##############ECHO OF PROBLEM################# ##############temp/cos_sqrt_linpostode.ode################# diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // 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_iter=1000000; glob_display_interval=0.1; glob_max_minutes=10; glob_max_h=0.00001; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; glob_max_minutes=30.0; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(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-16 est_needed_step_err = 1e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.188174820698805e-174 estimated_step_error = 6.188174820698805e-174 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.152813288011036e-166 estimated_step_error = 4.152813288011036e-166 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.786905101555517e-158 estimated_step_error = 2.786905101555517e-158 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.870259387951465e-150 estimated_step_error = 1.870259387951465e-150 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.255108531948291e-142 estimated_step_error = 1.255108531948291e-142 best_h = 1e-05 START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0.3792052304520231 y[1] (numeric) = 0.3792052304520231 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.487 Order of pole (three term test) = 1.671 Radius of convergence (six term test) for eq 1 = 4.528 Order of pole (six term test) = -0.774 TOP MAIN SOLVE Loop x[1] = 2.010000000000066 y[1] (analytic) = 0.3704005770756198 y[1] (numeric) = 0.370400586029134 absolute error = 8.9535142078212e-09 relative error = 2.417251689646606e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.497 Order of pole (three term test) = 1.67 Radius of convergence (six term test) for eq 1 = 4.545 Order of pole (six term test) = -0.7738 TOP MAIN SOLVE Loop x[1] = 2.020000000000131 y[1] (analytic) = 0.361578092327608 y[1] (numeric) = 0.3615781101591607 absolute error = 1.783155278989312e-08 relative error = 4.931591036145199e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.507 Order of pole (three term test) = 1.67 Radius of convergence (six term test) for eq 1 = 4.561 Order of pole (six term test) = -0.7735 TOP MAIN SOLVE Loop x[1] = 2.030000000000197 y[1] (analytic) = 0.3527379269631478 y[1] (numeric) = 0.3527379535974597 absolute error = 2.663431197813537e-08 relative error = 7.550736663743558e-06 % Correct digits = 8 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.517 Order of pole (three term test) = 1.67 Radius of convergence (six term test) for eq 1 = 4.578 Order of pole (six term test) = -0.7733 TOP MAIN SOLVE Loop x[1] = 2.040000000000262 y[1] (analytic) = 0.3438802313469563 y[1] (numeric) = 0.3438802667089421 absolute error = 3.53619857840215e-08 relative error = 1.028322728686988e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.527 Order of pole (three term test) = 1.67 Radius of convergence (six term test) for eq 1 = 4.594 Order of pole (six term test) = -0.7731 TOP MAIN SOLVE Loop x[1] = 2.050000000000328 y[1] (analytic) = 0.3350051554539381 y[1] (numeric) = 0.3350051994687082 absolute error = 4.401477016191535e-08 relative error = 1.3138535167399e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.537 Order of pole (three term test) = 1.67 Radius of convergence (six term test) for eq 1 = 4.611 Order of pole (six term test) = -0.7728 TOP MAIN SOLVE Loop x[1] = 2.060000000000393 y[1] (analytic) = 0.3261128488698211 y[1] (numeric) = 0.3261129014626796 absolute error = 5.259285856817897e-08 relative error = 1.612719607658672e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.547 Order of pole (three term test) = 1.67 Radius of convergence (six term test) for eq 1 = 4.627 Order of pole (six term test) = -0.7726 TOP MAIN SOLVE Loop x[1] = 2.070000000000459 y[1] (analytic) = 0.3172034607917849 y[1] (numeric) = 0.3172035218882303 absolute error = 6.109644540286396e-08 relative error = 1.92609643193547e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.557 Order of pole (three term test) = 1.67 Radius of convergence (six term test) for eq 1 = 4.644 Order of pole (six term test) = -0.7724 TOP MAIN SOLVE Loop x[1] = 2.080000000000524 y[1] (analytic) = 0.3082771400290987 y[1] (numeric) = 0.3082772095548231 absolute error = 6.952572439988813e-08 relative error = 2.255299383967475e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.567 Order of pole (three term test) = 1.67 Radius of convergence (six term test) for eq 1 = 4.66 Order of pole (six term test) = -0.7722 TOP MAIN SOLVE Loop x[1] = 2.09000000000059 y[1] (analytic) = 0.2993340350037449 y[1] (numeric) = 0.2993341128846344 absolute error = 7.788088951521388e-08 relative error = 2.60180535481839e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.577 Order of pole (three term test) = 1.67 Radius of convergence (six term test) for eq 1 = 4.676 Order of pole (six term test) = -0.772 TOP MAIN SOLVE Loop x[1] = 2.100000000000655 y[1] (analytic) = 0.2903742937510554 y[1] (numeric) = 0.2903743799131896 