##############ECHO OF PROBLEM################# ##############temp/sing4postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0); ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-2.0 x_end=1.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=50 ## Not Given = 0 ## No Pole = 3 ## Pole = 4 $glob_max_h=0.5 $glob_type_given_pole=4 ## Real Part $array_given_rad_poles[1][1]=0.0 ## Imag Part $array_given_rad_poles[1][2]=1.0 ## Order $array_given_ord_poles[1][1]=1.0 ## Not Used $array_given_ord_poles[1][2]=0.0 # ELIMINATED in preodein.rb #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.1 $glob_look_poles=true $glob_max_iter=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(1.0 / (x * x + 1.0)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 desired_abs_gbl_error 1.0e-10 range 3.0 estimated_steps 3000000.0 step_error 3.3333333333333335e-17 est_needed_step_err 3.3333333333333335e-17 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1444173827950832e-102 estimated_step_error 1.1444173827950832e-102 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.500055238870521e-98 estimated_step_error 7.500055238870521e-98 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.915238139881815e-93 estimated_step_error 4.915238139881815e-93 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.2212530082326007e-88 estimated_step_error 3.2212530082326007e-88 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 2.1110837018629505e-83 estimated_step_error 2.1110837018629505e-83 best_h 3.2e-05 opt_iter 6 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.383524180073924e-78 estimated_step_error 1.383524180073924e-78 best_h 6.4e-05 opt_iter 7 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.067121282759621e-74 estimated_step_error 9.067121282759621e-74 best_h 0.000128 opt_iter 8 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.942303599376916e-69 estimated_step_error 5.942303599376916e-69 best_h 0.000256 opt_iter 9 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.894446387763168e-64 estimated_step_error 3.894446387763168e-64 best_h 0.000512 opt_iter 10 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.5523932368532326e-59 estimated_step_error 2.5523932368532326e-59 best_h 0.001024 opt_iter 11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.67290533981166e-54 estimated_step_error 1.67290533981166e-54 best_h 0.002048 opt_iter 12 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0965766845223752e-49 estimated_step_error 1.0965766845223752e-49 best_h 0.004096 opt_iter 13 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.18942873664896e-45 estimated_step_error 7.18942873664896e-45 best_h 0.008192 opt_iter 14 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.715473476845421e-40 estimated_step_error 4.715473476845421e-40 best_h 0.016384 opt_iter 15 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.095334802326781e-35 estimated_step_error 3.095334802326781e-35 best_h 0.032768 opt_iter 16 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.035138486570559e-30 estimated_step_error 2.035138486570559e-30 best_h 0.065536 opt_iter 17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3424343618806097e-25 estimated_step_error 1.3424343618806097e-25 best_h 0.131072 opt_iter 18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.913242752753631e-21 estimated_step_error 8.913242752753631e-21 best_h 0.262144 opt_iter 19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.996960503691097e-16 estimated_step_error 5.996960503691097e-16 best_h 0.131072 START of Soultion TOP MAIN SOLVE Loop x[1] -2.0 y[1] (analytic) 0.2 y[1] (numeric) 0.2 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 2.23606797749979 Order of pole (given) 1.0 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 2.2360679774998014 Order of pole (six term test) 1.0000000000000657 TOP MAIN SOLVE Loop x[1] -1.9 y[1] (analytic) 0.2169197396963124 y[1] (numeric) 0.21691973969631237 absolute error 2.7755575615628914e-17 relative error 1.2795320358804928e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 2.1470910553583886 Order of pole (given) 1.0 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 2.1470910553584406 Order of pole (six term test) 1.0000000000002682 TOP MAIN SOLVE Loop x[1] -1.7999999999999998 y[1] (analytic) 0.23584905660377362 y[1] (numeric) 0.2358490566037736 absolute error 2.7755575615628914e-17 relative error 1.1768364061026658e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 2.0591260281974 Order of pole (given) 1.0 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 2.0591260281973907 Order of pole (six term test) 0.9999999999998632 TOP MAIN SOLVE Loop x[1] -1.6999999999999997 y[1] (analytic) 0.25706940874035994 y[1] (numeric) 0.2570694087403599 absolute error 5.551115123125783e-17 relative error 2.159383782895929e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.9723082923316018 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.9723082923316158 Order of pole (six term test) 1.0000000000001403 TOP MAIN SOLVE Loop x[1] -1.5999999999999996 y[1] (analytic) 0.28089887640449446 y[1] (numeric) 0.2808988764044944 