##############ECHO OF PROBLEM################# ##############temp/sin_sqrt_linpostode.ode################# diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=2.0; x_end=3.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.000005; glob_upper_ratio_limit=1.001; glob_lower_ratio_limit=0.999; glob_type_given_pole=1; array_given_rad_poles[1][1]=-1.5; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.5; array_given_ord_poles[1][2]=0.0; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(sin(sqrt(2.0*x+3.0))-sqrt(2.0*x+3.0)*cos(sqrt(2.0*x+3.0))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 1000000 step_error = 1e-13 est_needed_step_err = 1e-13 opt_iter = 1 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 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 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 1000000 step_error = 2.80289196959102e-13 est_needed_step_err = 2.80289196959102e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.791154658409449e-240 estimated_step_error = 1.791154658409449e-240 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 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 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 500000 step_error = 3.963887837262257e-13 est_needed_step_err = 3.963887837262257e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.230871943468012e-229 estimated_step_error = 1.230871943468012e-229 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 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 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 250000 step_error = 5.60578393918204e-13 est_needed_step_err = 5.60578393918204e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.45848531622724e-219 estimated_step_error = 8.45848531622724e-219 Double H and LOOP opt_iter = 4 SETTING H FOR MAX H Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 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 = 2.5 Order of pole (six term test) = -1.313 START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 2.80289196959102 y[1] (numeric) = 2.80289196959102 absolute error = 0 relative error = 0 % Correct digits = 16 h = 5e-06 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 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 = 4 Order of pole (six term test) = -1.313 TOP MAIN SOLVE Loop x[1] = 2.010004999999621 y[1] (analytic) = 2.807635424524277 y[1] (numeric) = 2.807635432842287 absolute error = 8.318009836472129e-09 relative error = 2.962638868214709e-07 % Correct digits = 9 h = 5e-06 Radius of convergence (given) for eq 1 = 3.51 Order of pole (given) = 0.5 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 = 4.007 Order of pole (six term test) = -1.315 TOP MAIN SOLVE Loop x[1] = 2.020004999999243 y[1] (analytic) = 2.812343235871377 y[1] (numeric) = 2.812343252508223 absolute error = 1.6636846567053e-08 relative error = 5.915652952616303e-07 % Correct digits = 9 h = 5e-06 Radius of convergence (given) for eq 1 = 3.52 Order of pole (given) = 0.5 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 = 4.014 Order of pole (six term test) = -1.317 TOP MAIN SOLVE Loop x[1] = 2.030004999998864 y[1] (analytic) = 2.817017762851848 y[1] (numeric) = 2.817017787812371 absolute error = 2.496052298184281e-08 relative error = 8.860619663460578e-07 % Correct digits = 9 h = 5e-06 Radius of convergence (given) for eq 1 = 3.53 Order of pole (given) = 0.5 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 = 4.021 Order of pole (six term test) = -1.318 TOP MAIN SOLVE Loop x[1] = 2.040004999998486 y[1] (analytic) = 2.821658986385467 y[1] (numeric) = 2.821659019674371 absolute error = 3.328890407772178e-08 relative error = 1.179763544721069e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.54 Order of pole (given) = 0.5 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 = 4.028 Order of pole (six term test) = -1.32 TOP MAIN SOLVE Loop x[1] = 2.050004999998107 y[1] (analytic) = 2.826266887943633 y[1] (numeric) = 2.826266929565469 absolute error = 4.162183619982329e-08 relative error = 1.472678902950562e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.55 Order of pole (given) = 0.5 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 = 4.035 Order of pole (six term test) = -1.322 TOP MAIN SOLVE Loop x[1] = 2.060004999997728 y[1] (analytic) = 2.83084144954575 y[1] (numeric) = 2.830841499504948 absolute error = 4.995919811179306e-08 relative error = 1.76481795262005e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.56 Order of pole (given) = 0.5 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 = 4.042 Order of pole (six term test) = -1.323 TOP MAIN SOLVE Loop x[1] = 2.07000499999735 y[1] (analytic) = 2.835382653755619 y[1] (numeric) = 2.835382712056471 absolute error = 5.830085170188681e-08 relative error = 2.056189898201717e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.57 Order of pole (given) = 0.5 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 = 4.049 Order of pole (six term test) = -1.325 TOP MAIN SOLVE Loop x[1] = 2.080004999996971 y[1] (analytic) = 2.839890483677875 y[1] (numeric) = 2.839890550324536 absolute error = 6.664666107880635e-08 relative error = 2.346803915920512e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.58 Order of pole (given) = 0.5 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 = 4.056 Order of pole (six term test) = -1.327 TOP MAIN SOLVE Loop x[1] = 2.090004999996593 y[1] (analytic) = 2.84436492295444 y[1] (numeric) = 2.84436499795094 absolute error = 7.499650012121606e-08 relative error = 2.636669420157145e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.59 Order of pole (given) = 0.5 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 = 4.063 Order of pole (six term test) = -1.329 TOP MAIN SOLVE Loop x[1] = 2.100004999996214 y[1] (analytic) = 2.848805955761007 y[1] (numeric) = 2.848806039111232 absolute error = 8.335022494421196e-08 relative error = 2.925795095859607e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 0.5 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 = 4.07 Order of pole (six term test) = -1.33 TOP MAIN SOLVE Loop x[1] = 2.110004999995835 y[1] (analytic) = 2.853213566803553 y[1] (numeric) = 2.853213658511249 absolute error = 9.170769565969294e-08 relative error = 3.214189667632655e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.61 Order of pole (given) = 0.5 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 = 4.077 Order of pole (six term test) = -1.332 TOP MAIN SOLVE Loop x[1] = 2.120004999995457 y[1] (analytic) = 2.857587741314874 y[1] (numeric) = 2.857587841383674 absolute error = 1.000688008012673e-07 relative error = 3.501862754885079e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.62 Order of pole (given) = 0.5 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 = 4.084 Order of pole (six term test) = -1.334 TOP MAIN SOLVE Loop x[1] = 2.130004999995078 y[1] (analytic) = 2.861928465051146 y[1] (numeric) = 2.861928573484532 absolute error = 1.084333858258901e-07 relative error = 3.788822367506391e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.63 Order of pole (given) = 0.5 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 = 4.091 Order of pole (six term test) = -1.335 TOP MAIN SOLVE Loop x[1] = 2.1400049999947 y[1] (analytic) = 2.866235724288521 y[1] (numeric) = 2.86623584108987 absolute error = 1.168013494812215e-07 relative error = 4.07507828094686e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.64 Order of pole (given) = 0.5 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 = 4.098 Order of pole (six term test) = -1.337 TOP MAIN SOLVE Loop x[1] = 2.150004999994321 y[1] (analytic) = 2.870509505819735 y[1] (numeric) = 2.87050963099228 absolute error = 1.251725447737329e-07 relative error = 4.360638573742928e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.65 Order of pole (given) = 0.5 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 = 4.105 Order of pole (six term test) = -1.339 TOP MAIN SOLVE Loop x[1] = 2.160004999993943 y[1] (analytic) = 2.874749796950753 y[1] (numeric) = 2.874749930497602 absolute error = 1.335468491348024e-07 relative error = 4.64551208165857e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.66 Order of pole (given) = 0.5 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 = 4.112 Order of pole (six term test) = -1.34 TOP MAIN SOLVE Loop x[1] = 2.170004999993564 y[1] (analytic) = 2.878956585497431 y[1] (numeric) = 2.878956727421573 absolute error = 1.419241426603435e-07 relative error = 4.929707636970899e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.67 Order of pole (given) = 0.5 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 = 4.118 Order of pole (six term test) = -1.342 TOP MAIN SOLVE Loop x[1] = 2.180004999993185 y[1] (analytic) = 2.883129859782211 y[1] (numeric) = 2.883130010086494 absolute error = 1.503042836858981e-07 relative error = 5.213233222080811e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.68 Order of pole (given) = 0.5 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 = 4.125 Order of pole (six term test) = -1.344 TOP MAIN SOLVE Loop x[1] = 2.190004999992807 y[1] (analytic) = 2.88726960863083 y[1] (numeric) = 2.88726976731799 absolute error = 1.586871607450746e-07 relative error = 5.496097775930442e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.69 Order of pole (given) = 0.5 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 = 4.132 Order of pole (six term test) = -1.345 TOP MAIN SOLVE Loop x[1] = 2.200004999992428 y[1] (analytic) = 2.891375821369063 y[1] (numeric) = 2.891375988441716 absolute error = 1.670726530456079e-07 relative error = 5.778309820910767e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 0.5 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 = 4.139 Order of pole (six term test) = -1.347 TOP MAIN SOLVE Loop x[1] = 2.21000499999205 y[1] (analytic) = 