##############ECHO OF PROBLEM################# ##############temp/sing4postode.ode################# diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-2.0); x_end=c(-1.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.1); glob_max_h=c(0.001); glob_min_h=c(0.001); glob_type_given_pole=2; array_given_rad_poles[1][1]=c(0.0); array_given_rad_poles[1][2]=c(1.0); array_given_ord_poles[1][1]=c(1.0); array_given_ord_poles[1][2]=c(0.0); /* 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 */ double exact_soln_y (double x) { return(c(1.0) / (c(x) * c( x) + c(1.0))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (closed_form) = 0.2 y[1] (numeric) = 0.2 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.990000000000001 y[1] (closed_form) = 0.201608838531481 y[1] (numeric) = 0.2016088385314813 absolute error = 2.220446049250313e-16 relative error = 1.101363444888649e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 2.227 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.227 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.980000000000002 y[1] (closed_form) = 0.203235509308186 y[1] (numeric) = 0.2032355093081864 absolute error = 4.163336342344337e-16 relative error = 2.048528013887111e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 2.218 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.218 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.970000000000003 y[1] (closed_form) = 0.2048802474953384 y[1] (numeric) = 0.2048802474953391 absolute error = 6.38378239159465e-16 relative error = 3.115860347513441e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 2.209 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.209 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.960000000000004 y[1] (closed_form) = 0.2065432914738922 y[1] (numeric) = 0.206543291473893 absolute error = 8.049116928532385e-16 relative error = 3.897060452118253e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.2 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.950000000000006 y[1] (closed_form) = 0.2082248828735024 y[1] (numeric) = 0.2082248828735034 absolute error = 9.992007221626409e-16 relative error = 4.798661468186105e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 2.191 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.191 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.940000000000007 y[1] (closed_form) = 0.2099252666050875 y[1] (numeric) = 0.2099252666050886 absolute error = 1.137978600240785e-15 relative error = 5.420874860107034e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 2.183 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.183 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.930000000000008 y[1] (closed_form) = 0.2116446908929276 y[1] (numeric) = 0.211644690892929 absolute error = 1.360023205165817e-15 relative error = 6.425973642088009e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 2.174 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.174 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.920000000000009 y[1] (closed_form) = 0.2133834073062463 y[1] (numeric) = 0.2133834073062479 absolute error = 1.52655665885959e-15 relative error = 7.154055126079635e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 2.165 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.165 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.91000000000001 y[1] (closed_form) = 0.2151416707902136 y[1] (numeric) = 0.2151416707902153 absolute error = 1.720845688168993e-15 relative error = 7.998662843178359e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 2.156 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.156 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.900000000000011 y[1] (closed_form) = 0.2169197396963104 y[1] (numeric) = 0.2169197396963123 absolute error = 1.915134717478395e-15 relative error = 8.828771047575481e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.147 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.890000000000012 y[1] (closed_form) = 0.218717875811988 y[1] (numeric) = 0.21871787581199 absolute error = 2.05391259555654e-15 relative error = 9.390693778144148e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 2.138 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.138 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.880000000000013 y[1] (closed_form) = 0.220536344389553 y[1] (numeric) = 0.2205363443895553 absolute error = 2.275957200481571e-15 relative error = 1.032010032986375e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.129 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.129 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.870000000000014 y[1] (closed_form) = 0.2223754141742063 y[1] (numeric) = 0.2223754141742087 absolute error = 2.442490654175344e-15 relative error = 1.098363622276124e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.121 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.121 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.860000000000015 y[1] (closed_form) = 0.2242353574311569 y[1] (numeric) = 0.2242353574311595 absolute error = 2.664535259100376e-15 relative error = 1.188276144148419e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.112 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.112 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.850000000000017 y[1] (closed_form) = 0.2261164499717323 y[1] (numeric) = 0.2261164499717352 absolute error = 2.886579864025407e-15 relative error = 1.276589944865254e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.103 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.840000000000018 y[1] (closed_form) = 0.2280189711783987 y[1] (numeric) = 0.2280189711784017 absolute error = 3.05311331771918e-15 relative error = 1.338973376618944e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.094 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.094 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.830000000000019 y[1] (closed_form) = 0.2299432040286014 y[1] (numeric) = 0.2299432040286046 absolute error = 3.247402347028583e-15 relative error = 1.412262806699282e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.085 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.085 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.82000000000002 y[1] (closed_form) = 0.2318894351173322 y[1] (numeric) = 0.2318894351173357 absolute error = 3.524958103184872e-15 relative error = 1.52010293241747e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.077 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.810000000000021 y[1] (closed_form) = 0.2338579546783242 y[1] (numeric) = 0.233857954678328 absolute