absolute error = 8.616213420520324e-08 relative error = 2.967278304568931e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.587 Order of pole (three term test) = 1.67 Radius of convergence (six term test) for eq 1 = 4.693 Order of pole (six term test) = -0.7718 TOP MAIN SOLVE Loop x[1] = 2.110000000000721 y[1] (analytic) = 0.2813980639203403 y[1] (numeric) = 0.2813981582899898 absolute error = 9.436964953923876e-08 relative error = 3.353599816022666e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.597 Order of pole (three term test) = 1.67 Radius of convergence (six term test) for eq 1 = 4.709 Order of pole (six term test) = -0.7716 TOP MAIN SOLVE Loop x[1] = 2.120000000000786 y[1] (analytic) = 0.2724054927755124 y[1] (numeric) = 0.2724055952791429 absolute error = 1.025036304724836e-07 relative error = 3.762906152445176e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.607 Order of pole (three term test) = 1.67 Radius of convergence (six term test) for eq 1 = 4.726 Order of pole (six term test) = -0.7715 TOP MAIN SOLVE Loop x[1] = 2.130000000000852 y[1] (analytic) = 0.2633967271957206 y[1] (numeric) = 0.2633968377599875 absolute error = 1.10564266908586e-07 relative error = 4.197632525115989e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.617 Order of pole (three term test) = 1.669 Radius of convergence (six term test) for eq 1 = 4.742 Order of pole (six term test) = -0.7713 TOP MAIN SOLVE Loop x[1] = 2.140000000000917 y[1] (analytic) = 0.2543719136759723 y[1] (numeric) = 0.2543720322277234 absolute error = 1.185517510826628e-07 relative error = 4.660567645596207e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.627 Order of pole (three term test) = 1.669 Radius of convergence (six term test) for eq 1 = 4.759 Order of pole (six term test) = -0.7711 TOP MAIN SOLVE Loop x[1] = 2.150000000000983 y[1] (analytic) = 0.2453311983277634 y[1] (numeric) = 0.2453313247940395 absolute error = 1.264662761457647e-07 relative error = 5.154920246906602e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.637 Order of pole (three term test) = 1.669 Radius of convergence (six term test) for eq 1 = 4.775 Order of pole (six term test) = -0.771 TOP MAIN SOLVE Loop x[1] = 2.160000000001048 y[1] (analytic) = 0.2362747268797023 y[1] (numeric) = 0.2362748611877349 absolute error = 1.343080326399182e-07 relative error = 5.684401138184374e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.647 Order of pole (three term test) = 1.669 Radius of convergence (six term test) for eq 1 = 4.792 Order of pole (six term test) = -0.7708 TOP MAIN SOLVE Loop x[1] = 2.170000000001114 y[1] (analytic) = 0.2272026446781363 y[1] (numeric) = 0.2272027867553467 absolute error = 1.420772104132606e-07 relative error = 6.253325555014222e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.657 Order of pole (three term test) = 1.669 Radius of convergence (six term test) for eq 1 = 4.808 Order of pole (six term test) = -0.7707 TOP MAIN SOLVE Loop x[1] = 2.180000000001179 y[1] (analytic) = 0.2181150966877716 y[1] (numeric) = 0.2181152464617743 absolute error = 1.497740027001093e-07 relative error = 6.866741687051056e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.667 Order of pole (three term test) = 1.669 Radius of convergence (six term test) for eq 1 = 4.825 Order of pole (six term test) = -0.7705 TOP MAIN SOLVE Loop x[1] = 2.190000000001245 y[1] (analytic) = 0.2090122274923047 y[1] (numeric) = 0.2090123848909019 absolute error = 1.573985971836667e-07 relative error = 7.530592782638118e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.677 Order of pole (three term test) = 1.669 Radius of convergence (six term test) for eq 1 = 4.841 Order of pole (six term test) = -0.7704 TOP MAIN SOLVE Loop x[1] = 2.20000000000131 y[1] (analytic) = 0.1998941812950356 y[1] (numeric) = 0.1998943462462215 absolute error = 1.649511859047603e-07 relative error = 8.251925335500345e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.687 Order of pole (three term test) = 1.669 Radius of convergence (six term test) for eq 1 = 4.857 Order of pole (six term test) = -0.7703 TOP MAIN SOLVE Loop x[1] = 2.210000000001376 y[1] (analytic) = 0.190761101919498 y[1] (numeric) = 0.1907612743514549 absolute error = 1.724319569074151e-07 relative error = 9.03915710133516e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.697 Order of pole (three term test) = 1.669 Radius of convergence (six term test) for eq 1 = 4.874 Order of pole (six term test) = -0.7702 TOP MAIN SOLVE Loop x[1] = 2.220000000001441 y[1] (analytic) = 0.1816131328100735 y[1] (numeric) = 0.1816133126511751 absolute error = 1.798411015663248e-07 relative error = 9.90242824313802e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.707 Order of pole (three term test) = 1.669 Radius of convergence (six term test) for eq 1 = 4.89 Order of pole (six term test) = -0.7701 TOP MAIN SOLVE Loop x[1] = 2.230000000001507 y[1] (analytic) = 0.1724504170326194 y[1] (numeric) = 0.1724506042114263 absolute error = 1.87178806898558e-07 