2.895448487819488 y[1] (numeric) = 2.895448663280081 absolute error = 1.754605931658659e-07 relative error = 6.059876178215219e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.71 Order of pole (given) = 0.5 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 = 4.146 Order of pole (six term test) = -1.349 TOP MAIN SOLVE Loop x[1] = 2.220004999991671 y[1] (analytic) = 2.89948759829827 y[1] (numeric) = 2.89948778214918 absolute error = 1.838509104956643e-07 relative error = 6.340806927526356e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.72 Order of pole (given) = 0.5 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 = 4.152 Order of pole (six term test) = -1.35 TOP MAIN SOLVE Loop x[1] = 2.230004999991293 y[1] (analytic) = 2.903493143611971 y[1] (numeric) = 2.903493335855442 absolute error = 1.922434713641508e-07 relative error = 6.621109878875009e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.73 Order of pole (given) = 0.5 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 = 4.159 Order of pole (six term test) = -1.352 TOP MAIN SOLVE Loop x[1] = 2.240004999990914 y[1] (analytic) = 2.907465115054388 y[1] (numeric) = 2.907465315692529 absolute error = 2.006381407682056e-07 relative error = 6.900792712157869e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.74 Order of pole (given) = 0.5 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 = 4.166 Order of pole (six term test) = -1.354 TOP MAIN SOLVE Loop x[1] = 2.250004999990535 y[1] (analytic) = 2.91140350440341 y[1] (numeric) = 2.911403713438212 absolute error = 2.090348028005451e-07 relative error = 7.179863680331026e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.75 Order of pole (given) = 0.5 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 = 4.172 Order of pole (six term test) = -1.355 TOP MAIN SOLVE Loop x[1] = 2.260004999990157 y[1] (analytic) = 2.915308303917894 y[1] (numeric) = 2.915308521351233 absolute error = 2.174333397775285e-07 relative error = 7.458330890263616e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.76 Order of pole (given) = 0.5 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 = 4.179 Order of pole (six term test) = -1.357 TOP MAIN SOLVE Loop x[1] = 2.270004999989778 y[1] (analytic) = 2.919179506334571 y[1] (numeric) = 2.919179732168213 absolute error = 2.258336415650319e-07 relative error = 7.73620262388718e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.77 Order of pole (given) = 0.5 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 = 4.186 Order of pole (six term test) = -1.358 TOP MAIN SOLVE Loop x[1] = 2.2800049999894 y[1] (analytic) = 2.923017104864976 y[1] (numeric) = 2.923017339100555 absolute error = 2.34235578489006e-07 relative error = 8.01348641098103e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.78 Order of pole (given) = 0.5 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 = 4.192 Order of pole (six term test) = -1.36 TOP MAIN SOLVE Loop x[1] = 2.290004999989021 y[1] (analytic) = 2.926821093192384 y[1] (numeric) = 2.926821335831424 absolute error = 2.426390395271483e-07 relative error = 8.290190339666219e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.79 Order of pole (given) = 0.5 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 = 4.199 Order of pole (six term test) = -1.362 TOP MAIN SOLVE Loop x[1] = 2.300004999988642 y[1] (analytic) = 2.930591465468792 y[1] (numeric) = 2.930591716512682 absolute error = 2.510438901204282e-07 relative error = 8.566321613861315e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 0.5 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 = 4.206 Order of pole (six term test) = -1.363 TOP MAIN SOLVE Loop x[1] = 2.310004999988264 y[1] (analytic) = 2.934328216311898 y[1] (numeric) = 2.934328475761919 absolute error = 2.594500201347216e-07 relative error = 8.841888194116861e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.81 Order of pole (given) = 0.5 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 = 4.212 Order of pole (six term test) = -1.365 TOP MAIN SOLVE Loop x[1] = 2.320004999987885 y[1] (analytic) = 2.938031340802129 y[1] (numeric) = 2.938031608659452 absolute error = 2.678573234327075e-07 relative error = 9.116898098152291e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 0.5 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 = 4.219 Order of pole (six term test) = -1.366 TOP MAIN SOLVE Loop x[1] = 2.330004999987507 y[1] (analytic) = 2.941700834479659 y[1] (numeric) = 2.94170111074535 absolute error = 2.762656907684402e-07 relative error = 9.391359159651164e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.83 Order of pole (given) = 0.5 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 = 4.225 Order of pole (six term test) = -1.368 TOP MAIN SOLVE Loop x[1] = 2.340004999987128 y[1] (analytic) = 2.945336693341477 y[1] (numeric) = 2.945336978016471 absolute error = 2.846749942442273e-07 relative error = 