999999999999995 y[1] (closed_form) 5.473947391727197 y[1] (numeric) 5.473947391727203 absolute error 5.329070518200751e-15 relative error 9.735333821904465e-14% Desired digits 16 Estimated correct digits 13 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] 1.7999999999999996 y[1] (closed_form) 6.049647464412944 y[1] (numeric) 6.049647464412949 absolute error 5.329070518200751e-15 relative error 8.808894319130186e-14% Desired digits 16 Estimated correct digits 13 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] 1.8999999999999997 y[1] (closed_form) 6.685894442279268 y[1] (numeric) 6.685894442279273 absolute error 5.329070518200751e-15 relative error 7.970617191473388e-14% Desired digits 16 Estimated correct digits 13 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] 1.9999999999999998 y[1] (closed_form) 7.389056098930649 y[1] (numeric) 7.389056098930654 absolute error 5.329070518200751e-15 relative error 7.212112679685812e-14% Desired digits 16 Estimated correct digits 13 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] 2.0999999999999996 y[1] (closed_form) 8.166169912567646 y[1] (numeric) 8.166169912567653 absolute error 7.105427357601002e-15 relative error 8.701052554228423e-14% Desired digits 16 Estimated correct digits 13 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] 2.1999999999999997 y[1] (closed_form) 9.025013499434118 y[1] (numeric) 9.025013499434124 absolute error 5.329070518200751e-15 relative error 5.904778445522427e-14% Desired digits 16 Estimated correct digits 13 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] 2.3 y[1] (closed_form) 9.974182454814718 y[1] (numeric) 9.974182454814724 absolute error 5.329070518200751e-15 relative error 5.3428644827208996e-14% Desired digits 16 Estimated correct digits 13 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] 2.4 y[1] (closed_form) 11.023176380641601 y[1] (numeric) 11.023176380641605 absolute error 3.552713678800501e-15 relative error 3.222949135640807e-14% Desired digits 16 Estimated correct digits 13 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] 2.5 y[1] (closed_form) 12.182493960703473 y[1] (numeric) 12.182493960703477 absolute error 3.552713678800501e-15 relative error 2.9162449743544557e-14% Desired digits 16 Estimated correct digits 13 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] 2.6 y[1] (closed_form) 13.463738035001692 y[1] (numeric) 13.463738035001693 absolute error 1.7763568394002505e-15 relative error 1.3193637864776143e-14% Desired digits 16 Estimated correct digits 13 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] 2.7 y[1] (closed_form) 14.879731724872837 y[1] (numeric) 14.879731724872837 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 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] 2.8000000000000003 y[1] (closed_form) 16.444646771097055 y[1] (numeric) 16.44464677109705 absolute error 3.552713678800501e-15 relative error 2.160407412973269e-14% Desired digits 16 Estimated correct digits 13 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] 2.9000000000000004 y[1] (closed_form) 18.174145369443067 y[1] (numeric) 18.174145369443064 absolute error 3.552713678800501e-15 relative error 1.9548174654604797e-14% Desired digits 16 Estimated correct digits 13 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] 3.0000000000000004 y[1] (closed_form) 20.085536923187675 y[1] (numeric) 20.08553692318767 absolute error 3.552713678800501e-15 relative error 1.768791988178859e-14% Desired digits 16 Estimated correct digits 13 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] 3.1000000000000005 y[1] (closed_form) 22.197951281441647 y[1] (numeric) 22.19795128144164 absolute error 7.105427357601002e-15 relative error 3.2009383512529e-14% Desired digits 16 Estimated correct digits 13 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] 3.2000000000000006 y[1] (closed_form) 24.532530197109363 y[1] (numeric) 24.532530197109356 absolute error 7.105427357601002e-15 relative error 2.896328793039955e-14% Desired digits 16 Estimated correct digits 13 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] 3.3000000000000007 y[1] (closed_form) 27.112638920657908 y[1] (numeric) 27.112638920657897 absolute error 1.0658141036401503e-14 relative error 3.93106000031622e-14% Desired digits 16 Estimated correct digits 13 