##############ECHO OF PROBLEM################# ##############temp/sing1_backpostode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.5; x_end=-2.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.0000001; glob_type_given_pole=2; array_given_rad_poles[1][1]=0.0; array_given_rad_poles[1][2]=0.001; array_given_ord_poles[1][1]=1.0; 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(1.0 / (x * x + 0.000001)) ; } /* 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 = -0.5 estimated_steps = 500000 step_error = 7.071067811865475e-15 est_needed_step_err = 7.071067811865475e-15 opt_iter = 1 SETTING H FOR MAX H Radius of convergence (given) for eq 1 = 1.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.15 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 0.15 Order of pole (six term test) = 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (analytic) = 0.444444246913668 y[1] (numeric) = 0.444444246913668 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = -1e-07 Radius of convergence (given) for eq 1 = 1.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.5 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.5 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.510000000005839 y[1] (analytic) = 0.4385770630302196 y[1] (numeric) = 0.4385770630336523 absolute error = 3.432754080989753e-12 relative error = 7.827026012879345e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = -1e-07 Radius of convergence (given) for eq 1 = 1.51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.51 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.51 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.520000000011677 y[1] (analytic) = 0.4328252974200734 y[1] (numeric) = 0.4328252974268517 absolute error = 6.778244632243968e-12 relative error = 1.566046317682172e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 Radius of convergence (given) for eq 1 = 1.52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.52 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.52 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.530000000017516 y[1] (analytic) = 0.4271859424969716 y[1] (numeric) = 0.4271859425070451 absolute error = 1.00734975916339e-11 relative error = 2.358106058629331e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 Radius of convergence (given) for eq 1 = 1.53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.53 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.53 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.540000000023355 y[1] (analytic) = 0.4216560880053892 y[1] (numeric) = 0.4216560880186862 absolute error = 1.329697463248181e-11 relative error = 3.153511833632497e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 Radius of convergence (given) for eq 1 = 1.54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.54 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.54 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.550000000029193 y[1] (analytic) = 0.4162329172651046 y[1] (numeric) = 0.4162329172815635 absolute error = 1.645888980661425e-11 relative error = 3.954249922077007e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 Radius of convergence (given) for eq 1 = 1.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.55 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.55 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.560000000035032 y[1] (analytic) = 0.4109137035837375 y[1] (numeric) = 0.4109137036033021 absolute error = 1.956462769570066e-11 relative error = 4.761249752702325e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 Radius of convergence (given) for eq 1 = 1.56 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.56 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.56 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.570000000040871 y[1] (analytic) = 0.4056958068287267 y[1] (numeric) = 0.4056958068513355 absolute error = 2.260880371807161e-11 relative error = 5.572846289637991e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 Radius of convergence (given) for eq 1 = 1.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.57 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.57 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.580000000046709 y[1] (analytic) = 0.4005766701506986 y[1] (numeric) = 0.4005766701762949 absolute error = 2.559630285503545e-11 relative error = 6.38986360473914e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 Radius of convergence (given) for eq 1 = 1.58 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.58 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.58 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.590000000052548 y[1] (analytic) = 0.3955538168506329 y[1] (numeric) = 0.3955538168791608 absolute error = 2.85279022627094e-11 relative error = 7.212141824302499e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 Radius of convergence (given) for eq 1 = 1.59 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.59 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.59 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.600000000058387 y[1] (analytic) = 0.3906248473836598 y[1] (numeric) = 0.390624847415066 absolute error = 3.140615545405012e-11 relative error = 8.039978937439162e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.6 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.610000000064225 y[1] (analytic) = 0.3857874364927203 y[1] (numeric) = 0.3857874365269499 absolute error = 3.422950811682313e-11 relative error = 8.87263422262042e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 Radius of convergence (given) for eq 1 = 1.61 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.61 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.61 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.620000000070064 y[1] (analytic) = 0.3810393304656953 y[1] (numeric) = 0.3810393305026947 absolute error = 3.69993480298092e-11 relative error = 9.710112597717842e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 Radius of convergence (given) for eq 1 = 1.62 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.62 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.62 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.630000000075903 y[1] (analytic) = 0.376378344509964 y[1] (numeric) = 0.3763783445496878 absolute error = 3.97237798210881e-11 relative error = 1.055421503402582e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.63 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.63 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.63 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.640000000081741 