##############ECHO OF PROBLEM################# ##############temp/divpostode.ode################# diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.0) x_end=c(1.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(1.570796327) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=8 $glob_max_minutes=(3.0) $glob_subiter_method=3 $glob_max_iter=100000 $glob_upper_ratio_limit=c(1.000001) $glob_lower_ratio_limit=c(0.999999) $glob_look_poles=true $glob_h=c(0.001) $glob_display_interval=c(0.01) #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(c(2.0) - ln(float_abs(cos(c(x))))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (closed_form) 2.0 y[1] (numeric) 2.0 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.570796327 Order of pole (given) 0.0 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] 0.010000000000000002 y[1] (closed_form) 2.0000500008333555 y[1] (numeric) 2.0000500008333555 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.560796327 Order of pole (given) 0.0 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] 0.02000000000000001 y[1] (closed_form) 2.000200013334756 y[1] (numeric) 2.0002000133347555 absolute error 4.440892098500626e-16 relative error 2.2202240120460357e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.550796327 Order of pole (given) 0.0 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] 0.03000000000000002 y[1] (closed_form) 2.0004500675162045 y[1] (numeric) 2.000450067516204 absolute error 4.440892098500626e-16 relative error 2.219946486349704e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.540796327 Order of pole (given) 0.0 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] 0.04000000000000003 y[1] (closed_form) 2.0008002134244 y[1] (numeric) 2.0008002134244 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.530796327 Order of pole (given) 0.0 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] 0.05000000000000004 y[1] (closed_form) 2.001250521180819 y[1] (numeric) 2.0012505211808196 absolute error 4.440892098500626e-16 relative error 2.2190585593853183e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.520796327 Order of pole (given) 0.0 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] 0.060000000000000046 y[1] (closed_form) 2.0018010810379345 y[1] (numeric) 2.0018010810379345 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.510796327 Order of pole (given) 0.0 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] 0.07000000000000005 y[1] (closed_form) 2.002452003451651 y[1] (numeric) 2.00245200345165 absolute error 8.881784197001252e-16 relative error 4.435454223967223e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.500796327 Order of pole (given) 0.0 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] 0.08000000000000006 y[1] (closed_form) 2.003203419170097 y[1] (numeric) 2.0032034191700965 absolute error 4.440892098500626e-16 relative error 2.2168952269163132e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.490796327 Order of pole (given) 0.0 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] 0.09000000000000007 y[1] (closed_form) 2.004055479338916 y[1] (numeric) 2.004055479338915 absolute error 8.881784197001252e-16 relative error 4.4319053482147684e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.480796327 Order of pole (given) 0.0 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] 0.10000000000000007 y[1] (closed_form) 2.0050083556232354 y[1] (numeric) 2.0050083556232345 absolute error 8.881784197001252e-16 relative error 4.429799093899758e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.470796327 Order of pole (given) 0.0 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] 0.11000000000000008 y[1] (closed_form) 2.0060622403465325 y[1] (numeric) 2.006062240346531 absolute error 1.3322676295501878e-15 relative error 6.641207848665994e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.460796327 Order of pole (given) 0.0 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] 0.12000000000000009 y[1] (closed_form) 2.0072173466466277 y[1] (numeric) 2.0072173466466263 absolute error 1.3322676295501878e-15 relative error 6.637385989992317e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.450796327 Order of pole (given) 0.0 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] 0.1300000000000001 y[1] (closed_form) 2.008473908649082 y[1] (numeric) 2.008473908649081 absolute error 1.3322676295501878e-15 relative error 6.633233440638933e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.440796327 Order of pole (given) 0.0 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] 0.1400000000000001 y[1] (closed_form) 2.009832181658296 y[1] (numeric) 2.009832181658294 absolute error 1.7763568394002505e-15 relative error 8.838334143573088e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.430796327 Order of pole (given) 0.0 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] 0.1500000000000001 y[1] (closed_form) 2.0112924423666416 y[1] (numeric) 2.0112924423666403 absolute error 1.3322676295501878e-15 relative error 6.62393792909866e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.420796327 Order of pole (given) 0.0 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] 0.16000000000000011 y[1] (closed_form) 2.0128549890820095 y[1] (numeric) 2.012854989082008 absolute error 1.3322676295501878e-15 relative error 6.618795873406594e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.410796327 Order of pole (given) 0.0 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] 0.17000000000000012 y[1] (closed_form) 2.014520141974147 y[1] (numeric) 2.0145201419741463 absolute error 8.881784197001252e-16 relative error 4.4088832928210225e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.400796327 Order of pole (given) 0.0 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] 0.18000000000000013 y[1] (closed_form) 2.016288243340249 y[1] (numeric) 2.0162882433402483 absolute error 8.881784197001252e-16 relative error 4.405017103252756e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3907963269999999 Order of pole (given) 0.0 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] 0.19000000000000014 y[1] (closed_form) 2.01815965789026 y[1] (numeric) 2.01815965789026 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3807963269999999 Order of pole (given) 0.0 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] 0.20000000000000015 y[1] (closed_form) 2.0201347730524084 y[1] (numeric) 2.0201347730524084 