absolute error 5.551115123125783e-17 relative error 1.976196983832778e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.8867962264113205 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.01321176394281809 Order of pole (three term test) 16.982924678833182 Derivative of radius w.r.t nth term -202443213176983060000.0 Derivative of order w.r.t nth term -261644311690771170000.0 Derivative of radius w.r.t (n-1)th term -87056838247550060000.0 Derivative of order w.r.t (n-1)th term 8641038205379611000000.0 Derivative of radius w.r.t (n-2)th term 12432271014100352.0 Derivative of order w.r.t (n-2)th term 1.0654927155985358e+63 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.025972337660628564 Guess error in order 0.05035126372160405 Radius of convergence (six term test) for eq 1 1.886796226411284 Order of pole (six term test) 0.999999999999682 TOP MAIN SOLVE Loop x[1] -1.4999999999999996 y[1] (analytic) 0.3076923076923078 y[1] (numeric) 0.3076923076923077 absolute error 1.1102230246251565e-16 relative error 3.6082248300317575e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.8027756377319943 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0033032990611909538 Order of pole (three term test) 16.052800524781762 Derivative of radius w.r.t nth term -769836934860271100.0 Derivative of order w.r.t nth term -220745723349784600000.0 Derivative of radius w.r.t (n-1)th term 1226120656940371500.0 Derivative of order w.r.t (n-1)th term 25372842748262746000000.0 Derivative of radius w.r.t (n-2)th term 2327110197486950400.0 Derivative of order w.r.t (n-2)th term 1.5855887887193945e+62 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.0003488318478839952 Guess error in order 0.1500378880936075 Radius of convergence (six term test) for eq 1 1.8027756377316593 Order of pole (six term test) 0.9999999999970246 TOP MAIN SOLVE Loop x[1] -1.3999999999999995 y[1] (analytic) 0.33783783783783805 y[1] (numeric) 0.3378378378378379 absolute error 1.6653345369377348e-16 relative error 4.929390229335692e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.7204650534085248 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.7204650534085226 Order of pole (six term test) 0.9999999999999805 TOP MAIN SOLVE Loop x[1] -1.2999999999999994 y[1] (analytic) 0.371747211895911 y[1] (numeric) 0.37174721189591087 absolute error 1.1102230246251565e-16 relative error 2.986499936241669e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.640121946685672 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.6401219466856791 Order of pole (six term test) 1.000000000000064 TOP MAIN SOLVE Loop x[1] -1.1999999999999993 y[1] (analytic) 0.4098360655737707 y[1] (numeric) 0.4098360655737706 absolute error 1.1102230246251565e-16 relative error 2.7089441800853804e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.5620499351813304 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.5620499351813335 Order of pole (six term test) 1.0000000000000284 TOP MAIN SOLVE Loop x[1] -1.0999999999999992 y[1] (analytic) 0.4524886877828058 y[1] (numeric) 0.4524886877828056 absolute error 2.220446049250313e-16 relative error 4.9071857688431875e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.48660687473185 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.486606874731843 Order of pole (six term test) 0.9999999999999218 TOP MAIN SOLVE Loop x[1] -0.9999999999999992 y[1] (analytic) 0.5000000000000004 y[1] (numeric) 0.5000000000000002 absolute error 2.220446049250313e-16 relative error 4.4408920985006224e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.4142135623730945 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.4142135623730951 Order of pole (six term test) 1.0000000000000089 TOP MAIN SOLVE Loop x[1] -0.8999999999999992 y[1] (analytic) 0.5524861878453042 y[1] (numeric) 0.5524861878453041 absolute error 1.1102230246251565e-16 relative error 2.009503674571532e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.3453624047073705 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.3453624047068735 Order of pole (six term test) 0.9999999999944595 TOP MAIN SOLVE Loop x[1] -0.7999999999999993 y[1] (analytic) 0.609756097560976 y[1] (numeric) 0.6097560975609759 absolute error 1.1102230246251565e-16 relative error 1.8207657603852555e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.2806248474865694 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.2806248474865698 Order of pole (six term test) 1.0000000000000053 TOP MAIN SOLVE Loop x[1] -0.6999999999999993 y[1] (analytic) 0.6711409395973159 y[1] (numeric) 0.6711409395973158 absolute error 1.1102230246251565e-16 relative error 1.654232306691482e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.2206555615733699 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.02155581038984074 Order of pole (three term test) 16.521630120630594 Derivative of radius w.r.t nth term -40700973431892104.0 Derivative of order w.r.t nth term -903242299812028400.0 Derivative of radius w.r.t (n-1)th term -480485689278044.0 Derivative of order w.r.t (n-1)th term 17106178620491117000.0 Derivative of radius w.r.t (n-2)th term 