relative error = 0.0001085406519273031 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.717 Order of pole (three term test) = 1.669 Radius of convergence (six term test) for eq 1 = 4.907 Order of pole (six term test) = -0.77 TOP MAIN SOLVE Loop x[1] = 2.240000000001572 y[1] (analytic) = 0.1632730972750807 y[1] (numeric) = 0.1632732917203442 absolute error = 1.944452635571636e-07 relative error = 0.0001190920407601287 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.727 Order of pole (three term test) = 1.668 Radius of convergence (six term test) for eq 1 = 4.923 Order of pole (six term test) = -0.7699 TOP MAIN SOLVE Loop x[1] = 2.250000000001638 y[1] (analytic) = 0.1540813158481154 y[1] (numeric) = 0.1540815174887745 absolute error = 2.016406591698328e-07 relative error = 0.0001308663922422617 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.737 Order of pole (three term test) = 1.668 Radius of convergence (six term test) for eq 1 = 4.939 Order of pole (six term test) = -0.7698 TOP MAIN SOLVE Loop x[1] = 2.260000000001703 y[1] (analytic) = 0.1448752146857099 y[1] (numeric) = 0.1448754234508905 absolute error = 2.08765180614856e-07 relative error = 0.0001440999974134624 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.747 Order of pole (three term test) = 1.668 Radius of convergence (six term test) for eq 1 = 4.956 Order of pole (six term test) = -0.7697 TOP MAIN SOLVE Loop x[1] = 2.270000000001769 y[1] (analytic) = 0.1356549353457934 y[1] (numeric) = 0.1356551511648116 absolute error = 2.158190181289488e-07 relative error = 0.0001590941144742075 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.757 Order of pole (three term test) = 1.668 Radius of convergence (six term test) for eq 1 = 4.972 Order of pole (six term test) = -0.7696 TOP MAIN SOLVE Loop x[1] = 2.280000000001834 y[1] (analytic) = 0.1264206190108625 y[1] (numeric) = 0.1264208418132205 absolute error = 2.228023579242677e-07 relative error = 0.0001762389392391155 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.767 Order of pole (three term test) = 1.668 Radius of convergence (six term test) for eq 1 = 4.989 Order of pole (six term test) = -0.7695 TOP MAIN SOLVE Loop x[1] = 2.2900000000019 y[1] (analytic) = 0.1171724064885891 y[1] (numeric) = 0.117172636203977 absolute error = 2.297153879476932e-07 relative error = 0.0001960490484336551 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.777 Order of pole (three term test) = 1.668 Radius of convergence (six term test) for eq 1 = 5.005 Order of pole (six term test) = -0.7695 TOP MAIN SOLVE Loop x[1] = 2.300000000001965 y[1] (analytic) = 0.1079104382124413 y[1] (numeric) = 0.1079106747707354 absolute error = 2.365582941199484e-07 relative error = 0.0002192172490804277 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.787 Order of pole (three term test) = 1.668 Radius of convergence (six term test) for eq 1 = 5.021 Order of pole (six term test) = -0.7694 TOP MAIN SOLVE Loop x[1] = 2.310000000002031 y[1] (analytic) = 0.09863485424229435 y[1] (numeric) = 0.09863509757355772 absolute error = 2.433312633748352e-07 relative error = 0.0002466990651976809 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.797 Order of pole (three term test) = 1.668 Radius of convergence (six term test) for eq 1 = 5.038 Order of pole (six term test) = -0.7694 TOP MAIN SOLVE Loop x[1] = 2.320000000002096 y[1] (analytic) = 0.08934579426504607 y[1] (numeric) = 0.08934604429952832 absolute error = 2.500344822436995e-07 relative error = 0.0002798503100235107 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.807 Order of pole (three term test) = 1.668 Radius of convergence (six term test) for eq 1 = 5.054 Order of pole (six term test) = -0.7693 TOP MAIN SOLVE Loop x[1] = 2.330000000002162 y[1] (analytic) = 0.08004339759522794 y[1] (numeric) = 0.08004365426336578 absolute error = 2.566681378407543e-07 relative error = 0.0003206612232263069 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.817 Order of pole (three term test) = 1.668 Radius of convergence (six term test) for eq 1 = 5.07 Order of pole (six term test) = -0.7693 TOP MAIN SOLVE Loop x[1] = 2.340000000002227 y[1] (analytic) = 0.07072780317562188 y[1] (numeric) = 0.07072806640803614 absolute error = 2.632324142548548e-07 relative error = 0.0003721767147231069 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.827 Order of pole (three term test) = 1.667 Radius of convergence (six term test) for eq 1 = 5.087 Order of pole (six term test) = -0.7693 TOP MAIN SOLVE Loop x[1] = 2.350000000002293 y[1] (analytic) = 0.06139914957786696 y[1] (numeric) = 0.06139941930536361 absolute error = 2.697274966503849e-07 relative error = 0.0004393016817086595 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.837 Order of pole (three term test) = 1.667 Radius of convergence (six term test) for eq 1 = 5.103 Order of pole (six term test) = -0.7692 TOP MAIN SOLVE Loop x[1] = 2.360000000002358 y[1] (analytic) = 0.05205757500307007 y[1] (numeric) = 0.05205785115664255 