9.665278502379443e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.84 Order of pole (given) = 0.5 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 = 4.232 Order of pole (six term test) = -1.37 TOP MAIN SOLVE Loop x[1] = 2.35000499998675 y[1] (analytic) = 2.948938913838454 y[1] (numeric) = 2.948939206923585 absolute error = 2.930851312754612e-07 relative error = 9.938664036074256e-06 % Correct digits = 8 h = 5e-06 Radius of convergence (given) for eq 1 = 3.85 Order of pole (given) = 0.5 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 = 4.239 Order of pole (six term test) = -1.371 TOP MAIN SOLVE Loop x[1] = 2.360004999986371 y[1] (analytic) = 2.952507492872448 y[1] (numeric) = 2.952507794368431 absolute error = 3.014959824021446e-07 relative error = 1.021152302339541e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 3.86 Order of pole (given) = 0.5 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 = 4.245 Order of pole (six term test) = -1.373 TOP MAIN SOLVE Loop x[1] = 2.370004999985992 y[1] (analytic) = 2.956042427793415 y[1] (numeric) = 2.956042737700863 absolute error = 3.099074481482944e-07 relative error = 1.048386333140793e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 3.87 Order of pole (given) = 0.5 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 = 4.252 Order of pole (six term test) = -1.374 TOP MAIN SOLVE Loop x[1] = 2.380004999985614 y[1] (analytic) = 2.959543716396548 y[1] (numeric) = 2.959544034715946 absolute error = 3.183193983957722e-07 relative error = 1.07556917180243e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 3.88 Order of pole (given) = 0.5 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 = 4.258 Order of pole (six term test) = -1.376 TOP MAIN SOLVE Loop x[1] = 2.390004999985235 y[1] (analytic) = 2.963011356919439 y[1] (numeric) = 2.963011683651173 absolute error = 3.267317345567733e-07 relative error = 1.102701593747745e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 3.89 Order of pole (given) = 0.5 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 = 4.265 Order of pole (six term test) = -1.377 TOP MAIN SOLVE Loop x[1] = 2.400004999984857 y[1] (analytic) = 2.966445348039251 y[1] (numeric) = 2.966445683183607 absolute error = 3.351443562671363e-07 relative error = 1.129784361234427e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 0.5 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 = 4.271 Order of pole (six term test) = -1.379 TOP MAIN SOLVE Loop x[1] = 2.410004999984478 y[1] (analytic) = 2.969845688869919 y[1] (numeric) = 2.969846032427053 absolute error = 3.435571334087228e-07 relative error = 1.156818129292949e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 3.91 Order of pole (given) = 0.5 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 = 4.278 Order of pole (six term test) = -1.38 TOP MAIN SOLVE Loop x[1] = 2.4200049999841 y[1] (analytic) = 2.973212378959366 y[1] (numeric) = 2.973212730929332 absolute error = 3.519699665055498e-07 relative error = 1.183803649535256e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 3.92 Order of pole (given) = 0.5 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 = 4.284 Order of pole (six term test) = -1.382 TOP MAIN SOLVE Loop x[1] = 2.430004999983721 y[1] (analytic) = 2.976545418286737 y[1] (numeric) = 2.976545778669486 absolute error = 3.603827480880284e-07 relative error = 1.210741639868745e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 3.93 Order of pole (given) = 0.5 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 = 4.291 Order of pole (six term test) = -1.383 TOP MAIN SOLVE Loop x[1] = 2.440004999983342 y[1] (analytic) = 2.97984480725966 y[1] (numeric) = 2.979845176055037 absolute error = 3.68795377347908e-07 relative error = 1.237632833929568e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 3.94 Order of pole (given) = 0.5 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 = 4.297 Order of pole (six term test) = -1.385 TOP MAIN SOLVE Loop x[1] = 2.450004999982964 y[1] (analytic) = 2.983110546711512 y[1] (numeric) = 2.983110923919262 absolute error = 3.772077503683136e-07 relative error = 1.264477948308472e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 3.95 Order of pole (given) = 0.5 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 = 4.304 Order of pole (six term test) = -1.386 TOP MAIN SOLVE Loop x[1] = 2.460004999982585 y[1] (analytic) = 2.986342637898721 y[1] (numeric) = 2.98634302351847 absolute error = 3.856197494656044e-07 relative error = 1.29127764701822e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 3.96 Order of pole (given) = 0.5 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 = 4.31 Order of pole (six term test) = -1.388 TOP MAIN SOLVE Loop x[1] = 2.470004999982207 y[1] (analytic) = 2.989541082498071 y[1] (numeric) = 2.989541476529353 absolute error = 3.940312822692249e-07 relative error = 1.3180326725598e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 