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3707963269999999 Order of pole (given) 0.0 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] 0.21000000000000016 y[1] (closed_form) 2.022213999299519 y[1] (numeric) 2.0222139992995185 absolute error 4.440892098500626e-16 relative error 2.1960544729879828e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3607963269999999 Order of pole (given) 0.0 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] 0.22000000000000017 y[1] (closed_form) 2.0243977704967033 y[1] (numeric) 2.0243977704967024 absolute error 8.881784197001252e-16 relative error 4.38737106236885e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3507963269999999 Order of pole (given) 0.0 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] 0.23000000000000018 y[1] (closed_form) 2.026686544271061 y[1] (numeric) 2.02668654427106 absolute error 8.881784197001252e-16 relative error 4.382416324866738e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3407963269999998 Order of pole (given) 0.0 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] 0.24000000000000019 y[1] (closed_form) 2.029080802404081 y[1] (numeric) 2.0290808024040805 absolute error 4.440892098500626e-16 relative error 2.1886225985870056e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3307963269999998 Order of pole (given) 0.0 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] 0.25000000000000017 y[1] (closed_form) 2.0315810512474695 y[1] (numeric) 2.031581051247469 absolute error 4.440892098500626e-16 relative error 2.1859290800993377e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3207963269999998 Order of pole (given) 0.0 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] 0.2600000000000002 y[1] (closed_form) 2.0341878221631884 y[1] (numeric) 2.0341878221631884 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3107963269999998 Order of pole (given) 0.0 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] 0.2700000000000002 y[1] (closed_form) 2.036901671988538 y[1] (numeric) 2.0369016719885384 absolute error 4.440892098500626e-16 relative error 2.180219182679141e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.3007963269999998 Order of pole (given) 0.0 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] 0.2800000000000002 y[1] (closed_form) 2.039723183527177 y[1] (numeric) 2.0397231835271765 absolute error 4.440892098500626e-16 relative error 2.177203325610706e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2907963269999998 Order of pole (given) 0.0 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] 0.2900000000000002 y[1] (closed_form) 2.042652966067024 y[1] (numeric) 2.042652966067024 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2807963269999998 Order of pole (given) 0.0 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] 0.3000000000000002 y[1] (closed_form) 2.045691655926058 y[1] (numeric) 2.0456916559260576 absolute error 4.440892098500626e-16 relative error 2.1708511571800355e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2707963269999998 Order of pole (given) 0.0 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] 0.3100000000000002 y[1] (closed_form) 2.048839917027086 y[1] (numeric) 2.048839917027085 absolute error 8.881784197001252e-16 relative error 4.3350308255849125e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2607963269999998 Order of pole (given) 0.0 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] 0.32000000000000023 y[1] (closed_form) 2.0520984415026304 y[1] (numeric) 2.05209844150263 absolute error 4.440892098500626e-16 relative error 2.1640736178566674e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2507963269999998 Order of pole (given) 0.0 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] 0.33000000000000024 y[1] (closed_form) 2.0554679503311526 y[1] (numeric) 2.055467950331152 absolute error 4.440892098500626e-16 relative error 2.160526072802625e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2407963269999998 Order of pole (given) 0.0 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] 0.34000000000000025 y[1] (closed_form) 2.058949194005907 y[1] (numeric) 2.0589491940059066 absolute error 4.440892098500626e-16 relative error 2.1568730843039372e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2307963269999997 Order of pole (given) 0.0 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] 0.35000000000000026 y[1] (closed_form) 2.062542953237805 y[1] (numeric) 2.062542953237805 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2207963269999997 Order of pole (given) 0.0 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] 0.36000000000000026 y[1] (closed_form) 2.066250039693758 y[1] (numeric) 2.066250039693758 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2107963269999997 Order of pole (given) 0.0 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] 0.3700000000000003 y[1] (closed_form) 2.0700712967720554 y[1] (numeric) 2.0700712967720554 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.2007963269999997 Order of pole (given) 0.0 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] 0.3800000000000003 y[1] (closed_form) 2.07400760041643 y[1] (numeric) 2.0740076004164307 absolute error 8.881784197001252e-16 relative error 4.2824260601638695e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1907963269999997 Order of pole (given) 0.0 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] 0.3900000000000003 y[1] (closed_form) 2.078059859970587 y[1] (numeric) 2.0780598599705877 absolute error 8.881784197001252e-16 relative error 4.2740752410890445e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1807963269999997 Order of pole (given) 0.0 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] 0.4000000000000003 y[1] (closed_form) 2.0822290190750556 y[1] (numeric) 2.082229019075056 absolute error 4.440892098500626e-16 relative error 2.132758720495265e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1707963269999997 Order of pole (given) 0.0 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] 0.4100000000000003 y[1] (closed_form) 2.086516056608366 y[1] (numeric) 2.0865160566083665 absolute error 4.440892098500626e-16 relative error 2.1283766709753008e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1607963269999997 Order of pole (given) 0.0 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] 0.4200000000000003 y[1] (closed_form) 2.0909219876746725 y[1] (numeric) 2.0909219876746725 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1507963269999997 Order of pole (given) 