absolute error = 2.761535724815634e-07 relative error = 0.0005304772119432712 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.847 Order of pole (three term test) = 1.667 Radius of convergence (six term test) for eq 1 = 5.119 Order of pole (six term test) = -0.7692 TOP MAIN SOLVE Loop x[1] = 2.370000000002424 y[1] (analytic) = 0.04270321728242099 y[1] (numeric) = 0.04270349979324618 absolute error = 2.825108251919284e-07 relative error = 0.0006615680109616132 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.857 Order of pole (three term test) = 1.667 Radius of convergence (six term test) for eq 1 = 5.136 Order of pole (six term test) = -0.7692 TOP MAIN SOLVE Loop x[1] = 2.380000000002489 y[1] (analytic) = 0.03333621387779806 y[1] (numeric) = 0.03333650267723645 absolute error = 2.887994383915515e-07 relative error = 0.0008663234506780392 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.867 Order of pole (three term test) = 1.667 Radius of convergence (six term test) for eq 1 = 5.152 Order of pole (six term test) = -0.7692 TOP MAIN SOLVE Loop x[1] = 2.390000000002555 y[1] (analytic) = 0.0239567018823752 y[1] (numeric) = 0.02395699690197265 absolute error = 2.95019597449514e-07 relative error = 0.001231470003250147 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.877 Order of pole (three term test) = 1.667 Radius of convergence (six term test) for eq 1 = 5.168 Order of pole (six term test) = -0.7692 TOP MAIN SOLVE Loop x[1] = 2.40000000000262 y[1] (analytic) = 0.01456481802123366 y[1] (numeric) = 0.01456511919271915 absolute error = 3.011714854866954e-07 relative error = 0.002067801225168934 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.887 Order of pole (three term test) = 1.667 Radius of convergence (six term test) for eq 1 = 5.185 Order of pole (six term test) = -0.7692 TOP MAIN SOLVE Loop x[1] = 2.410000000002686 y[1] (analytic) = 0.005160698651965223 y[1] (numeric) = 0.005161005907252458 absolute error = 3.072552872346659e-07 relative error = 0.00595375370576349 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.897 Order of pole (three term test) = 1.667 Radius of convergence (six term test) for eq 1 = 5.201 Order of pole (six term test) = -0.7693 TOP MAIN SOLVE Loop x[1] = 2.420000000002752 y[1] (analytic) = -0.004255520234716648 y[1] (numeric) = -0.004255206963532382 absolute error = 3.132711842660646e-07 relative error = 0.007361524960224367 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.907 Order of pole (three term test) = 1.666 Radius of convergence (six term test) for eq 1 = 5.217 Order of pole (six term test) = -0.7693 TOP MAIN SOLVE Loop x[1] = 2.430000000002817 y[1] (analytic) = -0.01368370301437727 y[1] (numeric) = -0.0136833837950162 absolute error = 3.192193610643962e-07 relative error = 0.002332843388438035 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.917 Order of pole (three term test) = 1.666 Radius of convergence (six term test) for eq 1 = 5.234 Order of pole (six term test) = -0.7693 TOP MAIN SOLVE Loop x[1] = 2.440000000002883 y[1] (analytic) = -0.02312371442825145 y[1] (numeric) = -0.0231233893282508 absolute error = 3.25100000649059e-07 relative error = 0.001405915998737068 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.927 Order of pole (three term test) = 1.666 Radius of convergence (six term test) for eq 1 = 5.25 Order of pole (six term test) = -0.7693 TOP MAIN SOLVE Loop x[1] = 2.450000000002948 y[1] (analytic) = -0.03257541958263888 y[1] (numeric) = -0.03257508866935484 absolute error = 3.309132840384477e-07 relative error = 0.001015837365345275 % Correct digits = 5 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.937 Order of pole (three term test) = 1.666 Radius of convergence (six term test) for eq 1 = 5.266 Order of pole (six term test) = -0.7694 TOP MAIN SOLVE Loop x[1] = 2.460000000003014 y[1] (analytic) = -0.04203868394830368 y[1] (numeric) = -0.0420383472889106 absolute error = 3.366593930784201e-07 relative error = 0.00080083237974914 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.947 Order of pole (three term test) = 1.666 Radius of convergence (six term test) for eq 1 = 5.282 Order of pole (six term test) = -0.7694 TOP MAIN SOLVE Loop x[1] = 2.470000000003079 y[1] (analytic) = -0.05151337335987172 y[1] (numeric) = -0.05151303102136071 absolute error = 3.423385110112864e-07 relative error = 0.0006645624013393848 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.957 Order of pole (three term test) = 1.666 Radius of convergence (six term test) for eq 1 = 5.299 Order of pole (six term test) = -0.7695 TOP MAIN SOLVE Loop x[1] = 2.480000000003145 y[1] (analytic) = -0.06099935401522438 y[1] (numeric) = -0.06099900606440681 absolute error = 3.479508175682766e-07 relative error = 0.0005704172170109114 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.967 Order of pole (three term test) = 1.666 Radius of convergence (six term test) for eq 1 = 5.315 Order of pole (six term test) = -0.7696 TOP MAIN SOLVE Loop x[1] = 2.49000000000321 