error = 3.747002708109903e-15 relative error = 1.602255828014904e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.068 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.800000000000022 y[1] (closed_form) = 0.2358490566037692 y[1] (numeric) = 0.2358490566037731 absolute error = 3.913536161803677e-15 relative error = 1.65933933260479e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.059 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.059 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.790000000000023 y[1] (closed_form) = 0.2378630384624486 y[1] (numeric) = 0.2378630384624528 absolute error = 4.163336342344337e-15 relative error = 1.750308231685017e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.05 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.780000000000024 y[1] (closed_form) = 0.2399002015161643 y[1] (numeric) = 0.2399002015161687 absolute error = 4.357625371653739e-15 relative error = 1.816432559920182e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.042 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.042 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.770000000000025 y[1] (closed_form) = 0.2419608507343459 y[1] (numeric) = 0.2419608507343505 absolute error = 4.579669976578771e-15 relative error = 1.892731804620281e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.033 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.033 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.760000000000026 y[1] (closed_form) = 0.2440452948067106 y[1] (numeric) = 0.2440452948067154 absolute error = 4.801714581503802e-15 relative error = 1.967550566917043e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.024 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.024 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.750000000000028 y[1] (closed_form) = 0.2461538461538403 y[1] (numeric) = 0.2461538461538453 absolute error = 4.968248035197576e-15 relative error = 2.018350764299063e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.016 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.016 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.740000000000029 y[1] (closed_form) = 0.2482868209355386 y[1] (numeric) = 0.2482868209355438 absolute error = 5.190292640122607e-15 relative error = 2.090442263735833e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 2.007 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.007 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.73000000000003 y[1] (closed_form) = 0.2504445390568194 y[1] (numeric) = 0.2504445390568248 absolute error = 5.440092820663267e-15 relative error = 2.172174662362692e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.998 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.998 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.720000000000031 y[1] (closed_form) = 0.2526273241713756 y[1] (numeric) = 0.2526273241713813 absolute error = 5.717648576819556e-15 relative error = 2.263274012648314e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.99 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.710000000000032 y[1] (closed_form) = 0.2548355036823659 y[1] (numeric) = 0.2548355036823718 absolute error = 5.939693181744587e-15 relative error = 2.330795001448459e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.981 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.981 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.700000000000033 y[1] (closed_form) = 0.2570694087403524 y[1] (numeric) = 0.2570694087403587 absolute error = 6.217248937900877e-15 relative error = 2.418509836843511e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.972 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.972 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.690000000000034 y[1] (closed_form) = 0.2593293742382122 y[1] (numeric) = 0.2593293742382186 absolute error = 6.439293542825908e-15 relative error = 2.483055983049173e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.964 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.964 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.680000000000035 y[1] (closed_form) = 0.2616157388028383 y[1] (numeric) = 0.2616157388028449 absolute error = 6.661338147750939e-15 relative error = 2.546229893596398e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.955 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.955 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.670000000000036 y[1] (closed_form) = 0.2639288447834379 y[1] (numeric) = 0.2639288447834449 absolute error = 6.994405055138486e-15 relative error = 2.650110131341506e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.947 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.947 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.660000000000037 y[1] (closed_form) = 0.2662690382362251 y[1] (numeric) = 0.2662690382362323 absolute error = 7.16093850883226e-15 relative error = 2.689362066377132e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.938 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.938 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.650000000000039 y[1] (closed_form) = 0.2686366689052964 y[1] (numeric) = 0.2686366689053038 absolute error = 7.382983113757291e-15 relative error = 2.748315464096245e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.929 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.929 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.64000000000004 y[1] (closed_form) = 0.2710320901994701 y[1] (numeric) = 0.2710320901994778 absolute error = 7.716050021144838e-15 relative error = 2.8469138158017e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.921 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.921 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.630000000000041 y[1] (closed_form) = 0.2734556591648565 y[1] (numeric) = 0.2734556591648645 absolute error = 7.993605777301127e-15 relative error = 2.923181696701355e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.912 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.912 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.620000000000042 y[1] (closed_form) = 0.2759077364529198 y[1] (numeric) = 0.275907736452928 absolute error = 8.215650382226158e-15 relative error = 2.97768032453416e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.904 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.904 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.610000000000043 y[1] (closed_form) = 0.2783886862837787 y[1] (numeric) = 0.2783886862837873 absolute error = 8.548717289613705e-15 relative error = 3.070784737602257e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.895 