0.0 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] 0.4300000000000003 y[1] (closed_form) 2.0954478646400734 y[1] (numeric) 2.0954478646400734 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1407963269999997 Order of pole (given) 0.0 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] 0.44000000000000034 y[1] (closed_form) 2.1000947782200377 y[1] (numeric) 2.1000947782200377 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1307963269999997 Order of pole (given) 0.0 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] 0.45000000000000034 y[1] (closed_form) 2.10486385862049 y[1] (numeric) 2.1048638586204897 absolute error 4.440892098500626e-16 relative error 2.109823911087128e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1207963269999996 Order of pole (given) 0.0 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] 0.46000000000000035 y[1] (closed_form) 2.109756276735282 y[1] (numeric) 2.109756276735282 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1107963269999996 Order of pole (given) 0.0 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] 0.47000000000000036 y[1] (closed_form) 2.1147732454029446 y[1] (numeric) 2.1147732454029446 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.1007963269999996 Order of pole (given) 0.0 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] 0.48000000000000037 y[1] (closed_form) 2.1199160207258236 y[1] (numeric) 2.1199160207258227 absolute error 8.881784197001252e-16 relative error 4.1896868131409654e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.0907963269999996 Order of pole (given) 0.0 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] 0.4900000000000004 y[1] (closed_form) 2.1251859034548866 y[1] (numeric) 2.1251859034548852 absolute error 1.3322676295501878e-15 relative error 6.268946294930425e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.0807963269999996 Order of pole (given) 0.0 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] 0.5000000000000003 y[1] (closed_form) 2.130584240443723 y[1] (numeric) 2.130584240443721 absolute error 1.7763568394002505e-15 relative error 8.337416590626335e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.0707963269999996 Order of pole (given) 0.0 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] 0.5100000000000003 y[1] (closed_form) 2.1361124261754862 y[1] (numeric) 2.1361124261754845 absolute error 1.7763568394002505e-15 relative error 8.315839642301294e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.0607963269999998 Order of pole (given) 0.0 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] 0.5200000000000004 y[1] (closed_form) 2.1417719043667884 y[1] (numeric) 2.141771904366786 absolute error 2.220446049250313e-15 relative error 1.036733204279652e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.0507963269999996 Order of pole (given) 0.0 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] 0.5300000000000004 y[1] (closed_form) 2.1475641696528216 y[1] (numeric) 2.1475641696528194 absolute error 2.220446049250313e-15 relative error 1.033936997379349e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.0407963269999998 Order of pole (given) 0.0 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] 0.5400000000000004 y[1] (closed_form) 2.1534907693582817 y[1] (numeric) 2.153490769358279 absolute error 2.6645352591003757e-15 relative error 1.2373098120566266e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.0307963269999996 Order of pole (given) 0.0 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] 0.5500000000000004 y[1] (closed_form) 2.159553305358981 y[1] (numeric) 2.1595533053589784 absolute error 2.6645352591003757e-15 relative error 1.2338362996126422e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.0207963269999998 Order of pole (given) 0.0 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] 0.5600000000000004 y[1] (closed_form) 2.1657534360393846 y[1] (numeric) 2.1657534360393824 absolute error 2.220446049250313e-15 relative error 1.0252533886364034e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 1.0107963269999996 Order of pole (given) 0.0 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] 0.5700000000000004 y[1] (closed_form) 2.172092878351663 y[1] (numeric) 2.1720928783516618 absolute error 1.3322676295501878e-15 relative error 6.133566583769688e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 1.0007963269999998 Order of pole (given) 0.0 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] 0.5800000000000004 y[1] (closed_form) 2.17857340998226 y[1] (numeric) 2.178573409982259 absolute error 8.881784197001252e-16 relative error 4.0768808415198534e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9907963269999996 Order of pole (given) 0.0 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] 0.5900000000000004 y[1] (closed_form) 2.1851968716324017 y[1] (numeric) 2.185196871632401 absolute error 8.881784197001252e-16 relative error 4.064523573277092e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9807963269999996 Order of pole (given) 0.0 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] 0.6000000000000004 y[1] (closed_form) 2.1919651694194378 y[1] (numeric) 2.1919651694194373 absolute error 4.440892098500626e-16 relative error 2.0259866171490478e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9707963269999996 Order of pole (given) 0.0 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] 0.6100000000000004 y[1] (closed_form) 2.198880277406405 y[1] (numeric) 2.198880277406404 absolute error 8.881784197001252e-16 relative error 4.039230461186082e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9607963269999996 Order of pole (given) 0.0 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] 0.6200000000000004 y[1] (closed_form) 2.2059442402677547 y[1] (numeric) 2.205944240267754 absolute error 8.881784197001252e-16 relative error 4.0262958758754446e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9507963269999996 Order of pole (given) 0.0 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] 0.6300000000000004 y[1] (closed_form) 2.2131591760997757 y[1] (numeric) 2.2131591760997757 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9407963269999996 Order of pole (given) 0.0 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] 0.6400000000000005 y[1] (closed_form) 2.220527279384879 y[1] (numeric) 2.2205272793848785 absolute error 4.440892098500626e-16 relative error 1.9999268370757522e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9307963269999996 