y[1] (analytic) = 0.3718023602386805 y[1] (numeric) = 0.3718023602810773 absolute error = 4.239675277517563e-11 relative error = 1.140303486722322e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.64 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.64 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.65000000008758 y[1] (analytic) = 0.3673093232633678 y[1] (numeric) = 0.3673093233083814 absolute error = 4.501354844421712e-11 relative error = 1.225494306659391e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.65 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.65 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.660000000093419 y[1] (analytic) = 0.3628972408877219 y[1] (numeric) = 0.3628972409353079 absolute error = 4.758604621457607e-11 relative error = 1.311281565496909e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.66 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.66 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.66 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.670000000099257 y[1] (analytic) = 0.3585641798977909 y[1] (numeric) = 0.3585641799479096 absolute error = 5.011874248950221e-11 relative error = 1.397762110643306e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.67 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.67 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.67 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.680000000105096 y[1] (analytic) = 0.3543082644439559 y[1] (numeric) = 0.3543082644965669 absolute error = 5.261097113518076e-11 relative error = 1.484892575614835e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.68 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.68 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.690000000110935 y[1] (analytic) = 0.3501276740103785 y[1] (numeric) = 0.3501276740654288 absolute error = 5.505029765373592e-11 relative error = 1.572292101997745e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.69 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.69 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.69 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.700000000116773 y[1] (analytic) = 0.3460206414678125 y[1] (numeric) = 0.3460206415252666 absolute error = 5.745415254665431e-11 relative error = 1.660425583367945e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.7 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.7 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.710000000122612 y[1] (analytic) = 0.3419854512058899 y[1] (numeric) = 0.3419854512657117 absolute error = 5.982181416896992e-11 relative error = 1.749250266583845e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.71 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.71 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.71 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.720000000128451 y[1] (analytic) = 0.3380204373411984 y[1] (numeric) = 0.3380204374033324 absolute error = 6.213407566235674e-11 relative error = 1.838175116010471e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.72 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.72 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.730000000134289 y[1] (analytic) = 0.3341239819976511 y[1] (numeric) = 0.3341239820620608 absolute error = 6.440969979593092e-11 relative error = 1.927718549588689e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.73 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.73 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.73 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.740000000140128 y[1] (analytic) = 0.3302945136558395 y[1] (numeric) = 0.3302945137224845 absolute error = 6.664507834486244e-11 relative error = 2.017747058744831e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.74 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.74 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.74 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.750000000145967 y[1] (analytic) = 0.3265305055682205 y[1] (numeric) = 0.3265305056370689 absolute error = 6.884842695953353e-11 relative error = 2.108483764471719e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.75 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.75 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.760000000151805 y[1] (analytic) = 0.3228304742371577 y[1] (numeric) = 0.32283047430817 absolute error = 7.101236265683042e-11 relative error = 2.199679656161064e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.76 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.76 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.76 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.770000000157644 y[1] (analytic) = 0.3191929779529807 y[1] (numeric) = 0.3191929780261194 absolute error = 7.313871730474375e-11 relative error = 2.291363606235648e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.77 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.77 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.780000000163483 y[1] (analytic) = 0.3156166153893751 y[1] (numeric) = 0.3156166154646048 absolute error = 7.5229766860474e-11 relative error = 2.383580685942763e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.78 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.78 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.78 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.790000000169321 y[1] (analytic) = 0.3121000242535469 y[1] (numeric) = 0.3121000243308274 absolute error = 7.728045980925913e-11 relative error = 2.476143986021522e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.79 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.79 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.79 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.80000000017516 y[1] (analytic) = 0.3086418799887338 y[1] (numeric) = 0.3086418800680323 absolute error = 7.929845668996904e-11 relative error = 2.569270790239602e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.8 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.810000000180999 y[1] (analytic) = 0.3052408945267565 y[1] (numeric) = 0.3052408946080339 absolute error = 8.127748474251462e-11 relative error = 2.662732490956912e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.81 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.81 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.81 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.820000000186837 y[1] (analytic) = 0.301895815088416 y[1] (numeric) = 0.3018958151716504 absolute error = 8.323447486802138e-11 relative