736944590829353.0 Derivative of order w.r.t (n-2)th term 1.1718247746101656e+53 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.02248831994788554 Guess error in order 0.7485964136445189 Radius of convergence (six term test) for eq 1 1.2206555615733599 Order of pole (six term test) 0.9999999999998685 TOP MAIN SOLVE Loop x[1] -0.5999999999999993 y[1] (analytic) 0.7352941176470592 y[1] (numeric) 0.7352941176470592 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.1661903789690597 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.1661903789690446 Order of pole (six term test) 0.9999999999997993 TOP MAIN SOLVE Loop x[1] -0.49999999999999933 y[1] (analytic) 0.8000000000000004 y[1] (numeric) 0.8000000000000004 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.1180339887498945 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.1180339887498942 Order of pole (six term test) 0.9999999999999964 TOP MAIN SOLVE Loop x[1] -0.39999999999999936 y[1] (analytic) 0.8620689655172418 y[1] (numeric) 0.8620689655172418 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.0770329614269005 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.0770329614268996 Order of pole (six term test) 0.9999999999999893 TOP MAIN SOLVE Loop x[1] -0.2999999999999994 y[1] (analytic) 0.9174311926605507 y[1] (numeric) 0.9174311926605508 absolute error 1.1102230246251565e-16 relative error 1.2101430968414203e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.0440306508910548 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.0440306508910548 Order of pole (six term test) 1.0 TOP MAIN SOLVE Loop x[1] -0.19999999999999937 y[1] (analytic) 0.9615384615384617 y[1] (numeric) 0.9615384615384618 absolute error 1.1102230246251565e-16 relative error 1.1546319456101626e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.0198039027185568 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0010835441320301853 Order of pole (three term test) 16.007394062903927 Derivative of radius w.r.t nth term -2850750979798.8257 Derivative of order w.r.t nth term -2611497090043704.0 Derivative of radius w.r.t (n-1)th term 15247315744254.336 Derivative of order w.r.t (n-1)th term 908433503469328400.0 Derivative of radius w.r.t (n-2)th term 87953050375178.83 Derivative of order w.r.t (n-2)th term 3.0303790120562674e+48 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 1.6023586942823112e-05 Guess error in order 0.022018172213097535 Radius of convergence (six term test) for eq 1 1.0198039027185533 Order of pole (six term test) 0.9999999999999449 TOP MAIN SOLVE Loop x[1] -0.09999999999999937 y[1] (analytic) 0.9900990099009903 y[1] (numeric) 0.9900990099009902 absolute error 1.1102230246251565e-16 relative error 1.1213252548714078e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.004987562112089 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.0049875621120883 Order of pole (six term test) 0.9999999999999911 TOP MAIN SOLVE Loop x[1] 6.38378239159465e-16 y[1] (analytic) 1.0 y[1] (numeric) 1.0 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.000000000000002 Order of pole (six term test) 1.000000000000032 TOP MAIN SOLVE Loop x[1] 0.10000000000000064 y[1] (analytic) 0.9900990099009899 y[1] (numeric) 0.99009900990099 absolute error 1.1102230246251565e-16 relative error 1.1213252548714084e-14% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.0049875621120892 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0073639554295288024 Order of pole (three term test) 16.985545454804214 Derivative of radius w.r.t nth term -813941115682243.4 Derivative of order w.r.t nth term -1597667008706048.0 Derivative of radius w.r.t (n-1)th term -631382882042287.5 Derivative of order w.r.t (n-1)th term 94699869390342080.0 Derivative of radius w.r.t (n-2)th term 115295045048.66797 Derivative of order w.r.t (n-2)th term 2.977109997570558e+48 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.014515025605905804 Guess error in order 0.0427368339569158 Radius of convergence (six term test) for eq 1 1.0049875621120887 Order of pole (six term test) 0.9999999999999947 TOP MAIN SOLVE Loop x[1] 0.20000000000000065 y[1] (analytic) 0.9615384615384613 y[1] (numeric) 0.9615384615384613 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.019803902718557 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.019803902718577 Order of pole (six term test) 1.000000000000318 TOP MAIN SOLVE Loop x[1] 0.30000000000000066 y[1] (analytic) 0.9174311926605502 y[1] (numeric) 0.9174311926605502 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.044030650891055 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.016106625572177413 Order of pole (three term test) 16.940684993822458 Derivative of radius w.r.t nth term 3822550981400898.0 Derivative of order w.r.t nth term 14077103491339776.0 Derivative of radius w.r.t (n-1)th term 1230433253968805.0 Derivative of order w.r.t (n-1)th term -379102123612372200.0 Derivative of radius w.r.t (n-2)th term -1905918899120.4375 Derivative of order w.r.t (n-2)th term -2.0697112083371453e+49 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.03030252195372857 Guess error