y[1] (analytic) = -0.07049649247490497 y[1] (numeric) = -0.07049613897840816 absolute error = 3.534964968104903e-07 relative error = 0.0005014384182820535 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.977 Order of pole (three term test) = 1.666 Radius of convergence (six term test) for eq 1 = 5.331 Order of pole (six term test) = -0.7696 TOP MAIN SOLVE Loop x[1] = 2.500000000003276 y[1] (analytic) = -0.08000465566150683 y[1] (numeric) = -0.08000429668578096 absolute error = 3.589757258670723e-07 relative error = 0.000448693545268002 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.987 Order of pole (three term test) = 1.665 Radius of convergence (six term test) for eq 1 = 5.347 Order of pole (six term test) = -0.7697 TOP MAIN SOLVE Loop x[1] = 2.510000000003341 y[1] (analytic) = -0.08952371085908761 y[1] (numeric) = -0.08952334647039872 absolute error = 3.643886888893277e-07 relative error = 0.0004070303670307903 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.997 Order of pole (three term test) = 1.665 Radius of convergence (six term test) for eq 1 = 5.364 Order of pole (six term test) = -0.7698 TOP MAIN SOLVE Loop x[1] = 2.520000000003407 y[1] (analytic) = -0.09905352571255754 y[1] (numeric) = -0.0990531559769937 absolute error = 3.697355638460076e-07 relative error = 0.0003732684537842092 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.007 Order of pole (three term test) = 1.665 Radius of convergence (six term test) for eq 1 = 5.38 Order of pole (six term test) = -0.7699 TOP MAIN SOLVE Loop x[1] = 2.530000000003472 y[1] (analytic) = -0.108593968227088 y[1] (numeric) = -0.1085935932105575 absolute error = 3.750165304960973e-07 relative error = 0.00034533826935201 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.017 Order of pole (three term test) = 1.665 Radius of convergence (six term test) for eq 1 = 5.396 Order of pole (six term test) = -0.77 TOP MAIN SOLVE Loop x[1] = 2.540000000003538 y[1] (analytic) = -0.1181449067675155 y[1] (numeric) = -0.1181445265357447 absolute error = 3.802317708467839e-07 relative error = 0.0003218350932342775 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.027 Order of pole (three term test) = 1.665 Radius of convergence (six term test) for eq 1 = 5.412 Order of pole (six term test) = -0.7701 TOP MAIN SOLVE Loop x[1] = 2.550000000003603 y[1] (analytic) = -0.1277062100577373 y[1] (numeric) = -0.1277058246762752 absolute error = 3.853814621312956e-07 relative error = 0.0003017719044023472 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.036 Order of pole (three term test) = 1.665 Radius of convergence (six term test) for eq 1 = 5.429 Order of pole (six term test) = -0.7702 TOP MAIN SOLVE Loop x[1] = 2.560000000003669 y[1] (analytic) = -0.1372777471801205 y[1] (numeric) = -0.1372773567143373 absolute error = 3.904657832343172e-07 relative error = 0.000284434871095307 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.046 Order of pole (three term test) = 1.665 Radius of convergence (six term test) for eq 1 = 5.445 Order of pole (six term test) = -0.7703 TOP MAIN SOLVE Loop x[1] = 2.570000000003734 y[1] (analytic) = -0.1468593875749108 y[1] (numeric) = -0.1468589920899956 absolute error = 3.954849152054685e-07 relative error = 0.0002692949505892073 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.056 Order of pole (three term test) = 1.664 Radius of convergence (six term test) for eq 1 = 5.461 Order of pole (six term test) = -0.7704 TOP MAIN SOLVE Loop x[1] = 2.5800000000038 y[1] (analytic) = -0.1564510010396252 y[1] (numeric) = -0.1564506006005919 absolute error = 4.004390332656982e-07 relative error = 0.0002559517232902056 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.066 Order of pole (three term test) = 1.664 Radius of convergence (six term test) for eq 1 = 5.477 Order of pole (six term test) = -0.7705 TOP MAIN SOLVE Loop x[1] = 2.590000000003865 y[1] (analytic) = -0.1660524577284737 y[1] (numeric) = -0.1660520524001534 absolute error = 4.053283202132274e-07 relative error = 0.0002440965498240405 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.076 Order of pole (three term test) = 1.664 Radius of convergence (six term test) for eq 1 = 5.493 Order of pole (six term test) = -0.7707 TOP MAIN SOLVE Loop x[1] = 2.600000000003931 y[1] (analytic) = -0.1756636281517512 y[1] (numeric) = -0.1756632179988019 absolute error = 4.101529492983591e-07 relative error = 0.0002334876910000053 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.086 Order of pole (three term test) = 1.664 Radius of convergence (six term test) for eq 1 = 5.509 Order of pole (six term test) = -0.7708 TOP MAIN SOLVE Loop x[1] = 2.610000000003996 y[1] (analytic) = -0.1852843831752574 y[1] (numeric) = -0.1852839682621559 absolute error = 4.149131015429575e-07 relative error = 0.0002239331207695459 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.096 Order of pole (three term test) = 1.664 Radius of convergence (six term test) for eq 1 = 5.526 Order of pole (six term test) = -0.771 