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.895 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.600000000000044 y[1] (closed_form) = 0.2808988764044832 y[1] (numeric) = 0.2808988764044922 absolute error = 8.93729534823251e-15 relative error = 3.1816771439709e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.887 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.590000000000045 y[1] (closed_form) = 0.2834386780419941 y[1] (numeric) = 0.2834386780420033 absolute error = 9.270362255620057e-15 relative error = 3.270676507405445e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.878 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.878 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.580000000000046 y[1] (closed_form) = 0.2860084658505772 y[1] (numeric) = 0.2860084658505868 absolute error = 9.603429163007604e-15 relative error = 3.357742972554119e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.87 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.570000000000047 y[1] (closed_form) = 0.2886086178533167 y[1] (numeric) = 0.2886086178533266 absolute error = 9.880984919163893e-15 relative error = 3.423662464641244e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.861 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.861 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.560000000000048 y[1] (closed_form) = 0.2912395153774336 y[1] (numeric) = 0.2912395153774437 absolute error = 1.010302952408892e-14 relative error = 3.468976217391326e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.853 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.853 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.55000000000005 y[1] (closed_form) = 0.2939015429830874 y[1] (numeric) = 0.2939015429830978 absolute error = 1.038058528024521e-14 relative error = 3.531994141603593e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.845 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.540000000000051 y[1] (closed_form) = 0.2965950883853226 y[1] (numeric) = 0.2965950883853333 absolute error = 1.06581410364015e-14 relative error = 3.593498831833297e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.836 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.530000000000052 y[1] (closed_form) = 0.2993205423688086 y[1] (numeric) = 0.2993205423688195 absolute error = 1.093569679255779e-14 relative error = 3.653506941425806e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.828 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.828 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.520000000000053 y[1] (closed_form) = 0.3020782986950071 y[1] (numeric) = 0.3020782986950183 absolute error = 1.126876369994534e-14 relative error = 3.730411535230086e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.819 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.819 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.510000000000054 y[1] (closed_form) = 0.3048687540013872 y[1] (numeric) = 0.3048687540013987 absolute error = 1.149080830487037e-14 relative error = 3.769100032080717e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.811 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.811 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.500000000000055 y[1] (closed_form) = 0.3076923076922921 y[1] (numeric) = 0.3076923076923038 absolute error = 1.176836406102666e-14 relative error = 3.824718319833859e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.803 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.803 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.490000000000056 y[1] (closed_form) = 0.3105493618210453 y[1] (numeric) = 0.3105493618210574 absolute error = 1.204591981718295e-14 relative error = 3.878906640331283e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.794 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.794 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.480000000000057 y[1] (closed_form) = 0.313440320962872 y[1] (numeric) = 0.3134403209628844 absolute error = 1.23789867245705e-14 relative error = 3.949391924607181e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.786 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.786 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.470000000000058 y[1] (closed_form) = 0.3163655920781884 y[1] (numeric) = 0.3163655920782011 absolute error = 1.271205363195804e-14 relative error = 4.018153032525836e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.778 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.778 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.460000000000059 y[1] (closed_form) = 0.3193255843658017 y[1] (numeric) = 0.3193255843658147 absolute error = 1.304512053934559e-14 relative error = 4.085209948101691e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.77 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.450000000000061 y[1] (closed_form) = 0.3223207091055418 y[1] (numeric) = 0.3223207091055551 absolute error = 1.332267629550188e-14 relative error = 4.133360320679692e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.761 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.761 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.440000000000062 y[1] (closed_form) = 0.3253513794898302 y[1] (numeric) = 0.3253513794898438 absolute error = 1.354472090042691e-14 relative error = 4.163105415955456e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.753 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.753 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.430000000000063 y[1] (closed_form) = 0.3284180104436734 y[1] (numeric) = 0.3284180104436872 absolute error = 1.38222766565832e-14 relative error = 4.208745019163267e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.745 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.745 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.420000000000064 y[1] (closed_form) = 0.3315210184325487 y[1] (numeric) = 0.3315210184325629 absolute error = 1.4210854715202e-14 relative error = 4.286562216293791e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.737 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.737 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.410000000000065 y[1] (closed_form) = 0.3346608212576349 y[1] (numeric) = 0.3346608212576493 absolute error = 1.448841047135829e-14 relative error = 4.329281932946837e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.729 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.729 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.400000000000066 y[1] (closed_form) = 0.3378378378378167 y[1] (numeric) = 0.3378378378378316 