in order 0.16739020865912754 Radius of convergence (six term test) for eq 1 1.0440306508910553 Order of pole (six term test) 1.0000000000000018 TOP MAIN SOLVE Loop x[1] 0.4000000000000007 y[1] (analytic) 0.862068965517241 y[1] (numeric) 0.862068965517241 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.077032961426901 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0149901126907869 Order of pole (three term test) 15.870919331339422 Derivative of radius w.r.t nth term 1372336772545055.2 Derivative of order w.r.t nth term 103366729305844220.0 Derivative of radius w.r.t (n-1)th term -677552913246175.8 Derivative of order w.r.t (n-1)th term -2541806830574033000.0 Derivative of radius w.r.t (n-2)th term -286241068699744.75 Derivative of order w.r.t (n-2)th term 7.873492611270861e+49 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius -0.0038698675388484545 Guess error in order -0.4372274630473285 Radius of convergence (six term test) for eq 1 1.0770329614268987 Order of pole (six term test) 0.9999999999999662 TOP MAIN SOLVE Loop x[1] 0.5000000000000007 y[1] (analytic) 0.7999999999999996 y[1] (numeric) 0.7999999999999996 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.1180339887498951 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.002088776269561217 Order of pole (three term test) 16.999076008574566 Derivative of radius w.r.t nth term -1763749842832079.2 Derivative of order w.r.t nth term -780212680093696.0 Derivative of radius w.r.t (n-1)th term -4957843693469858.0 Derivative of order w.r.t (n-1)th term 163348229623043260.0 Derivative of radius w.r.t (n-2)th term 12688787268.511719 Derivative of order w.r.t (n-2)th term 8.49396288241215e+50 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.004173692516396989 Guess error in order 0.0027694129958443815 Radius of convergence (six term test) for eq 1 1.1180339887498956 Order of pole (six term test) 1.000000000000007 TOP MAIN SOLVE Loop x[1] 0.6000000000000006 y[1] (analytic) 0.7352941176470584 y[1] (numeric) 0.7352941176470584 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.1661903789690604 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0688462236127611 Order of pole (three term test) 15.692105613436649 Derivative of radius w.r.t nth term -113154195845194370.0 Derivative of order w.r.t nth term -2149627529237315600.0 Derivative of radius w.r.t (n-1)th term 15621624857162140.0 Derivative of order w.r.t (n-1)th term 11169306923338007000.0 Derivative of radius w.r.t (n-2)th term 1501366993306705.0 Derivative of order w.r.t (n-2)th term -3.277228364733049e+51 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius -0.04239473157290852 Guess error in order -1.2080800195217107 Radius of convergence (six term test) for eq 1 1.1661903789690558 Order of pole (six term test) 0.999999999999936 TOP MAIN SOLVE Loop x[1] 0.7000000000000006 y[1] (analytic) 0.671140939597315 y[1] (numeric) 0.671140939597315 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.2206555615733707 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 1.220655561573371 Order of pole (six term test) 1.000000000000007 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y[1] (analytic) 0.6097560975609753 y[1] (numeric) 0.6097560975609753 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.2806248474865702 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.05652057925265383 Order of pole (three term test) 16.67048101201705 Derivative of radius w.r.t nth term 795753898101179500.0 Derivative of order w.r.t nth term 4639301696000819000.0 Derivative of radius w.r.t (n-1)th term 28237696086792810.0 Derivative of order w.r.t (n-1)th term -34252884823039070000.0 Derivative of radius w.r.t (n-2)th term -994391842360508.2 Derivative of order w.r.t (n-2)th term -6.268244461806373e+53 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius 0.07579195035421873 Guess error in order 0.6628086736249235 Radius of convergence (six term test) for eq 1 1.2806248474865716 Order of pole (six term test) 1.000000000000016 TOP MAIN SOLVE Loop x[1] 0.9000000000000006 y[1] (analytic) 0.5524861878453036 y[1] (numeric) 0.5524861878453036 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 1.3453624047073713 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11864689493859071 Order of pole (three term test) 15.118473959942317 Derivative of radius w.r.t nth term 3730710603555348000.0 Derivative of order w.r.t nth term 59162350200077350000.0 Derivative of radius w.r.t (n-1)th term -511064052153256300.0 Derivative of order w.r.t (n-1)th term -160954703977354130000.0 Derivative of radius w.r.t (n-2)th term -34492952482234816.0 Derivative of order w.r.t (n-2)th term 1.541502078642482e+55 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius -0.20918065492071117 Guess error in order -4.975842598072367 Radius of convergence (six term test) for eq 1 1.3453624047071542 Order of pole (six term test) 0.9999999999975806 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0); Iterations 30 Total Elapsed Time 0.0 Seconds Elapsed Time(since restart) 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 103.33333333333336%