##############ECHO OF PROBLEM################# ##############temp/div_sin_lin_newpostode.ode################# diff ( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 1.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=1.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 $glob_max_h=0.001 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=1000000000 $glob_max_minutes=10.0 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(sin(x)/(2*x+1)) 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 10 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 0.9 estimated_steps 900000.0000000001 step_error 1.111111111111111e-16 est_needed_step_err 1.111111111111111e-16 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.504046601192705e-152 estimated_step_error 4.504046601192705e-152 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.0226120825400837e-144 estimated_step_error 3.0226120825400837e-144 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.028437376207862e-136 estimated_step_error 2.028437376207862e-136 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.361256910671959e-128 estimated_step_error 1.361256910671959e-128 best_h 1.6e-05 opt_iter 5 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.13518184350067e-121 estimated_step_error 9.13518184350067e-121 best_h 3.2e-05 opt_iter 6 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.13043804872516e-113 estimated_step_error 6.13043804872516e-113 best_h 6.4e-05 opt_iter 7 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.113961692974021e-105 estimated_step_error 4.113961692974021e-105 best_h 0.000128 opt_iter 8 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.760691181215538e-97 estimated_step_error 2.760691181215538e-97 best_h 0.000256 opt_iter 9 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8524782306397448e-89 estimated_step_error 1.8524782306397448e-89 best_h 0.000512 opt_iter 10 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2429218130523883e-81 estimated_step_error 1.2429218130523883e-81 best_h 0.001024 opt_iter 11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.33768284879288e-74 estimated_step_error 8.33768284879288e-74 best_h 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (analytic) 0.0831945138723568 y[1] (numeric) 0.0831945138723568 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6000000000000016 Order of pole (three term test) 8.10665947465073e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11000000000000001 y[1] (analytic) 0.08998221380096297 y[1] (numeric) 0.08998221380096298 absolute error 1.3877787807814457e-17 relative error 1.542281215542392e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.609999999999995 Order of pole (three term test) 8.961594333553554e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12000000000000002 y[1] (analytic) 0.09654210265235434 y[1] (numeric) 0.09654210265235436 absolute error 1.3877787807814457e-17 relative error 1.4374855556842404e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6199999999999954 Order of pole (three term test) 2.9339119805157936e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.13000000000000003 y[1] (analytic) 0.10288424017436101 y[1] (numeric) 0.10288424017436104 absolute error 2.7755575615628914e-17 relative error 2.697748029104429e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6300000000000024 Order of pole (three term test) 1.0540055663988814e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.14000000000000004 y[1] (analytic) 0.10901805831580978 y[1] (numeric) 0.1090180583158098 absolute error 1.3877787807814457e-17 relative error 1.2729806439601486e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.639999999999996 Order of pole (three term test) 1.1222959240848307e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15000000000000005 y[1] (analytic) 0.11495240959507635 y[1] (numeric) 0.11495240959507635 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6499999999999948 Order of pole (three term test) 1.1810878299853018e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16000000000000006 y[1] (analytic) 0.1206956110713985 y[1] (numeric) 0.12069561107139849 absolute error 1.3877787807814457e-17 relative error 1.1498171047499758e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6599999999999931 Order of pole (three term test) 1.22891769542185e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17000000000000007 y[1] (analytic) 0.1262554843783553 y[1] (numeric) 0.12625548437835526 absolute error 2.7755575615628914e-17 relative error 2.1983659365206326e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6699999999999964 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000008 y[1] (analytic) 0.13163939222487078 y[1] (numeric) 0.13163939222487078 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6799999999999975 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000009 y[1] (analytic) 0.1368542717221019 y[1] (numeric) 0.13685427172210193 absolute error 2.7755575615628914e-17 relative error 2.0281117473621688e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6899999999999951 Order of pole (three term test) 1.2974521890945587e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2000000000000001 y[1] (analytic) 0.1419066648536152 y[1] (numeric) 0.14190666485361528 absolute error 8.326672684688674e-17 relative error 5.867710789537695e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6999999999999971 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2100000000000001 y[1] (analytic) 0.1468027463704927 y[1] (numeric) 0.14680274637049281 absolute error 1.1102230246251565e-16 relative error 7.56268565864045e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7100000000000005 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2200000000000001 y[1] (analytic) 0.15154834936171488 y[1] (numeric) 0.151548349361715 absolute error 1.1102230246251565e-16 relative error 7.325866822708055e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7199999999999916 