Order of pole (given) 0.0 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] 0.6500000000000005 y[1] (closed_form) 2.2280508241196166 y[1] (numeric) 2.2280508241196157 absolute error 8.881784197001252e-16 relative error 3.986347214727818e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9207963269999996 Order of pole (given) 0.0 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] 0.6600000000000005 y[1] (closed_form) 2.235732167117059 y[1] (numeric) 2.235732167117058 absolute error 8.881784197001252e-16 relative error 3.9726512538638166e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9107963269999996 Order of pole (given) 0.0 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] 0.6700000000000005 y[1] (closed_form) 2.2435737514949814 y[1] (numeric) 2.2435737514949814 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.9007963269999996 Order of pole (given) 0.0 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] 0.6800000000000005 y[1] (closed_form) 2.251578110362207 y[1] (numeric) 2.251578110362207 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8907963269999996 Order of pole (given) 0.0 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] 0.6900000000000005 y[1] (closed_form) 2.259747870716431 y[1] (numeric) 2.259747870716432 absolute error 8.881784197001252e-16 relative error 3.930431492866224e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8807963269999995 Order of pole (given) 0.0 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] 0.7000000000000005 y[1] (closed_form) 2.2680857575679316 y[1] (numeric) 2.268085757567932 absolute error 4.440892098500626e-16 relative error 1.957991263638371e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8707963269999995 Order of pole (given) 0.0 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] 0.7100000000000005 y[1] (closed_form) 2.2765945983047113 y[1] (numeric) 2.2765945983047122 absolute error 8.881784197001252e-16 relative error 3.901346424881778e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8607963269999995 Order of pole (given) 0.0 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] 0.7200000000000005 y[1] (closed_form) 2.285277327315926 y[1] (numeric) 2.285277327315927 absolute error 8.881784197001252e-16 relative error 3.886523570175603e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8507963269999995 Order of pole (given) 0.0 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] 0.7300000000000005 y[1] (closed_form) 2.294136990891822 y[1] (numeric) 2.2941369908918223 absolute error 4.440892098500626e-16 relative error 1.935757156670176e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8407963269999995 Order of pole (given) 0.0 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] 0.7400000000000005 y[1] (closed_form) 2.303176752419951 y[1] (numeric) 2.3031767524199513 absolute error 4.440892098500626e-16 relative error 1.9281594839972984e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8307963269999995 Order of pole (given) 0.0 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] 0.7500000000000006 y[1] (closed_form) 2.312399897899106 y[1] (numeric) 2.312399897899106 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8207963269999995 Order of pole (given) 0.0 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] 0.7600000000000006 y[1] (closed_form) 2.32180984179426 y[1] (numeric) 2.3218098417942596 absolute error 4.440892098500626e-16 relative error 1.9126855346038034e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8107963269999995 Order of pole (given) 0.0 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] 0.7700000000000006 y[1] (closed_form) 2.3314101332578185 y[1] (numeric) 2.3314101332578177 absolute error 8.881784197001252e-16 relative error 3.809618938470601e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.8007963269999995 Order of pole (given) 0.0 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] 0.7800000000000006 y[1] (closed_form) 2.341204462744726 y[1] (numeric) 2.341204462744725 absolute error 8.881784197001252e-16 relative error 3.7936815593579707e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7907963269999995 Order of pole (given) 0.0 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] 0.7900000000000006 y[1] (closed_form) 2.351196669051421 y[1] (numeric) 2.35119666905142 absolute error 1.3322676295501878e-15 relative error 5.6663385376761557e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7807963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7807963259696714 Order of pole (three term test) 2.4037059242205803e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y[1] (closed_form) 2.3613907468113444 y[1] (numeric) 2.3613907468113426 absolute error 1.7763568394002505e-15 relative error 7.522502753087e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7707963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7707963262406597 Order of pole (three term test) 1.6355558752504304e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y[1] (closed_form) 2.371790854482695 y[1] (numeric) 2.3717908544826933 absolute error 1.7763568394002505e-15 relative error 7.48951719770286e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7607963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7607963264239463 Order of pole (three term test) 1.109218738671669e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y[1] (closed_form) 2.3824013228674414 y[1] (numeric) 2.382401322867439 absolute error 2.220446049250313e-15 relative error 9.320201545967075e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7507963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7507963265474851 Order of pole (three term test) 7.497766308329694e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8300000000000006 y[1] (closed_form) 2.393226664204251 y[1] (numeric) 2.3932266642042483 absolute error 2.6645352591003757e-15 relative error 1.1133651897474303e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7407963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7407963266304927 Order of pole (three term test) 5.050202263125101e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y[1] (closed_form) 2.4042715818820777 y[1] (numeric) 2.404271581882075 absolute error 2.6645352591003757e-15 relative error 1.1082505317533896e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7307963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7307963266860479 Order of pole (three term test) 