3.97 Order of pole (given) = 0.5 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 = 4.316 Order of pole (six term test) = -1.389 TOP MAIN SOLVE Loop x[1] = 2.480004999981828 y[1] (analytic) = 2.992705882604036 y[1] (numeric) = 2.992706285046263 absolute error = 4.024422266546424e-07 relative error = 1.344743661560441e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 3.98 Order of pole (given) = 0.5 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 = 4.323 Order of pole (six term test) = -1.391 TOP MAIN SOLVE Loop x[1] = 2.49000499998145 y[1] (analytic) = 2.995837040726125 y[1] (numeric) = 2.995837451578625 absolute error = 4.108525004653529e-07 relative error = 1.371411378122794e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 3.99 Order of pole (given) = 0.5 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 = 4.329 Order of pole (six term test) = -1.392 TOP MAIN SOLVE Loop x[1] = 2.500004999981071 y[1] (analytic) = 2.998934559786253 y[1] (numeric) = 2.998934979048248 absolute error = 4.192619948995002e-07 relative error = 1.398036491097634e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 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 = 4.336 Order of pole (six term test) = -1.394 TOP MAIN SOLVE Loop x[1] = 2.510004999980692 y[1] (analytic) = 3.00199844311612 y[1] (numeric) = 3.001998870786713 absolute error = 4.27670593161622e-07 relative error = 1.424619636770009e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.01 Order of pole (given) = 0.5 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 = 4.342 Order of pole (six term test) = -1.395 TOP MAIN SOLVE Loop x[1] = 2.520004999980314 y[1] (analytic) = 3.005028694454617 y[1] (numeric) = 3.005029130532822 absolute error = 4.36078205545698e-07 relative error = 1.451161535829667e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.02 Order of pole (given) = 0.5 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 = 4.348 Order of pole (six term test) = -1.397 TOP MAIN SOLVE Loop x[1] = 2.530004999979935 y[1] (analytic) = 3.008025317945244 y[1] (numeric) = 3.008025762429976 absolute error = 4.444847316875666e-07 relative error = 1.47766286751599e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.03 Order of pole (given) = 0.5 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 = 4.355 Order of pole (six term test) = -1.398 TOP MAIN SOLVE Loop x[1] = 2.540004999979557 y[1] (analytic) = 3.010988318133548 y[1] (numeric) = 3.010988771023615 absolute error = 4.528900663380853e-07 relative error = 1.504124289060088e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.04 Order of pole (given) = 0.5 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 = 4.361 Order of pole (six term test) = -1.399 TOP MAIN SOLVE Loop x[1] = 2.550004999979178 y[1] (analytic) = 3.013917699964576 y[1] (numeric) = 3.013918161258688 absolute error = 4.612941126858061e-07 relative error = 1.530546480055603e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.05 Order of pole (given) = 0.5 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 = 4.367 Order of pole (six term test) = -1.401 TOP MAIN SOLVE Loop x[1] = 2.560004999978799 y[1] (analytic) = 3.016813468780346 y[1] (numeric) = 3.016813938477118 absolute error = 4.696967725870138e-07 relative error = 1.556930110024023e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.06 Order of pole (given) = 0.5 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 = 4.374 Order of pole (six term test) = -1.402 TOP MAIN SOLVE Loop x[1] = 2.570004999978421 y[1] (analytic) = 3.019675630317337 y[1] (numeric) = 3.01967610841528 absolute error = 4.780979434571009e-07 relative error = 1.583275828228139e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.07 Order of pole (given) = 0.5 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 = 4.38 Order of pole (six term test) = -1.404 TOP MAIN SOLVE Loop x[1] = 2.580004999978042 y[1] (analytic) = 3.022504190703994 y[1] (numeric) = 3.022504677201528 absolute error = 4.864975333696009e-07 relative error = 1.609584313781504e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.08 Order of pole (given) = 0.5 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 = 4.386 Order of pole (six term test) = -1.405 TOP MAIN SOLVE Loop x[1] = 2.590004999977664 y[1] (analytic) = 3.025299156458249 y[1] (numeric) = 3.0252996513537 absolute error = 4.948954512862258e-07 relative error = 1.635856243273493e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.09 Order of pole (given) = 0.5 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 = 4.393 Order of pole (six term test) = -1.407 TOP MAIN SOLVE Loop x[1] = 2.600004999977285 y[1] (analytic) = 3.028060534485056 y[1] (numeric) = 3.028061037776641 absolute error = 5.032915852964948e-07 relative error = 1.662092218978981e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 0.5 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 = 4.399 Order of pole (six term test) = -1.408 TOP MAIN SOLVE Loop x[1] = 2.610004999976907 y[1] (analytic) = 3.030788332073951 y[1] (numeric) = 3.030788843759803 absolute error = 5.116858523557255e-07 relative error = 1.688292933362264e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.11 Order of pole (given) = 0.5 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 = 4.405 Order of pole (six term test) = -1.409 TOP MAIN SOLVE Loop x[1] = 2.620004999976528 y[1] (analytic) = 3.033482556896618 y[1] (numeric) = 3.033483076974777 absolute error = 5.200781587610948e-07 relative error = 1.714459038436525e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.12 Order of pole (given) = 0.5 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 = 4.412 Order of pole (six term test) = -1.411 TOP MAIN SOLVE Loop x[1] = 2.630004999976149 y[1] (analytic) = 3.036143217004481 y[1] (numeric) = 3.036143745472879 absolute error = 5.284683983752814e-07 relative error = 1.740591140152732e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.13 Order of pole (given) = 0.5 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 = 4.418 Order of pole (six term test) = -1.412 TOP MAIN SOLVE Loop x[1] = 2.640004999975771 y[1] (analytic) = 3.038770320826297 y[1] (numeric) = 3.038770857682778 absolute error = 5.368564801599973e-07 relative error = 1.766689889264208e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.14 Order of pole (given) = 0.5 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 = 4.424 Order of pole (six term test) = -1.413 TOP MAIN SOLVE Loop x[1] = 2.650004999975392 y[1] (analytic) = 3.041363877165785 y[1] (numeric) = 3.041364422408106 absolute error = 5.452423201823819e-07 relative error = 1.792755954905624e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.15 Order of pole (given) = 0.5 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 = 4.431 Order of pole (six term test) = -1.415 TOP MAIN SOLVE Loop x[1] = 2.660004999975014 y[1] (analytic) = 3.043923895199253 y[1] (numeric) = 3.043924448825071 absolute error = 5.536258171900954e-07 relative error = 1.818789944332217e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.16 Order of pole (given) = 0.5 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 = 4.437 Order of pole (six term test) = -1.416 TOP MAIN SOLVE Loop x[1] = 2.670004999974635 y[1] (analytic) = 3.046450384473248 y[1] (numeric) = 3.046450946480135 absolute error = 5.620068868061878e-07 relative error = 1.844792515481464e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.17 Order of pole (given) = 0.5 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 = 4.443 Order of pole (six term test) = -1.418 TOP MAIN SOLVE Loop x[1] = 2.680004999974257 y[1] (analytic) = 3.048943354902223 y[1] (numeric) = 3.048943925287647 absolute error = 5.703854242256057e-07 relative error = 1.870764254470374e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.18 Order of pole (given) = 0.5 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 = 4.449 Order of pole (six term test) = -1.419 TOP MAIN SOLVE Loop x[1] = 2.690004999973878 y[1] (analytic) = 3.051402816766212 y[1] (numeric) = 3.051403395527559 absolute error = 5.787613464036667e-07 relative error = 1.896705814203256e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.19 Order of pole (given) = 0.5 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 = 4.456 Order of pole (six term test) = -1.42 TOP MAIN SOLVE Loop x[1] = 2.700004999973499 y[1] (analytic) = 3.053828780708531 y[1] (numeric) = 3.053829367843093 absolute error = 5.871345614139045e-07 relative error = 1.922617813817581e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 0.5 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 = 4.462 Order of pole (six term test) = -1.421 TOP MAIN SOLVE Loop x[1] = 2.710004999973121 y[1] (analytic) = 3.056221257733483 y[1] (numeric) = 3.056221853238456 absolute error = 5.955049728889605e-07 relative error = 1.948500853405462e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.21 Order of pole (given) = 0.5 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 = 4.468 Order of pole (six term test) = -1.423 TOP MAIN SOLVE Loop x[1] = 2.720004999972742 y[1] (analytic) = 3.058580259204082 y[1] (numeric) = 3.058580863076582 absolute error = 6.038725000045986e-07 relative error = 1.97435557947968e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.22 Order of pole (given) = 0.5 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 = 4.475 Order of pole (six term test) = -1.424 TOP MAIN SOLVE Loop x[1] = 2.730004999972364 y[1] (analytic) = 3.060905796839795 y[1] (numeric) = 3.060906409076852 absolute error = 6.122370566075119e-07 relative error = 2.000182616660763e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.23 Order of pole (given) = 0.5 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 = 4.481 Order of pole (six term test) = -1.425 TOP MAIN SOLVE Loop x[1] = 2.740004999971985 y[1] (analytic) = 