Order of pole (three term test) 1.250895334175327e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.23000000000000012 y[1] (analytic) 0.15614898872273184 y[1] (numeric) 0.15614898872273197 absolute error 1.3877787807814457e-16 relative error 8.887529737676847e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7299999999999995 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.24000000000000013 y[1] (analytic) 0.16060988272103696 y[1] (numeric) 0.16060988272103707 absolute error 1.1102230246251565e-16 relative error 6.91254489335193e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7400000000000015 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y[1] (analytic) 0.16493597283634867 y[1] (numeric) 0.1649359728363488 absolute error 1.3877787807814457e-16 relative error 8.41404550454506e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7499999999999954 Order of pole (three term test) 1.1095183823959057e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y[1] (analytic) 0.16913194203431262 y[1] (numeric) 0.16913194203431273 absolute error 1.1102230246251565e-16 relative error 6.564242160714504e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7599999999999882 Order of pole (three term test) 3.143018189431881e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (analytic) 0.17320223161612416 y[1] (numeric) 0.17320223161612427 absolute error 1.1102230246251565e-16 relative error 6.409981062402207e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.769999999999996 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (analytic) 0.17715105677186785 y[1] (numeric) 0.177151056771868 absolute error 1.3877787807814457e-16 relative error 7.833872436722768e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.780000000000002 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y[1] (analytic) 0.18098242095242761 y[1] (numeric) 0.18098242095242778 absolute error 1.6653345369377348e-16 relative error 9.201636977634854e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7899999999999938 Order of pole (three term test) 1.6797633116123082e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y[1] (analytic) 0.18470012916333728 y[1] (numeric) 0.18470012916333747 absolute error 1.942890293094024e-16 relative error 1.0519160446151355e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7999999999999975 Order of pole (three term test) 1.536211582134322e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y[1] (analytic) 0.18830780027373062 y[1] (numeric) 0.18830780027373079 absolute error 1.6653345369377348e-16 relative error 8.843683238383901e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8099999999999916 Order of pole (three term test) 3.4860845144676154e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y[1] (analytic) 0.19180887842446212 y[1] (numeric) 0.19180887842446234 absolute error 2.220446049250313e-16 relative error 1.1576346556474787e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8199999999999943 Order of pole (three term test) 1.2565180805961292e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y[1] (analytic) 0.19520664361136655 y[1] (numeric) 0.19520664361136678 absolute error 2.220446049250313e-16 relative error 1.1374848766269246e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8299999999999976 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y[1] (analytic) 0.19850422151238958 y[1] (numeric) 0.19850422151238983 absolute error 2.498001805406602e-16 relative error 1.2584124339394414e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8399999999999975 Order of pole (three term test) 9.988221340231992e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y[1] (analytic) 0.2017045926208538 y[1] (numeric) 0.20170459262085405 absolute error 2.498001805406602e-16 relative error 1.2384456759009557e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.849999999999992 Order of pole (three term test) 1.7628398881747244e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y[1] (analytic) 0.20481060074133145 y[1] (numeric) 0.20481060074133167 absolute error 2.220446049250313e-16 relative error 1.0841460555328667e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8599999999999944 Order of pole (three term test) 1.5453401505318868e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y[1] (analytic) 0.20782496089940353 y[1] (numeric) 0.20782496089940372 absolute error 1.942890293094024e-16 relative error 9.348685955170076e-14% Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8699999999999999 Order of pole (three term test) 6.729591063066295e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y[1] (analytic) 0.21075026671192204 y[1] (numeric) 0.2107502667119223 absolute error 2.498001805406602e-16 relative error 1.1852899853366076e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8799999999999918 Order of pole (three term test) 1.1648263610656633e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y[1] (analytic) 0.2135889972602031 y[1] (numeric) 0.2135889972602034 absolute error 2.7755575615628914e-16 relative error 1.2994852717912197e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8899999999999975 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y[1] (analytic) 0.21634352350480587 y[1] (numeric) 0.21634352350480615 absolute error 2.7755575615628914e-16 relative error 1.282939982024114e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9000000000000051 Order of pole (three term test) 8.565201276428627e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y[1] (analytic) 0.2190161142771555 y[1] (numeric) 0.21901611427715575 absolute error 2.498001805406602e-16 relative error 1.1405561703306854e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9100000000000033 Order of pole (three term test) 1.4558615894915382e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y[1] (analytic) 0.22160894188020125 y[1] (numeric) 0.2216089418802015 absolute error 