TOP MAIN SOLVE Loop x[1] = 2.620000000004062 y[1] (analytic) = -0.1949145940196956 y[1] (numeric) = -0.1949141744107436 absolute error = 4.196089520014379e-07 relative error = 0.000215278365435806 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.106 Order of pole (three term test) = 1.664 Radius of convergence (six term test) for eq 1 = 5.542 Order of pole (six term test) = -0.7711 TOP MAIN SOLVE Loop x[1] = 2.630000000004127 y[1] (analytic) = -0.2045541322600871 y[1] (numeric) = -0.2045537080194093 absolute error = 4.242406778653951e-07 relative error = 0.0002073977549013677 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.116 Order of pole (three term test) = 1.664 Radius of convergence (six term test) for eq 1 = 5.558 Order of pole (six term test) = -0.7713 TOP MAIN SOLVE Loop x[1] = 2.640000000004193 y[1] (analytic) = -0.2142028698251819 y[1] (numeric) = -0.2142024410167237 absolute error = 4.288084581582918e-07 relative error = 0.0002001880079889951 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.126 Order of pole (three term test) = 1.663 Radius of convergence (six term test) for eq 1 = 5.574 Order of pole (six term test) = -0.7714 TOP MAIN SOLVE Loop x[1] = 2.650000000004258 y[1] (analytic) = -0.2238606789968616 y[1] (numeric) = -0.2238602456843952 absolute error = 4.333124663247201e-07 relative error = 0.0001935634557468643 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.136 Order of pole (three term test) = 1.663 Radius of convergence (six term test) for eq 1 = 5.59 Order of pole (six term test) = -0.7716 TOP MAIN SOLVE Loop x[1] = 2.660000000004324 y[1] (analytic) = -0.2335274324095578 y[1] (numeric) = -0.2335269946566785 absolute error = 4.377528792509633e-07 relative error = 0.0001874524439095606 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.146 Order of pole (three term test) = 1.663 Radius of convergence (six term test) for eq 1 = 5.606 Order of pole (six term test) = -0.7718 TOP MAIN SOLVE Loop x[1] = 2.670000000004389 y[1] (analytic) = -0.2432030030496621 y[1] (numeric) = -0.2432025609197893 absolute error = 4.421298728518597e-07 relative error = 0.0001817945779072377 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.156 Order of pole (three term test) = 1.663 Radius of convergence (six term test) for eq 1 = 5.622 Order of pole (six term test) = -0.772 TOP MAIN SOLVE Loop x[1] = 2.680000000004455 y[1] (analytic) = -0.2528872642549389 y[1] (numeric) = -0.2528868178113142 absolute error = 4.464436246798265e-07 relative error = 0.0001765385955655564 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.166 Order of pole (three term test) = 1.663 Radius of convergence (six term test) for eq 1 = 5.639 Order of pole (six term test) = -0.7722 TOP MAIN SOLVE Loop x[1] = 2.69000000000452 y[1] (analytic) = -0.262580089713935 y[1] (numeric) = -0.2625796390196277 absolute error = 4.506943072635217e-07 relative error = 0.0001716407012254911 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.176 Order of pole (three term test) = 1.663 Radius of convergence (six term test) for eq 1 = 5.655 Order of pole (six term test) = -0.7724 TOP MAIN SOLVE Loop x[1] = 2.700000000004586 y[1] (analytic) = -0.2722813534653982 y[1] (numeric) = -0.2722808985833003 absolute error = 4.548820978778068e-07 relative error = 0.0001670632572111163 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.186 Order of pole (three term test) = 1.663 Radius of convergence (six term test) for eq 1 = 5.671 Order of pole (six term test) = -0.7726 TOP MAIN SOLVE Loop x[1] = 2.710000000004651 y[1] (analytic) = -0.2819909298976889 y[1] (numeric) = -0.2819904708905202 absolute error = 4.590071687182729e-07 relative error = 0.0001627737349158033 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.196 Order of pole (three term test) = 1.662 Radius of convergence (six term test) for eq 1 = 5.687 Order of pole (six term test) = -0.7728 TOP MAIN SOLVE Loop x[1] = 2.720000000004717 y[1] (analytic) = -0.2917086937481974 y[1] (numeric) = -0.291708230678502 absolute error = 4.630696954222024e-07 relative error = 0.0001587438788581062 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.206 Order of pole (three term test) = 1.662 Radius of convergence (six term test) for eq 1 = 5.703 Order of pole (six term test) = -0.773 TOP MAIN SOLVE Loop x[1] = 2.730000000004782 y[1] (analytic) = -0.30143452010276 y[1] (numeric) = -0.3014340530329075 absolute error = 4.670698524056327e-07 relative error = 0.0001549490258270377 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.216 Order of pole (three term test) = 1.662 Radius of convergence (six term test) for eq 1 = 5.719 Order of pole (six term test) = -0.7732 TOP MAIN SOLVE Loop x[1] = 2.740000000004848 y[1] (analytic) = -0.3111682843950743 y[1] (numeric) = -0.3111678133872611 absolute error = 4.710078131409112e-07 relative error = 0.0001513675515024201 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.226 Order of pole (three term test) = 1.662 Radius of convergence (six term test) for eq 