3.063197882714295 y[1] (numeric) = 3.063198503312838 absolute error = 6.205985432217176e-07 relative error = 2.025982541721419e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.24 Order of pole (given) = 0.5 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 = 4.487 Order of pole (six term test) = -1.427 TOP MAIN SOLVE Loop x[1] = 2.750004999971607 y[1] (analytic) = 3.065456529253225 y[1] (numeric) = 3.065457158210113 absolute error = 6.289568883488528e-07 relative error = 2.051756018546682e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.25 Order of pole (given) = 0.5 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 = 4.493 Order of pole (six term test) = -1.428 TOP MAIN SOLVE Loop x[1] = 2.760004999971228 y[1] (analytic) = 3.067681749231983 y[1] (numeric) = 3.067682386543972 absolute error = 6.373119889602208e-07 relative error = 2.07750360388517e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.26 Order of pole (given) = 0.5 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 = 4.5 Order of pole (six term test) = -1.429 TOP MAIN SOLVE Loop x[1] = 2.770004999970849 y[1] (analytic) = 3.069873555773521 y[1] (numeric) = 3.069874201437286 absolute error = 6.456637651197639e-07 relative error = 2.103225925724081e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.27 Order of pole (given) = 0.5 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 = 4.506 Order of pole (six term test) = -1.43 TOP MAIN SOLVE Loop x[1] = 2.780004999970471 y[1] (analytic) = 3.072031962346149 y[1] (numeric) = 3.072032616358276 absolute error = 6.540121271214616e-07 relative error = 2.128923576114047e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.28 Order of pole (given) = 0.5 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 = 4.512 Order of pole (six term test) = -1.432 TOP MAIN SOLVE Loop x[1] = 2.790004999970092 y[1] (analytic) = 3.074156982761364 y[1] (numeric) = 3.074157645118352 absolute error = 6.623569883679181e-07 relative error = 2.154597153242823e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.29 Order of pole (given) = 0.5 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 = 4.519 Order of pole (six term test) = -1.433 TOP MAIN SOLVE Loop x[1] = 2.800004999969714 y[1] (analytic) = 3.076248631171686 y[1] (numeric) = 3.07624930186996 absolute error = 6.706982742521461e-07 relative error = 2.180247290339109e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 0.5 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 = 4.525 Order of pole (six term test) = -1.434 TOP MAIN SOLVE Loop x[1] = 2.810004999969335 y[1] (analytic) = 3.078306922068509 y[1] (numeric) = 3.078307601104403 absolute error = 6.790358941799468e-07 relative error = 2.205874564722285e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.31 Order of pole (given) = 0.5 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 = 4.531 Order of pole (six term test) = -1.435 TOP MAIN SOLVE Loop x[1] = 2.820004999968956 y[1] (analytic) = 3.080331870279966 y[1] (numeric) = 3.080332557649726 absolute error = 6.873697593334782e-07 relative error = 2.231479555711003e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.32 Order of pole (given) = 0.5 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 = 4.537 Order of pole (six term test) = -1.437 TOP MAIN SOLVE Loop x[1] = 2.830004999968578 y[1] (analytic) = 3.082323490968812 y[1] (numeric) = 3.08232418666861 absolute error = 6.956997977702883e-07 relative error = 2.257062893653713e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.33 Order of pole (given) = 0.5 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 = 4.544 Order of pole (six term test) = -1.438 TOP MAIN SOLVE Loop x[1] = 2.840004999968199 y[1] (analytic) = 3.084281799630307 y[1] (numeric) = 3.084282503656215 absolute error = 7.040259082380373e-07 relative error = 2.282625110074003e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.34 Order of pole (given) = 0.5 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 = 4.55 Order of pole (six term test) = -1.439 TOP MAIN SOLVE Loop x[1] = 2.850004999967821 y[1] (analytic) = 3.086206812090127 y[1] (numeric) = 3.086207524438166 absolute error = 7.123480387782877e-07 relative error = 2.308166892729562e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.35 Order of pole (given) = 0.5 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 = 4.556 Order of pole (six term test) = -1.44 TOP MAIN SOLVE Loop x[1] = 2.860004999967442 y[1] (analytic) = 3.088098544502283 y[1] (numeric) = 3.088099265168366 absolute error = 7.206660832537182e-07 relative error = 2.333688750110369e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.36 Order of pole (given) = 0.5 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 = 4.563 Order of pole (six term test) = -1.442 TOP MAIN SOLVE Loop x[1] = 2.870004999967064 y[1] (analytic) = 3.089957013347047 y[1] (numeric) = 3.089957742327012 absolute error = 7.289799652809847e-07 