2.498001805406602e-16 relative error 1.1272116477849471e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9199999999999966 Order of pole (three term test) 1.2301499163122546e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y[1] (analytic) 0.22412408732753272 y[1] (numeric) 0.22412408732753303 absolute error 3.0531133177191805e-16 relative error 1.3622423872974398e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9299999999999915 Order of pole (three term test) 2.0671216956762558e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y[1] (analytic) 0.22656354524787217 y[1] (numeric) 0.22656354524787248 absolute error 3.0531133177191805e-16 relative error 1.347574833532428e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9399999999999935 Order of pole (three term test) 1.7271775765157908e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y[1] (analytic) 0.2289292284795949 y[1] (numeric) 0.22892922847959524 absolute error 3.3306690738754696e-16 relative error 1.454890271546231e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9499999999999874 Order of pole (three term test) 2.1529966454745729e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y[1] (analytic) 0.23122297237787492 y[1] (numeric) 0.23122297237787529 absolute error 3.608224830031759e-16 relative error 1.560495824841762e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9600000000000013 Order of pole (three term test) 1.1864815267142058e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y[1] (analytic) 0.2334465388551899 y[1] (numeric) 0.23344653885519023 absolute error 3.3306690738754696e-16 relative error 1.42673739786801e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9699999999999989 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y[1] (analytic) 0.23560162017422603 y[1] (numeric) 0.23560162017422634 absolute error 3.0531133177191805e-16 relative error 1.2958795934685936e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9799999999999867 Order of pole (three term test) 3.193089064132931e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y[1] (analytic) 0.23768984251068592 y[1] (numeric) 0.23768984251068626 absolute error 3.3306690738754696e-16 relative error 1.4012668941567125e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.989999999999993 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5000000000000003 y[1] (analytic) 0.23971276930210153 y[1] (numeric) 0.2397127693021019 absolute error 3.608224830031759e-16 relative error 1.5052284617697778e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9999999999999903 Order of pole (three term test) 3.1588283125634974e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5100000000000003 y[1] (analytic) 0.24167190439747907 y[1] (numeric) 0.24167190439747938 absolute error 3.0531133177191805e-16 relative error 1.2633298543043335e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0099999999999931 Order of pole (three term test) 1.6978748970849874e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5200000000000004 y[1] (analytic) 0.2435686950214396 y[1] (numeric) 0.24356869502144 absolute error 3.885780586188048e-16 relative error 1.5953530423300132e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0200000000000007 Order of pole (three term test) 6.812526598400843e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y[1] (analytic) 0.24540453456545977 y[1] (numeric) 0.24540453456546013 absolute error 3.608224830031759e-16 relative error 1.4703170976122664e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0299999999999994 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5400000000000004 y[1] (analytic) 0.24718076521784288 y[1] (numeric) 0.24718076521784332 absolute error 4.440892098500626e-16 relative error 1.7966171819991025e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0399999999999958 Order of pole (three term test) 8.654610908300277e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y[1] (analytic) 0.2488986804431711 y[1] (numeric) 0.2488986804431715 absolute error 4.163336342344337e-16 relative error 1.6727032601906123e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0499999999999952 Order of pole (three term test) 1.3703493851595722e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5600000000000004 y[1] (analytic) 0.2505595273211714 y[1] (numeric) 0.2505595273211719 absolute error 4.996003610813204e-16 relative error 1.9939387914031474e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0599999999999954 Order of pole (three term test) 1.0801912243446113e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y[1] (analytic) 0.2521645087541913 y[1] (numeric) 0.2521645087541918 absolute error 4.996003610813204e-16 relative error 1.9812477320840118e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.070000000000005 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5800000000000004 y[1] (analytic) 0.25371478555179333 y[1] (numeric) 0.2537147855517939 absolute error 5.551115123125783e-16 relative error 2.1879352088420477e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0800000000000025 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y[1] (analytic) 0.2552114784003596 y[1] (numeric) 0.2552114784003601 absolute error 4.996003610813204e-16 relative error 1.957593616920235e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0899999999999825 Order of pole (three term test) 3.095329984783713e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6000000000000004 y[1] (analytic) 0.2566556697250161 y[1] (numeric) 0.25665566972501674 absolute error 6.661338147750939e-16 relative error 2.5954377531920395e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0999999999999945 Order of pole (three term test) 1.599912392482752e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6100000000000004 y[1] (analytic) 0.2580484054506673 y[1] (numeric) 0.2580484054506679 absolute error 5.551115123125783e-16 relative error 2.1511914066785517e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1099999999999979 