3.3898153970056583e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y[1] (closed_form) 2.4155409808256354 y[1] (numeric) 2.4155409808256323 absolute error 3.1086244689504383e-15 relative error 1.286926818309622e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7207963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7207963267231191 Order of pole (three term test) 2.2667137538906852e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y[1] (closed_form) 2.427039978609021 y[1] (numeric) 2.4270399786090184 absolute error 2.6645352591003757e-15 relative error 1.097853880687811e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.7107963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7107963267477574 Order of pole (three term test) 1.5097524938561957e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y[1] (closed_form) 2.4387739173593155 y[1] (numeric) 2.4387739173593133 absolute error 2.220446049250313e-15 relative error 9.104763805472358e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.7007963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.700796326764066 Order of pole (three term test) 1.0016606218122232e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y[1] (closed_form) 2.4507483765182263 y[1] (numeric) 2.450748376518225 absolute error 1.3322676295501878e-15 relative error 5.436166529029545e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.6907963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6907963267748116 Order of pole (three term test) 6.621217912643122e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y[1] (closed_form) 2.462969186536775 y[1] (numeric) 2.4629691865367724 absolute error 2.6645352591003757e-15 relative error 1.0818386497343989e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6807963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6807963267818851 Order of pole (three term test) 4.353293522027423e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y[1] (closed_form) 2.4754424435858153 y[1] (numeric) 2.475442443585812 absolute error 3.552713678800501e-15 relative error 1.435183309555846e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6707963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6707963267864948 Order of pole (three term test) 2.854155232670969e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y[1] (closed_form) 2.488174525373867 y[1] (numeric) 2.488174525373864 absolute error 3.1086244689504383e-15 relative error 1.2493594951838613e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6607963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6607963267894958 Order of pole (three term test) 1.8613280048577267e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y[1] (closed_form) 2.501172108173523 y[1] (numeric) 2.50117210817352 absolute error 3.1086244689504383e-15 relative error 1.242867077716018e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6507963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6507963267914519 Order of pole (three term test) 1.206549705571506e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y[1] (closed_form) 2.5144421851686616 y[1] (numeric) 2.514442185168658 absolute error 3.552713678800501e-15 relative error 1.4129231921720225e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6407963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6407963267926974 Order of pole (three term test) 7.814559304745372e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y[1] (closed_form) 2.5279920862470626 y[1] (numeric) 2.5279920862470586 absolute error 3.9968028886505635e-15 relative error 1.581018750174977e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6307963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6307963267935018 Order of pole (three term test) 5.033651029699896e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y[1] (closed_form) 2.5418294993769632 y[1] (numeric) 2.5418294993769592 absolute error 3.9968028886505635e-15 relative error 1.5724118748445691e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6207963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6207963267940191 Order of pole (three term test) 3.22765569994697e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y[1] (closed_form) 2.555962493721842 y[1] (numeric) 2.555962493721838 absolute error 3.9968028886505635e-15 relative error 1.5637173465838515e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6107963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.6107963267943408 Order of pole (three term test) 2.0756598930177894e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y[1] (closed_form) 2.570399544665549 y[1] (numeric) 2.570399544665546 absolute error 3.1086244689504383e-15 relative error 1.209393487250606e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.6007963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.60079632679455 Order of pole (three term test) 1.315189641037449e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y[1] (closed_form) 2.5851495609401414 y[1] (numeric) 2.5851495609401383 absolute error 3.1086244689504383e-15 relative error 1.2024930843149845e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.5907963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5907963267946756 Order of pole (three term test) 8.578957455721484e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9900000000000008 y[1] (closed_form) 2.6002219140717493 y[1] (numeric) 2.6002219140717466 absolute error 2.6645352591003757e-15 relative error 1.0247337908663021e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.5807963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5807963267947645 Order of pole (three term test) 5.215941123734067e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0000000000000007 y[1] (closed_form) 2.6156264703860153 y[1] (numeric) 2.6156264703860135 absolute error 1.7763568394002505e-15 relative error 6.791324600481256e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5707963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5707963267948153 Order of pole (three term test) 3.1282943779388086e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0099999999999996 y[1] (closed_form) 2.6313736258445024 y[1] (numeric) 2.631373625844502 absolute error 4.440892098500626e-16 relative error 1.6876706731737436e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5607963270000005 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5607963267948427 Order of pole (three term test) 2.19676469566423e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0199999999999985 