error = 2.757059578439157e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.82 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.82 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.82 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.830000000192676 y[1] (analytic) = 0.2986054230296522 y[1] (numeric) = 0.2986054231148044 absolute error = 8.515221860960764e-11 relative error = 2.851663501139825e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.83 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.83 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.83 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.840000000198515 y[1] (analytic) = 0.2953685327314775 y[1] (numeric) = 0.2953685328185212 absolute error = 8.704365006551029e-11 relative error = 2.946950687690301e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.84 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.84 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.850000000204354 y[1] (analytic) = 0.2921839905318004 y[1] (numeric) = 0.2921839906206959 absolute error = 8.889550207058505e-11 relative error = 3.04244944799294e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.85 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.85 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.860000000210192 y[1] (analytic) = 0.2890506736973388 y[1] (numeric) = 0.2890506737880668 absolute error = 9.072803619503134e-11 relative error = 3.138828048193082e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.86 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.86 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.86 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.870000000216031 y[1] (analytic) = 0.2859674894339162 y[1] (numeric) = 0.2859674895264287 absolute error = 9.251249766251135e-11 relative error = 3.235070456632796e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.87 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.87 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.88000000022187 y[1] (analytic) = 0.2829333739335091 y[1] (numeric) = 0.2829333740277885 absolute error = 9.427930658389982e-11 relative error = 3.332208755480927e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.88 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.88 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.890000000227708 y[1] (analytic) = 0.2799472914564955 y[1] (numeric) = 0.2799472915525213 absolute error = 9.602585393508889e-11 relative error = 3.43014048950038e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.89 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.89 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.900000000233547 y[1] (analytic) = 0.2770082334476254 y[1] (numeric) = 0.2770082335453621 absolute error = 9.773670761603626e-11 relative error = 3.528296123173377e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.9 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.910000000239386 y[1] (analytic) = 0.274115217684306 y[1] (numeric) = 0.274115217783729 absolute error = 9.942296985698817e-11 relative error = 3.627050358491661e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.91 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.91 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.91 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.920000000245224 y[1] (analytic) = 0.2712672874558569 y[1] (numeric) = 0.271267287556943 absolute error = 1.010860839478767e-10 relative error = 3.726438410467253e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.92 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.92 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.92 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.930000000251063 y[1] (analytic) = 0.2684635107724557 y[1] (numeric) = 0.2684635108751818 absolute error = 1.027260498887017e-10 relative error = 3.826443660560271e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.93 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.93 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.93 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.940000000256902 y[1] (analytic) = 0.2657029796025543 y[1] (numeric) = 0.2657029797068907 absolute error = 1.04336317363618e-10 relative error = 3.926802684700304e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.94 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.94 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.94 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.95000000026274 y[1] (analytic) = 0.2629848091375973 y[1] (numeric) = 0.2629848092435237 absolute error = 1.059264342906374e-10 relative error = 4.027853724251245e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.95 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.95 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.960000000268579 y[1] (analytic) = 0.2603081370829349 y[1] (numeric) = 0.2603081371904252 absolute error = 1.074902944431244e-10 relative error = 4.129348227361701e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.96 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.96 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.96 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.970000000274418 y[1] (analytic) = 0.257672122973867 y[1] (numeric) = 0.2576721230829025 absolute error = 1.090355583599489e-10 relative error = 4.231562075925741e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.97 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.97 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.97 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.980000000280256 y[1] (analytic) = 0.2550759475158059 y[1] (numeric) = 0.2550759476263578 absolute error = 1.105519564781332e-10 relative error = 4.334080008515222e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.98 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.98 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.98 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.990000000286095 y[1] (analytic) = 0.2525188119475911 y[1] (numeric) = 0.2525188120596286 absolute error = 1.120374903962329e-10 relative error = 4.436797778831847e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.99 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.99 Order of pole (six term test) = 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; Iterations = 5000000 Total Elapsed Time = 1 Minutes 18.0 Seconds Elapsed Time(since restart) = 1 Minutes 18.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 1 Minutes 18.0 Seconds Time to Timeout = 8 Minutes 42.0 Seconds Percent Done = 0 %