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6200000000000004 y[1] (analytic) 0.2593906966684398 y[1] (numeric) 0.25939069666844045 absolute error 6.661338147750939e-16 relative error 2.5680713430773665e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1199999999999846 Order of pole (three term test) 3.801935175856854e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y[1] (analytic) 0.26068352121339367 y[1] (numeric) 0.2606835212133942 absolute error 5.551115123125783e-16 relative error 2.1294461181463326e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.129999999999993 Order of pole (three term test) 2.18522315681269e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y[1] (analytic) 0.2619278251589439 y[1] (numeric) 0.2619278251589445 absolute error 6.106226635438361e-16 relative error 2.331263061392183e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.139999999999998 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y[1] (analytic) 0.2631245242330607 y[1] (numeric) 0.2631245242330614 absolute error 6.661338147750939e-16 relative error 2.531629526805607e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.149999999999996 Order of pole (three term test) 8.461044081132065e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y[1] (analytic) 0.26427450516096285 y[1] (numeric) 0.2642745051609635 absolute error 6.661338147750939e-16 relative error 2.5206132327042627e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1600000000000097 Order of pole (three term test) 1.2826281634122808e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y[1] (analytic) 0.2653786269387008 y[1] (numeric) 0.2653786269387014 absolute error 6.106226635438361e-16 relative error 2.300948914340726e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.16999999999999 Order of pole (three term test) 2.9062337817500334e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y[1] (analytic) 0.266437722041724 y[1] (numeric) 0.26643772204172467 absolute error 6.661338147750939e-16 relative error 2.5001482885774623e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1799999999999864 Order of pole (three term test) 2.916529537706477e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y[1] (analytic) 0.2674525975722555 y[1] (numeric) 0.2674525975722562 absolute error 7.216449660063518e-16 relative error 2.698216329012811e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1899999999999922 Order of pole (three term test) 1.0938260916416818e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y[1] (analytic) 0.26842403634903794 y[1] (numeric) 0.26842403634903866 absolute error 7.216449660063518e-16 relative error 2.6884513615911067e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2000000000000066 Order of pole (three term test) 8.177123719449947e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y[1] (analytic) 0.26935279794278383 y[1] (numeric) 0.2693527979427845 absolute error 6.661338147750939e-16 relative error 2.473090385036931e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2099999999999922 Order of pole (three term test) 1.2185637066676647e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7200000000000005 y[1] (analytic) 0.27023961966043986 y[1] (numeric) 0.2702396196604406 absolute error 7.216449660063518e-16 relative error 2.670389215737905e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2200000000000089 Order of pole (three term test) 1.8100296918046139e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7300000000000005 y[1] (analytic) 0.27108521748117803 y[1] (numeric) 0.27108521748117864 absolute error 6.106226635438361e-16 relative error 2.2525118456015876e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2299999999999962 Order of pole (three term test) 6.700030772876476e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7400000000000005 y[1] (analytic) 0.2718902869468327 y[1] (numeric) 0.27189028694683326 absolute error 5.551115123125783e-16 relative error 2.0416746715969615e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2400000000000053 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7500000000000006 y[1] (analytic) 0.27265550400933375 y[1] (numeric) 0.2726555040093343 absolute error 5.551115123125783e-16 relative error 2.0359446413140272e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2500000000000056 Order of pole (three term test) 7.275829619259826e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7600000000000006 y[1] (analytic) 0.2733815258375204 y[1] (numeric) 0.27338152583752107 absolute error 6.661338147750939e-16 relative error 2.436645317324767e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2599999999999971 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7700000000000006 y[1] (analytic) 0.2740689915855736 y[1] (numeric) 0.2740689915855742 absolute error 6.106226635438361e-16 relative error 2.2279888724776773e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2699999999999945 Order of pole (three term test) 1.5611532820138834e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7800000000000006 y[1] (analytic) 0.27471852312516026 y[1] (numeric) 0.274718523125161 absolute error 7.216449660063518e-16 relative error 2.626852233322375e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2799999999999951 Order of pole (three term test) 1.1383450641240524e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7900000000000006 y[1] (analytic) 0.2753307257432589 y[1] (numeric) 0.2753307257432596 absolute error 7.216449660063518e-16 relative error 2.6210113820688254e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.290000000000007 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y[1] (analytic) 0.2759061888075087 y[1] (numeric) 0.2759061888075095 absolute error 7.771561172376096e-16 relative error 2.8167404312188427e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3000000000000054 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y[1] (analytic) 