relative error = 2.359191283672107e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.37 Order of pole (given) = 0.5 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 = 4.569 Order of pole (six term test) = -1.443 TOP MAIN SOLVE Loop x[1] = 2.880004999966685 y[1] (analytic) = 3.091782235428899 y[1] (numeric) = 3.091782972718499 absolute error = 7.372896004831375e-07 relative error = 2.384675065515599e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.38 Order of pole (given) = 0.5 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 = 4.575 Order of pole (six term test) = -1.444 TOP MAIN SOLVE Loop x[1] = 2.890004999966306 y[1] (analytic) = 3.093574227874483 y[1] (numeric) = 3.093574973469399 absolute error = 7.455949155854569e-07 relative error = 2.410140700253171e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.39 Order of pole (given) = 0.5 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 = 4.582 Order of pole (six term test) = -1.445 TOP MAIN SOLVE Loop x[1] = 2.900004999965928 y[1] (analytic) = 3.095333008130577 y[1] (numeric) = 3.0953337620264 absolute error = 7.538958226582793e-07 relative error = 2.435588741754134e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 0.5 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 = 4.588 Order of pole (six term test) = -1.446 TOP MAIN SOLVE Loop x[1] = 2.910004999965549 y[1] (analytic) = 3.097058593962072 y[1] (numeric) = 3.097059356154329 absolute error = 7.621922573086692e-07 relative error = 2.461019816656408e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.41 Order of pole (given) = 0.5 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 = 4.594 Order of pole (six term test) = -1.447 TOP MAIN SOLVE Loop x[1] = 2.920004999965171 y[1] (analytic) = 3.098751003449968 y[1] (numeric) = 3.098751773934096 absolute error = 7.704841276101604e-07 relative error = 2.486434459407511e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.42 Order of pole (given) = 0.5 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 = 4.601 Order of pole (six term test) = -1.449 TOP MAIN SOLVE Loop x[1] = 2.930004999964792 y[1] (analytic) = 3.100410254989382 y[1] (numeric) = 3.100411033760735 absolute error = 7.787713527385165e-07 relative error = 2.51183323718294e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.43 Order of pole (given) = 0.5 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 = 4.607 Order of pole (six term test) = -1.45 TOP MAIN SOLVE Loop x[1] = 2.940004999964414 y[1] (analytic) = 3.102036367287561 y[1] (numeric) = 3.10203715434142 absolute error = 7.870538589749287e-07 relative error = 2.537216736962801e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.44 Order of pole (given) = 0.5 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 = 4.613 Order of pole (six term test) = -1.451 TOP MAIN SOLVE Loop x[1] = 2.950004999964035 y[1] (analytic) = 3.10362935936192 y[1] (numeric) = 3.103630154693495 absolute error = 7.953315748210343e-07 relative error = 2.562585549791769e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.45 Order of pole (given) = 0.5 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 = 4.62 Order of pole (six term test) = -1.452 TOP MAIN SOLVE Loop x[1] = 2.960004999963656 y[1] (analytic) = 3.10518925053808 y[1] (numeric) = 3.105190054142505 absolute error = 8.036044247816676e-07 relative error = 2.587940250799257e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.46 Order of pole (given) = 0.5 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 = 4.626 Order of pole (six term test) = -1.453 TOP MAIN SOLVE Loop x[1] = 2.970004999963278 y[1] (analytic) = 3.106716060447923 y[1] (numeric) = 3.106716872320238 absolute error = 8.118723151540053e-07 relative error = 2.613281353549093e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.47 Order of pole (given) = 0.5 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 = 4.632 Order of pole (six term test) = -1.454 TOP MAIN SOLVE Loop x[1] = 2.980004999962899 y[1] (analytic) = 3.108209809027659 y[1] (numeric) = 3.108210629162849 absolute error = 8.201351899828069e-07 relative error = 2.638609490262724e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.48 Order of pole (given) = 0.5 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 = 4.639 Order of pole (six term test) = -1.455 TOP MAIN SOLVE Loop x[1] = 2.990004999962521 y[1] (analytic) = 3.109670516515906 y[1] (numeric) = 3.109671344908864 absolute error = 8.283929577856952e-07 relative error = 2.663925175950254e-05 % Correct digits = 7 h = 5e-06 Radius of convergence (given) for eq 1 = 4.49 Order of pole (given) = 0.5 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 = 4.645 Order of pole (six term test) = -1.456 Finished! diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 200001 Total Elapsed Time = 11.0 Seconds Elapsed Time(since restart) = 11.0 Seconds Time to Timeout = 9 Minutes 49.0 Seconds Percent Done = 100 %