y[1] (closed_form) 2.6474743440177004 y[1] (numeric) 2.647474344017701 absolute error 4.440892098500626e-16 relative error 1.677407038347842e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5507963270000016 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5507963267948663 Order of pole (three term test) 1.3138734493069762e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0299999999999974 y[1] (closed_form) 2.6639401975394144 y[1] (numeric) 2.663940197539416 absolute error 1.7763568394002505e-15 relative error 6.668155843141702e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5407963270000027 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5407963267948797 Order of pole (three term test) 7.831533100014392e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0399999999999963 y[1] (closed_form) 2.680783413432427 y[1] (numeric) 2.6807834134324304 absolute error 3.552713678800501e-15 relative error 1.3252520367737096e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.5307963270000038 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5307963267948919 Order of pole (three term test) 3.6875367732038563e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0499999999999952 y[1] (closed_form) 2.6980169227472173 y[1] (numeric) 2.6980169227472226 absolute error 5.329070518200751e-15 relative error 1.9751805384432138e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.5207963270000049 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5207963267948886 Order of pole (three term test) 4.919562774547909e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.059999999999994 y[1] (closed_form) 2.715654415015488 y[1] (numeric) 2.7156544150154955 absolute error 7.549516567451064e-15 relative error 2.7799990034475753e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.510796327000006 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.5107963267948982 Order of pole (three term test) 2.0165070633912463e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.069999999999993 y[1] (closed_form) 2.7337103980897286 y[1] (numeric) 2.7337103980897384 absolute error 9.769962616701378e-15 relative error 3.573883547989745e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.5007963270000071 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.500796326794895 Order of pole (three term test) 3.248439063563655e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0799999999999919 y[1] (closed_form) 2.7522002640207033 y[1] (numeric) 2.752200264020715 absolute error 1.1546319456101628e-14 relative error 4.1953049736408176e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4907963270000082 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49079632679490354 Order of pole (three term test) 1.2844656544241854e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0899999999999908 y[1] (closed_form) 2.771140361718708 y[1] (numeric) 2.771140361718721 absolute error 1.3322676295501878e-14 relative error 4.807651203650663e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4807963270000093 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.48079632679489887 Order of pole (three term test) 3.9862542985536306e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0999999999999897 y[1] (closed_form) 2.7905480772542113 y[1] (numeric) 2.7905480772542264 absolute error 1.509903313490213e-14 relative error 5.410776921556922e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4707963270000104 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4707963267948967 Order of pole (three term test) 4.547731246069231e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1099999999999886 y[1] (closed_form) 2.8104419227821107 y[1] (numeric) 2.8104419227821276 absolute error 1.687538997430238e-14 relative error 6.004532538995542e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4607963270000115 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.46079632679489746 Order of pole (three term test) 5.646338381095418e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1199999999999875 y[1] (closed_form) 2.830841635225032 y[1] (numeric) 2.8308416352250507 absolute error 1.865174681370263e-14 relative error 6.588763773152555e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4507963270000126 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4507963267949093 Order of pole (three term test) 1.6464155379122894e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1299999999999863 y[1] (closed_form) 2.8517682860294555 y[1] (numeric) 2.8517682860294773 absolute error 2.1760371282653068e-14 relative error 7.630483650882534e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4407963270000137 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.44079632679490743 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1399999999999852 y[1] (closed_form) 2.87324440351954 y[1] (numeric) 2.8732444035195646 absolute error 2.4424906541753444e-14 relative error 8.500810620855817e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4307963270000148 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4307963267949084 Order of pole (three term test) 3.266435561584007e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1499999999999841 y[1] (closed_form) 2.895294109624292 y[1] (numeric) 2.895294109624319 absolute error 2.708944180085382e-14 relative error 9.356369603628655e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 Radius of convergence (given) for eq 1 0.4207963270000159 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4207963267949095 Order of pole (three term test) 2.217694516682388e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.159999999999983 y[1] (closed_form) 2.9179432730527655 y[1] (numeric) 2.9179432730527948 absolute error 2.930988785010413e-14 relative error 1.0044707901206042e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.410796327000017 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4107963267949123 Order of pole (three term test) 7.3352319513828e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.169999999999982 y[1] (closed_form) 2.941219681350006 y[1] (numeric) 2.941219681350037 absolute error 3.108624468950438e-14 relative error 1.0569167915820536e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.4007963270000181 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4007963267949122 Order of pole (three term test) 2.8331229722599857e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1799999999999808 y[1] (closed_form) 2.965153234696853 y[1] (numeric) 