1 = 5.735 Order of pole (six term test) = -0.7734 TOP MAIN SOLVE Loop x[1] = 2.750000000004913 y[1] (analytic) = -0.3209098624061173 y[1] (numeric) = -0.3209093875223651 absolute error = 4.748837521550975e-07 relative error = 0.0001479804168667535 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.236 Order of pole (three term test) = 1.662 Radius of convergence (six term test) for eq 1 = 5.751 Order of pole (six term test) = -0.7737 TOP MAIN SOLVE Loop x[1] = 2.760000000004979 y[1] (analytic) = -0.330659130263563 y[1] (numeric) = -0.3306586515657241 absolute error = 4.78697838868225e-07 relative error = 0.0001447707911427284 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.246 Order of pole (three term test) = 1.662 Radius of convergence (six term test) for eq 1 = 5.767 Order of pole (six term test) = -0.7739 TOP MAIN SOLVE Loop x[1] = 2.770000000005044 y[1] (analytic) = -0.3404159644412059 y[1] (numeric) = -0.3404154819909547 absolute error = 4.824502511935336e-07 relative error = 0.0001417237443565484 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.256 Order of pole (three term test) = 1.661 Radius of convergence (six term test) for eq 1 = 5.783 Order of pole (six term test) = -0.7742 TOP MAIN SOLVE Loop x[1] = 2.78000000000511 y[1] (analytic) = -0.350180241758373 y[1] (numeric) = -0.3501797556172148 absolute error = 4.861411582735009e-07 relative error = 0.0001388259816808688 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.266 Order of pole (three term test) = 1.661 Radius of convergence (six term test) for eq 1 = 5.799 Order of pole (six term test) = -0.7744 TOP MAIN SOLVE Loop x[1] = 2.790000000005175 y[1] (analytic) = -0.3599518393793499 y[1] (numeric) = -0.3599513496086138 absolute error = 4.897707361339876e-07 relative error = 0.0001360656294960123 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.276 Order of pole (three term test) = 1.661 Radius of convergence (six term test) for eq 1 = 5.815 Order of pole (six term test) = -0.7747 TOP MAIN SOLVE Loop x[1] = 2.800000000005241 y[1] (analytic) = -0.3697306348127989 y[1] (numeric) = -0.3697301414736466 absolute error = 4.93339152307648e-07 relative error = 0.0001334320464295403 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.286 Order of pole (three term test) = 1.661 Radius of convergence (six term test) for eq 1 = 5.831 Order of pole (six term test) = -0.7749 TOP MAIN SOLVE Loop x[1] = 2.810000000005306 y[1] (analytic) = -0.3795165059111835 y[1] (numeric) = -0.3795160090646021 absolute error = 4.968465813770528e-07 relative error = 0.0001309156712918641 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.296 Order of pole (three term test) = 1.661 Radius of convergence (six term test) for eq 1 = 5.847 Order of pole (six term test) = -0.7752 TOP MAIN SOLVE Loop x[1] = 2.820000000005372 y[1] (analytic) = -0.3893093308701896 y[1] (numeric) = -0.3893088305769951 absolute error = 5.002931944830813e-07 relative error = 0.0001285078868684753 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.306 Order of pole (three term test) = 1.661 Radius of convergence (six term test) for eq 1 = 5.863 Order of pole (six term test) = -0.7755 TOP MAIN SOLVE Loop x[1] = 2.830000000005437 y[1] (analytic) = -0.3991089882281471 y[1] (numeric) = -0.3991084845489852 absolute error = 5.036791619339454e-07 relative error = 0.0001262009067172453 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.316 Order of pole (three term test) = 1.66 Radius of convergence (six term test) for eq 1 = 5.879 Order of pole (six term test) = -0.7758 TOP MAIN SOLVE Loop x[1] = 2.840000000005503 y[1] (analytic) = -0.4089153568654548 y[1] (numeric) = -0.4089148498608005 absolute error = 5.070046543154128e-07 relative error = 0.0001239876775971102 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.326 Order of pole (three term test) = 1.66 Radius of convergence (six term test) for eq 1 = 5.895 Order of pole (six term test) = -0.776 TOP MAIN SOLVE Loop x[1] = 2.850000000005569 y[1] (analytic) = -0.4187283160040074 y[1] (numeric) = -0.418727805734164 absolute error = 5.102698434344966e-07 relative error = 0.0001218617953292686 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.336 Order of pole (three term test) = 1.66 Radius of convergence (six term test) for eq 1 = 5.911 Order of pole (six term test) = -0.7763 TOP MAIN SOLVE Loop x[1] = 2.860000000005634 y[1] (analytic) = -0.4285477452066172 y[1] (numeric) = -0.4285472317317199 absolute error = 5.134748973234515e-07 relative error = 0.0001198174306286195 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.346 Order of pole (three term test) = 1.66 Radius of convergence (six term test) for eq 1 = 5.927 Order of pole (six term test) = -0.7766 TOP MAIN SOLVE Loop x[1] = 2.8700000000057 y[1] (analytic) = -0.4383735243764431 y[1] (numeric) = -0.4383730077564545 absolute error = 5.166199885109357e-07 relative error = 0.0001178492677553447 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.356 Order of pole (three term test) = 1.66 