absolute error = 1.48769885299771e-14 relative error = 4.403588604873496e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.72 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.390000000000067 y[1] (closed_form) = 0.3410524879778781 y[1] (numeric) = 0.3410524879778933 absolute error = 1.52655665885959e-14 relative error = 4.47601677944249e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.712 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.712 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.380000000000068 y[1] (closed_form) = 0.3443051921222749 y[1] (numeric) = 0.3443051921222905 absolute error = 1.565414464721471e-14 relative error = 4.546589771337335e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.704 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.704 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.370000000000069 y[1] (closed_form) = 0.3475963710938628 y[1] (numeric) = 0.3475963710938789 absolute error = 1.609823385706477e-14 relative error = 4.631300898339269e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.696 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.696 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.36000000000007 y[1] (closed_form) = 0.3509264458169332 y[1] (numeric) = 0.3509264458169497 absolute error = 1.648681191568357e-14 relative error = 4.698081923493507e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.688 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.688 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.350000000000072 y[1] (closed_form) = 0.3542958370238907 y[1] (numeric) = 0.3542958370239075 absolute error = 1.687538997430238e-14 relative error = 4.763078820247173e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.68 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.340000000000073 y[1] (closed_form) = 0.3577049649448885 y[1] (numeric) = 0.3577049649449057 absolute error = 1.720845688168993e-14 relative error = 4.810796205845571e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.672 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.672 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.330000000000074 y[1] (closed_form) = 0.3611542489797137 y[1] (numeric) = 0.3611542489797313 absolute error = 1.765254609153999e-14 relative error = 4.887813487286854e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.664 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.664 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.320000000000075 y[1] (closed_form) = 0.3646441073511989 y[1] (numeric) = 0.3646441073512169 absolute error = 1.804112415015879e-14 relative error = 4.947597886939905e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.656 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.656 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.310000000000076 y[1] (closed_form) = 0.3681749567394156 y[1] (numeric) = 0.368174956739434 absolute error = 1.837419105754634e-14 relative error = 4.990614033140527e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.648 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.648 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.300000000000077 y[1] (closed_form) = 0.3717472118958831 y[1] (numeric) = 0.3717472118959019 absolute error = 1.88182802673964e-14 relative error = 5.062117391930009e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.64 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.290000000000078 y[1] (closed_form) = 0.3753612852370122 y[1] (numeric) = 0.3753612852370314 absolute error = 1.926236947724647e-14 relative error = 5.131687852433621e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.632 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.632 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.280000000000079 y[1] (closed_form) = 0.3790175864159805 y[1] (numeric) = 0.3790175864160002 absolute error = 1.970645868709653e-14 relative error = 5.199352060003949e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.624 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.624 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.27000000000008 y[1] (closed_form) = 0.3827165218722193 y[1] (numeric) = 0.3827165218722394 absolute error = 2.003952559448408e-14 relative error = 5.236127642583153e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.616 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.616 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.260000000000081 y[1] (closed_form) = 0.3864584943576753 y[1] (numeric) = 0.3864584943576957 absolute error = 2.037259250187162e-14 relative error = 5.271612035784719e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.609 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.609 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.250000000000083 y[1] (closed_form) = 0.3902439024389929 y[1] (numeric) = 0.3902439024390137 absolute error = 2.081668171172169e-14 relative error = 5.334274688629112e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.601 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.601 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.240000000000084 y[1] (closed_form) = 0.3940731399747471 y[1] (numeric) = 0.3940731399747684 absolute error = 2.131628207280301e-14 relative error = 5.409219738794933e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.593 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.593 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.230000000000085 y[1] (closed_form) = 0.3979465955668419 y[1] (numeric) = 0.3979465955668637 absolute error = 2.187139358511558e-14 relative error = 5.496062494004152e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.585 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.585 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.220000000000086 y[1] (closed_form) = 0.4018646519851775 y[1] (numeric) = 0.4018646519851998 absolute error = 2.225997164373439e-14 relative error = 5.539171343827332e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.577 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.577 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.210000000000087 y[1] (closed_form) = 0.4058276855646745 y[1] (numeric) = 0.4058276855646972 absolute error = 2.270406085358445e-14 relative error = 5.594507634932223e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.57 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.200000000000088 y[1] (closed_form) = 0.4098360655737349 y[1] (numeric) = 0.4098360655737581 absolute error = 2.320366121466577e-14 relative error = 5.661693336378939e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.562 