2.965153234696887 absolute error 3.419486915845482e-14 relative error 1.1532243513867096e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3907963270000192 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3907963267949138 Order of pole (three term test) 1.181501338052502e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1899999999999797 y[1] (closed_form) 2.989776164836439 y[1] (numeric) 2.9897761648364765 absolute error 3.730349362740526e-14 relative error 1.2477018870556823e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3807963270000203 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.38079632679491515 Order of pole (three term test) 1.4342966124849235e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1999999999999786 y[1] (closed_form) 3.0151232831406047 y[1] (numeric) 3.0151232831406443 absolute error 3.952393967665557e-14 relative error 1.3108565045302807e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3707963270000214 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.37079632679491786 Order of pole (three term test) 8.433967367119583e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2099999999999775 y[1] (closed_form) 3.041232262597803 y[1] (numeric) 3.041232262597846 absolute error 4.3076653355456074e-14 relative error 1.4164210305549057e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3607963270000225 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3607963267949148 Order of pole (three term test) 2.877667642876105e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2199999999999764 y[1] (closed_form) 3.0681439594452433 y[1] (numeric) 3.068143959445289 absolute error 4.574118861455645e-14 relative error 1.4908423209329133e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3507963270000236 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3507963267949175 Order of pole (three term test) 2.106124963971328e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2299999999999753 y[1] (closed_form) 3.095902781327071 y[1] (numeric) 3.0959027813271196 absolute error 4.8405723873656825e-14 relative error 1.5635414705402188e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3407963270000247 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.34079632679492305 Order of pole (three term test) 2.2272965970981065e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2399999999999742 y[1] (closed_form) 3.1245571102957586 y[1] (numeric) 3.124557110295809 absolute error 5.062616992290714e-14 relative error 1.62026706940604e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3307963270000258 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3307963267949192 Order of pole (three term test) 2.263933239053468e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2499999999999731 y[1] (closed_form) 3.154159790761873 y[1] (numeric) 3.154159790761926 absolute error 5.3290705182007514e-14 relative error 1.6895372687867341e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3207963270000269 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3207963267949223 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.259999999999972 y[1] (closed_form) 3.184768694738706 y[1] (numeric) 3.184768694738764 absolute error 5.773159728050814e-14 relative error 1.8127406670343674e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.310796327000028 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.31079632679492325 Order of pole (three term test) 1.0281411776837341e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.269999999999971 y[1] (closed_form) 3.216447379556299 y[1] (numeric) 3.21644737955636 absolute error 6.128431095930864e-14 relative error 1.9053416309195975e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.3007963270000291 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.30079632679492396 Order of pole (three term test) 9.136054835952368e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2799999999999698 y[1] (closed_form) 3.2492658568128756 y[1] (numeric) 3.24926585681294 absolute error 6.439293542825908e-14 relative error 1.981768752262719e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.2907963270000302 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.29079632679492506 Order of pole (three term test) 7.715650235178758e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2899999999999687 y[1] (closed_form) 3.2833014959319478 y[1] (numeric) 3.283301495932016 absolute error 6.838973831690964e-14 relative error 2.0829563901349113e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.2807963270000313 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.28079632679492955 Order of pole (three term test) 1.2341779721151515e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2999999999999676 y[1] (closed_form) 3.318640091629052 y[1] (numeric) 3.3186400916291245 absolute error 7.238654120556021e-14 relative error 2.181210954093764e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.2707963270000324 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2707963267949279 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3099999999999665 y[1] (closed_form) 3.355377132316079 y[1] (numeric) 3.355377132316155 absolute error 7.638334409421077e-14 relative error 2.2764458682916065e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.2607963270000335 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2607963267949274 Order of pole (three term test) 2.638881992105344e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3199999999999654 y[1] (closed_form) 3.393619316613149 y[1] (numeric) 3.39361931661323 absolute error 8.08242361927114e-14 relative error 2.3816529979377424e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.2507963270000346 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.25079632679493086 Order of pole (three term test) 8.736876978596626e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3299999999999643 y[1] (closed_form) 3.4334863785845537 y[1] (numeric) 3.4334863785846395 absolute error 8.570921750106208e-14 relative error 2.496273701146748e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.24079632700003573 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24079632679492968 Order of pole (three term test) 2.1507789233904818e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3399999999999632 y[1] (closed_form) 3.4751133003291814 y[1] (numeric) 3.4751133003292716 absolute error 9.015010959956271e-14 relative error 2.5941631770976563e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.23079632700003683 