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] 3.400000000000001 y[1] (closed_form) 29.964100047397036 y[1] (numeric) 29.964100047397025 absolute error 1.0658141036401503e-14 relative error 3.556970180830567e-14% Desired digits 16 Estimated correct digits 13 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] 3.500000000000001 y[1] (closed_form) 33.11545195869234 y[1] (numeric) 33.115451958692326 absolute error 1.4210854715202004e-14 relative error 4.291306285938173e-14% Desired digits 16 Estimated correct digits 13 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] 3.600000000000001 y[1] (closed_form) 36.598234443678024 y[1] (numeric) 36.598234443678 absolute error 2.1316282072803006e-14 relative error 5.82440174965467e-14% Desired digits 16 Estimated correct digits 13 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] 3.700000000000001 y[1] (closed_form) 40.447304360067434 y[1] (numeric) 40.447304360067406 absolute error 2.842170943040401e-14 relative error 7.026848854348874e-14% Desired digits 16 Estimated correct digits 13 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] 3.800000000000001 y[1] (closed_form) 44.70118449330087 y[1] (numeric) 44.70118449330084 absolute error 2.842170943040401e-14 relative error 6.358155774297975e-14% Desired digits 16 Estimated correct digits 13 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] 3.9000000000000012 y[1] (closed_form) 49.40244910553024 y[1] (numeric) 49.402449105530195 absolute error 4.263256414560601e-14 relative error 8.62964588142931e-14% Desired digits 16 Estimated correct digits 13 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] 4.000000000000001 y[1] (closed_form) 54.598150033144286 y[1] (numeric) 54.598150033144265 absolute error 2.1316282072803006e-14 relative error 3.904213248958576e-14% Desired digits 16 Estimated correct digits 13 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] 4.1000000000000005 y[1] (closed_form) 60.340287597362 y[1] (numeric) 60.340287597362 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 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] 4.2 y[1] (closed_form) 66.68633104092515 y[1] (numeric) 66.68633104092518 absolute error 2.842170943040401e-14 relative error 4.261999271329189e-14% Desired digits 16 Estimated correct digits 13 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] 4.3 y[1] (closed_form) 73.69979369959579 y[1] (numeric) 73.69979369959584 absolute error 5.684341886080802e-14 relative error 7.712832832681291e-14% Desired digits 16 Estimated correct digits 13 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] 4.3999999999999995 y[1] (closed_form) 81.45086866496807 y[1] (numeric) 81.45086866496817 absolute error 9.947598300641403e-14 relative error 1.2213004555616059e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 4.499999999999999 y[1] (closed_form) 90.01713130052174 y[1] (numeric) 90.01713130052187 absolute error 1.2789769243681803e-13 relative error 1.420815022529792e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 4.599999999999999 y[1] (closed_form) 99.48431564193369 y[1] (numeric) 99.48431564193388 absolute error 1.8474111129762605e-13 relative error 1.8569873060448106e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 4.699999999999998 y[1] (closed_form) 109.94717245212333 y[1] (numeric) 109.94717245212357 absolute error 2.4158453015843406e-13 relative error 2.1972782452739514e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 4.799999999999998 y[1] (closed_form) 121.51041751873464 y[1] (numeric) 121.51041751873495 absolute error 3.126388037344441e-13 relative error 2.5729382724426984e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 4.899999999999998 y[1] (closed_form) 134.28977968493518 y[1] (numeric) 134.28977968493558 absolute error 3.979039320256561e-13 relative error 2.963024684076487e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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] 4.999999999999997 y[1] (closed_form) 148.4131591025762 y[1] (numeric) 148.4131591025767 absolute error 5.115907697472721e-13 relative error 3.4470714917784656e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 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 Finished! diff ( y , x , 1 ) = y ; Iterations 101 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 101.99999999999996%