Radius of convergence (six term test) for eq 1 = 5.943 Order of pole (six term test) = -0.7769 TOP MAIN SOLVE Loop x[1] = 2.880000000005765 y[1] (analytic) = -0.4482055337564145 y[1] (numeric) = -0.4482050140511284 absolute error = 5.197052860839158e-07 relative error = 0.0001159524474694146 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.366 Order of pole (three term test) = 1.659 Radius of convergence (six term test) for eq 1 = 5.959 Order of pole (six term test) = -0.7773 TOP MAIN SOLVE Loop x[1] = 2.890000000005831 y[1] (analytic) = -0.4580436539286618 y[1] (numeric) = -0.4580431311977018 absolute error = 5.227309599620256e-07 relative error = 0.0001141225198686932 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.376 Order of pole (three term test) = 1.659 Radius of convergence (six term test) for eq 1 = 5.975 Order of pole (six term test) = -0.7776 TOP MAIN SOLVE Loop x[1] = 2.900000000005896 y[1] (analytic) = -0.46788776581394 y[1] (numeric) = -0.4678872401167612 absolute error = 5.256971787326314e-07 relative error = 0.0001123554016887203 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.386 Order of pole (three term test) = 1.659 Radius of convergence (six term test) for eq 1 = 5.991 Order of pole (six term test) = -0.7779 TOP MAIN SOLVE Loop x[1] = 2.910000000005962 y[1] (analytic) = -0.4777377506710645 y[1] (numeric) = -0.4777372220669538 absolute error = 5.286041107055439e-07 relative error = 0.0001106473394583176 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.396 Order of pole (three term test) = 1.659 Radius of convergence (six term test) for eq 1 = 6.007 Order of pole (six term test) = -0.7782 TOP MAIN SOLVE Loop x[1] = 2.920000000006027 y[1] (analytic) = -0.4875934900963336 y[1] (numeric) = -0.4875929586444093 absolute error = 5.31451924357107e-07 relative error = 0.0001089948769111147 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.406 Order of pole (three term test) = 1.659 Radius of convergence (six term test) for eq 1 = 6.022 Order of pole (six term test) = -0.7786 TOP MAIN SOLVE Loop x[1] = 2.930000000006093 y[1] (analytic) = -0.4974548660229628 y[1] (numeric) = -0.4974543317821727 absolute error = 5.342407901065549e-07 relative error = 0.0001073948264648986 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.416 Order of pole (three term test) = 1.659 Radius of convergence (six term test) for eq 1 = 6.038 Order of pole (six term test) = -0.7789 TOP MAIN SOLVE Loop x[1] = 2.940000000006158 y[1] (analytic) = -0.5073217607205147 y[1] (numeric) = -0.5073212237496389 absolute error = 5.369708757640979e-07 relative error = 0.0001058442427152099 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.426 Order of pole (three term test) = 1.658 Radius of convergence (six term test) for eq 1 = 6.054 Order of pole (six term test) = -0.7793 TOP MAIN SOLVE Loop x[1] = 2.950000000006224 y[1] (analytic) = -0.5171940567943303 y[1] (numeric) = -0.5171935171519826 absolute error = 5.396423476966561e-07 relative error = 0.0001043404000118379 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.436 Order of pole (three term test) = 1.658 Radius of convergence (six term test) for eq 1 = 6.07 Order of pole (six term test) = -0.7796 TOP MAIN SOLVE Loop x[1] = 2.960000000006289 y[1] (analytic) = -0.52707163718496 y[1] (numeric) = -0.5270710949295893 absolute error = 5.422553707168376e-07 relative error = 0.0001028807722633251 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.446 Order of pole (three term test) = 1.658 Radius of convergence (six term test) for eq 1 = 6.086 Order of pole (six term test) = -0.78 TOP MAIN SOLVE Loop x[1] = 2.970000000006355 y[1] (analytic) = -0.5369543851676023 y[1] (numeric) = -0.5369538403574849 absolute error = 5.448101173533004e-07 relative error = 0.0001014630166737992 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.456 Order of pole (three term test) = 1.658 Radius of convergence (six term test) for eq 1 = 6.102 Order of pole (six term test) = -0.7803 TOP MAIN SOLVE Loop x[1] = 2.98000000000642 y[1] (analytic) = -0.5468421843515292 y[1] (numeric) = -0.5468416370447791 absolute error = 5.473067501426954e-07 relative error = 0.0001000849542709872 % Correct digits = 6 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.466 Order of pole (three term test) = 1.658 Radius of convergence (six term test) for eq 1 = 6.118 Order of pole (six term test) = -0.7807 TOP MAIN SOLVE Loop x[1] = 2.990000000006486 y[1] (analytic) = -0.5567349186795278 y[1] (numeric) = -0.5567343689340902 absolute error = 5.497454376168776e-07 relative error = 9.874455852720212e-05 % Correct digits = 7 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.476 Order of pole (three term test) = 1.657 Radius of convergence (six term test) for eq 1 = 6.133 Order of pole (six term test) = -0.7811 Finished! diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 100000 Total Elapsed Time = 2.0 Seconds Elapsed Time(since restart) = 2.0 Seconds Time to Timeout = 29 Minutes 58.0 Seconds Percent Done = 100 %