0.2764454864008178 y[1] (numeric) 0.2764454864008185 absolute error 7.216449660063518e-16 relative error 2.610442208342082e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3099999999999938 Order of pole (three term test) 8.676512969397103e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y[1] (analytic) 0.27694917792685453 y[1] (numeric) 0.27694917792685536 absolute error 8.326672684688674e-16 relative error 3.006570644845115e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.319999999999986 Order of pole (three term test) 2.502289571288041e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8300000000000006 y[1] (analytic) 0.27741780868795596 y[1] (numeric) 0.2774178086879568 absolute error 8.326672684688674e-16 relative error 3.001491765820503e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.329999999999985 Order of pole (three term test) 2.698895351144819e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y[1] (analytic) 0.2778519104368878 y[1] (numeric) 0.27785191043688867 absolute error 8.881784197001252e-16 relative error 3.1965892129500725e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3399999999999879 Order of pole (three term test) 2.58062927961631e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y[1] (analytic) 0.27825200190381216 y[1] (numeric) 0.278252001903813 absolute error 8.326672684688674e-16 relative error 2.992493361311768e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3499999999999885 Order of pole (three term test) 2.768724305113023e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y[1] (analytic) 0.2786185892997342 y[1] (numeric) 0.2786185892997351 absolute error 8.881784197001252e-16 relative error 3.1877931114805643e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.35999999999998 Order of pole (three term test) 2.633669607368709e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y[1] (analytic) 0.27895216679762963 y[1] (numeric) 0.2789521667976305 absolute error 8.881784197001252e-16 relative error 3.1839810742336646e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3700000000000014 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y[1] (analytic) 0.2792532169923802 y[1] (numeric) 0.27925321699238115 absolute error 9.43689570931383e-16 relative error 3.379332854586713e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3799999999999932 Order of pole (three term test) 6.651618233438951e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y[1] (analytic) 0.27952221134058414 y[1] (numeric) 0.27952221134058514 absolute error 9.992007221626409e-16 relative error 3.574673788428082e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3900000000000003 Order of pole (three term test) 9.419867696256471e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y[1] (analytic) 0.2797596105812441 y[1] (numeric) 0.27975961058124504 absolute error 9.43689570931383e-16 relative error 3.3732159155166153e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3999999999999861 Order of pole (three term test) 3.326985910298101e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y[1] (analytic) 0.2799658651382803 y[1] (numeric) 0.2799658651382813 absolute error 9.992007221626409e-16 relative error 3.5690091064105874e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.41000000000002 Order of pole (three term test) 2.813412364217295e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y[1] (analytic) 0.28014141550576266 y[1] (numeric) 0.28014141550576377 absolute error 1.1102230246251565e-15 relative error 3.963080655606663e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4199999999999988 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y[1] (analytic) 0.2802866926167053 y[1] (numeric) 0.28028669261670636 absolute error 1.0547118733938987e-15 relative error 3.762975200667936e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4299999999999966 Order of pole (three term test) 9.249187510098702e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y[1] (analytic) 0.2804021181962202 y[1] (numeric) 0.28040211819622124 absolute error 1.0547118733938987e-15 relative error 3.761426198128186e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4399999999999893 Order of pole (three term test) 1.2945687940836567e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y[1] (analytic) 0.28048810509978406 y[1] (numeric) 0.28048810509978506 absolute error 9.992007221626409e-16 relative error 3.562363979061336e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4500000000000066 Order of pole (three term test) 1.8078995907555048e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y[1] (analytic) 0.2805450576373282 y[1] (numeric) 0.2805450576373292 absolute error 9.992007221626409e-16 relative error 3.5616407951636333e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4599999999999906 Order of pole (three term test) 1.2596099445536776e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y[1] (analytic) 0.2805733718838266 y[1] (numeric) 0.28057337188382764 absolute error 1.0547118733938987e-15 relative error 3.759130334829528e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4700000000000026 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y[1] (analytic) 0.28057343597701706 y[1] (numeric) 0.28057343597701806 absolute error 9.992007221626409e-16 relative error 3.5612805563121433e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4800000000000142 Order of pole (three term test) 1.214999413227152e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9900000000000008 y[1] (analytic) 0.28054563040285924 y[1] (numeric) 0.28054563040286024 absolute error 9.992007221626409e-16 relative error 3.561633523672438e-13% Correct digits 15 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4899999999999944 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 1.0 ) ; Iterations 900 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 9 Minutes 59.0 Seconds Percent Done 100.11111111111117%