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23079632679493367 Order of pole (three term test) 1.2226196364323065e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3499999999999621 y[1] (closed_form) 3.5186530149602184 y[1] (numeric) 3.5186530149603135 absolute error 9.50350909079134e-14 relative error 2.7008940780421867e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.22079632700003793 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2207963267949321 Order of pole (three term test) 1.2749029444934255e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.359999999999961 y[1] (closed_form) 3.564279736472824 y[1] (numeric) 3.5642797364729253 absolute error 1.0125233984581428e-13 relative error 2.840751774046012e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.21079632700003903 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.21079632679493726 Order of pole (three term test) 2.4192016215656054e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.36999999999996 y[1] (closed_form) 3.6121930994905003 y[1] (numeric) 3.6121930994906064 absolute error 1.0613732115416497e-13 relative error 2.938306957320073e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.20079632700004013 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.20079632679493395 Order of pole (three term test) 2.0693188045364386e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3799999999999588 y[1] (closed_form) 3.6626233574001663 y[1] (numeric) 3.662623357400278 absolute error 1.1146639167236572e-13 relative error 3.043348463531006e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.19079632700004123 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.19079632679493824 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3899999999999577 y[1] (closed_form) 3.7158379811675877 y[1] (numeric) 3.715837981167706 absolute error 1.1812772982011666e-13 relative error 3.179033381401593e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.18079632700004233 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1807963267949379 Order of pole (three term test) 1.0616074673937807e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3999999999999566 y[1] (closed_form) 3.7721501376694473 y[1] (numeric) 3.7721501376695716 absolute error 1.2434497875801753e-13 relative error 3.296395271128889e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.17079632700004344 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.17079632679493928 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4099999999999555 y[1] (closed_form) 3.8319297289556067 y[1] (numeric) 3.8319297289557377 absolute error 1.3100631690576847e-13 relative error 3.4188079159132772e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.16079632700004454 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1607963267949424 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4199999999999544 y[1] (closed_form) 3.8956179807142446 y[1] (numeric) 3.8956179807143823 absolute error 1.376676550535194e-13 relative error 3.5339105562984038e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.15079632700004564 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1507963267949421 Order of pole (three term test) 1.0317566465961992e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4299999999999533 y[1] (closed_form) 3.963747043924039 y[1] (numeric) 3.9637470439241844 absolute error 1.4521717162097048e-13 relative error 3.663633678228065e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.14079632700004674 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.14079632679494405 Order of pole (three term test) 7.029478498101435e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4399999999999522 y[1] (closed_form) 4.036966830539075 y[1] (numeric) 4.036966830539229 absolute error 1.5365486660812167e-13 relative error 3.8061959153527005e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.13079632700004784 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1307963267949441 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.449999999999951 y[1] (closed_form) 4.116082544013317 y[1] (numeric) 4.116082544013478 absolute error 1.616484723854228e-13 relative error 3.927240784335928e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.12079632700004894 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.12079632679494587 Order of pole (three term test) 1.251767366330203e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.45999999999995 y[1] (closed_form) 4.2021084657464485 y[1] (numeric) 4.202108465746621 absolute error 1.723066134218243e-13 relative error 4.100479909702101e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.11079632700005004 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11079632679494582 Order of pole (three term test) 2.2567841981524467e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.469999999999949 y[1] (closed_form) 4.29634725495213 y[1] (numeric) 4.296347254952313 absolute error 1.829647544582258e-13 relative error 4.258611876573379e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.10079632700005114 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1007963267949463 Order of pole (three term test) 2.4825530414968933e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4799999999999478 y[1] (closed_form) 4.40051082125701 y[1] (numeric) 4.400510821257202 absolute error 1.9273471707492718e-13 relative error 4.3798259998340906e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.09079632700005225 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09079632679494898 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4899999999999467 y[1] (closed_form) 4.5169120195345895 y[1] (numeric) 4.516912019534796 absolute error 2.0605739337042905e-13 relative error 4.56190850030461e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.08079632700005335 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.08079632679494937 Order of pole (three term test) 1.5519452308937594e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4999999999999456 y[1] (closed_form) 4.648783653977668 y[1] (numeric) 4.6487836539778895 absolute error 2.2115642650533118e-13 relative error 4.757296595553585e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Radius of convergence (given) for eq 1 0.07079632700005445 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.07079632679495124 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; Iterations 1501 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.13333333332969%