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.562 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.190000000000089 y[1] (closed_form) = 0.4138901535532106 y[1] (numeric) = 0.4138901535532342 absolute error = 2.359223927328458e-14 relative error = 5.700120930818788e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.554 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.554 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.18000000000009 y[1] (closed_form) = 0.4179903026249419 y[1] (numeric) = 0.4179903026249659 absolute error = 2.403632848313464e-14 relative error = 5.750451226305643e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.547 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.547 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.170000000000091 y[1] (closed_form) = 0.4221368567689264 y[1] (numeric) = 0.4221368567689509 absolute error = 2.44804176929847e-14 relative error = 5.79916614729167e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.539 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.539 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.160000000000093 y[1] (closed_form) = 0.4263301500681738 y[1] (numeric) = 0.4263301500681987 absolute error = 2.492450690283476e-14 relative error = 5.846292339129457e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.532 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.532 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.150000000000094 y[1] (closed_form) = 0.4305705059203045 y[1] (numeric) = 0.4305705059203299 absolute error = 2.542410726391608e-14 relative error = 5.904748912045058e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.524 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.524 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.140000000000095 y[1] (closed_form) = 0.4348582362149531 y[1] (numeric) = 0.434858236214979 absolute error = 2.586819647376615e-14 relative error = 5.948650461107821e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.516 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.516 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.130000000000096 y[1] (closed_form) = 0.4391936404760441 y[1] (numeric) = 0.4391936404760705 absolute error = 2.636779683484747e-14 relative error = 6.003683661326991e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.509 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.509 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.120000000000097 y[1] (closed_form) = 0.4435770049680197 y[1] (numeric) = 0.4435770049680466 absolute error = 2.692290834716005e-14 relative error = 6.069500457784345e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.501 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.501 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.110000000000098 y[1] (closed_form) = 0.4480086017651102 y[1] (numeric) = 0.4480086017651376 absolute error = 2.742250870824137e-14 relative error = 6.120978168767153e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.494 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.494 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.100000000000099 y[1] (closed_form) = 0.4524886877827608 y[1] (numeric) = 0.4524886877827888 absolute error = 2.797762022055394e-14 relative error = 6.183054068743032e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.487 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.487 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.0900000000001 y[1] (closed_form) = 0.4570175037703488 y[1] (numeric) = 0.4570175037703772 absolute error = 2.842170943040401e-14 relative error = 6.218954240467322e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.479 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.479 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.080000000000101 y[1] (closed_form) = 0.4615952732643551 y[1] (numeric) = 0.4615952732643842 absolute error = 2.903233209394784e-14 relative error = 6.289564424833497e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.472 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.472 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.070000000000102 y[1] (closed_form) = 0.4662222015011879 y[1] (numeric) = 0.4662222015012174 absolute error = 2.953193245502916e-14 relative error = 6.334304192279852e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.465 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.465 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.060000000000104 y[1] (closed_form) = 0.4708984742888946 y[1] (numeric) = 0.4708984742889248 absolute error = 3.0142555118573e-14 relative error = 6.401073004980824e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.457 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.050000000000105 y[1] (closed_form) = 0.4756242568370491 y[1] (numeric) = 0.4756242568370796 absolute error = 3.05311331771918e-14 relative error = 6.419170750505247e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.45 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.040000000000106 y[1] (closed_form) = 0.4803996925441459 y[1] (numeric) = 0.4803996925441771 absolute error = 3.114175584073564e-14 relative error = 6.482467895808217e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.443 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.443 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.030000000000107 y[1] (closed_form) = 0.4852249017419056 y[1] (numeric) = 0.4852249017419372 absolute error = 3.164135620181696e-14 relative error = 6.520967099633154e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.436 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.436 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.020000000000108 y[1] (closed_form) = 0.4900999803959479 y[1] (numeric) = 0.49009998039598 absolute error = 3.214095656289828e-14 relative error = 6.558040777094473e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.428 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.428 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.010000000000109 y[1] (closed_form) = 0.4950249987623835 y[1] (numeric) = 0.4950249987624161 absolute error = 3.26405569239796e-14 relative error = 6.593718904213839e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.421 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.421 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.00000000000011 y[1] (closed_form) = 0.4999999999999449 y[1] (numeric) = 0.4999999999999781 absolute error = 3.319566843629218e-14 relative error = 6.639133687259167e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; Iterations = 1001 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %