##############ECHO OF PROBLEM################# ##############temp/sing1postode.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=-2.0; x_end=-1.5; 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 = 2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 0.2 Order of pole (six term test) = 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = 0.2499999375000156 y[1] (numeric) = 0.2499999375000156 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 = 2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 2 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.989999999994161 y[1] (analytic) = 0.2525188120216803 y[1] (numeric) = 0.2525188120202046 absolute error = 1.475652933180527e-12 relative error = 5.843734656306846e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 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 TOP MAIN SOLVE Loop x[1] = -1.979999999988323 y[1] (analytic) = 0.2550759475910233 y[1] (numeric) = 0.2550759475880512 absolute error = 2.972067036921544e-12 relative error = 1.165169458347682e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.969999999982484 y[1] (analytic) = 0.2576721230502357 y[1] (numeric) = 0.257672123045742 absolute error = 4.493683203321552e-12 relative error = 1.743953963714369e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.959999999976645 y[1] (analytic) = 0.2603081371604785 y[1] (numeric) = 0.2603081371544452 absolute error = 6.033229471569257e-12 relative error = 2.317726037065759e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.949999999970807 y[1] (analytic) = 0.2629848092163399 y[1] (numeric) = 0.2629848092087425 absolute error = 7.597478202114871e-12 relative error = 2.8889418460155e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.939999999964968 y[1] (analytic) = 0.2657029796825209 y[1] (numeric) = 0.2657029796733431 absolute error = 9.17782516651755e-12 relative error = 3.454167197328313e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.929999999959129 y[1] (analytic) = 0.2684635108536718 y[1] (numeric) = 0.2684635108428765 absolute error = 1.079530909109394e-11 relative error = 4.021145762702183e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.919999999953291 y[1] (analytic) = 0.2712672875383486 y[1] (numeric) = 0.2712672875259131 absolute error = 1.243549707652392e-11 relative error = 4.584222885616436e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.909999999947452 y[1] (analytic) = 0.2741152177681002 y[1] (numeric) = 0.2741152177539967 absolute error = 1.410349614872075e-11 relative error = 5.145097840081327e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.899999999941613 y[1] (analytic) = 0.2770082335327496 y[1] (numeric) = 0.2770082335169528 absolute error = 1.579686381703027e-11 relative error = 5.702669417283826e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.889999999935775 y[1] (analytic) = 0.279947291542978 y[1] (numeric) = 0.2799472915254629 absolute error = 1.751515599224263e-11 relative error = 6.256590623079369e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.879999999929936 y[1] (analytic) = 0.2829333740213791 y[1] (numeric) = 0.2829333740021208 absolute error = 1.925831716320658e-11 relative error = 6.806661543488108e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.869999999924097 y[1] (analytic) = 0.2859674895232034 y[1] (numeric) = 0.2859674895021849 absolute error = 2.101846474644731e-11 relative error = 7.349949038434969e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.859999999918259 y[1] (analytic) = 0.2890506737880738 y[1] (numeric) = 0.2890506737652566 absolute error = 2.281724809094499e-11 relative error = 7.893857430574315e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.84999999991242 y[1] (analytic) = 0.2921839906240147 y[1] (numeric) = 0.2921839905993768 absolute error = 2.463790282902778e-11 relative error = 8.43232470622666e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.839999999906581 y[1] (analytic) = 0.2953685328252035 y[1] (numeric) = 0.2953685327987092 absolute error = 2.64943067485035e-11 relative error = 8.969915141293198e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.829999999900743 y[1] (analytic) = 0.2986054231249231 y[1] (numeric) = 0.2986054230965347 absolute error = 2.838840273966525e-11 relative error = 9.506995031295471e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 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] = -1.819999999894904 y[1] (analytic) = 0.301895815185266 y[1] (numeric) = 0.3018958151549528 absolute error = 3.031319639745789e-11 relative error = 1.004094620485396e-08 % Desired digits = 10 Estimated correct digits = 10 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] = -1.809999999889065 y[1] (analytic) = 0.3052408946252206 y[1] (numeric) = 0.3052408945929516 absolute error = 3.226902078878879e-11 relative error = 1.05716571262213e-08 % Desired digits = 10 Estimated correct digits = 10 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] = -1.799999999883227 y[1] (analytic) = 0.3086418800888482 y[1] (numeric) = 0.3086418800545905 absolute error = 3.425765227049737e-11 relative error = 1.109948275996624e-08 % Desired digits = 10 Estimated correct digits = 10 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] = -1.789999999877388 y[1] (analytic) = 0.3121000243553486 y[1] (numeric) = 0.3121000243190738 absolute error = 3.627476097278759e-11 relative error = 1.162279978917468e-08 % Desired digits = 10 Estimated correct digits = 10 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] = -1.779999999871549 y[1] (analytic) = 0.3156166154929022 y[1] (numeric) = 0.3156166154545725 absolute error = 3.832967276906629e-11 relative error = 1.214437735136548e-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] = -1.769999999865711 y[1] (analytic) = 0.3191929780582723 y[1] (numeric) = 0.319192978017861 absolute error = 4.041134094023846e-11 relative error = 1.266047304238031e-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] = -1.759999999859872 y[1] (analytic) = 0.3228304743442543 y[1] (numeric) = 0.322830474301726 absolute error = 4.252831420359371e-11 relative error = 1.31735748584389e-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] = -1.749999999854033 y[1] (analytic) = 0.3265305056771636 y[1] (numeric) = 0.3265305056324832 absolute error = 4.468037051452711e-11 relative error = 1.368336793582833e-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] = -1.739999999848195 y[1] (analytic) = 0.3302945137666717 y[1] (numeric) = 0.330294513719796 absolute error = 4.68757255234209e-11 relative error = 1.41920993445671e-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] = -1.729999999842356 y[1] (analytic) = 0.3341239821104164 y[1] (numeric) = 0.3341239820612985 absolute error = 4.911793194395386e-11 relative error = 1.470051076062002e-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] = -1.719999999836517 y[1] (analytic) = 0.338020437455942 y[1] (numeric) = 0.33802043740455 absolute error = 5.139200176529357e-11 relative error = 1.520381493855444e-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] = -1.709999999830679 y[1] (analytic) = 0.3419854513226583 y[1] (numeric) = 0.3419854512689551 absolute error = 5.370326405795822e-11 relative error = 1.570337681040412e-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] = -1.69999999982484 y[1] (analytic) = 0.3460206415866536 y[1] (numeric) = 0.3460206415306044 absolute error = 5.604927633129364e-11 relative error = 1.619824646133351e-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] = -1.689999999819001 y[1] (analytic) = 0.3501276741313419 y[1] (numeric) = 0.3501276740728883 absolute error = 5.845363082457311e-11 relative error = 1.669494734159336e-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] = -1.679999999813163 y[1] (analytic) = 0.3543082645670921 y[1] (numeric) = 0.3543082645061991 absolute error = 6.08930128542795e-11 relative error = 1.718645003347043e-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] = -1.669999999807324 y[1] (analytic) = 0.3585641800231524 y[1] (numeric) = 0.3585641799597868 absolute error = 6.336559055242219e-11 relative error = 1.767203588164626e-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] = -1.659999999801485 y[1] (analytic) = 0.3628972410153627 y[1] (numeric) = 0.3628972409494671 absolute error = 6.589562229208923e-11 relative error = 1.815820426402736e-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] = -1.649999999795646 y[1] (analytic) = 0.3673093233933435 y[1] (numeric) = 0.3673093233248783 absolute error = 6.846523348258415e-11 relative error = 1.863966665753982e-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] = -1.639999999789808 y[1] (analytic) = 0.3718023603710482 y[1] (numeric) = 0.3718023602999546 absolute error = 7.109368649338421e-11 relative error = 1.912136502372785e-08 % Desired digits = 10 Estimated correct digits = 9 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] = -1.629999999783969 y[1] (analytic) = 0.3763783446447829 y[1] (numeric) = 0.3763783445710187 absolute error = 7.376421695681756e-11 relative error = 1.959842217448364e-08 % Desired digits = 10 Estimated correct digits = 9 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] = -1.61999999977813 y[1] (analytic) = 0.3810393306030263 y[1] (numeric) = 0.3810393305265438 absolute error = 7.64824870103098e-11 relative error = 2.007207153373641e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 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] = -1.609999999772292 y[1] (analytic) = 0.3857874366326263 y[1] (numeric) = 0.3857874365533787 absolute error = 7.924760847544121e-11 relative error = 2.054178051186937e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 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] = -1.599999999766453 y[1] (analytic) = 0.3906248475262055 y[1] (numeric) = 0.3906248474441302 absolute error = 8.207529100801025e-11 relative error = 2.101128269944583e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 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] = -1.589999999760614 y[1] (analytic) = 0.3955538169958849 y[1] (numeric) = 0.3955538169109257 absolute error = 8.495920633677656e-11 relative error = 2.147854544345363e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 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] = -1.579999999754776 y[1] (analytic) = 0.4005766702987262 y[1] (numeric) = 0.4005766702108355 absolute error = 8.789069472214806e-11 relative error = 2.194104181269579e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 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] = -1.569999999748937 y[1] (analytic) = 0.4056958069796008 y[1] (numeric) = 0.405695806888719 absolute error = 9.088185759509315e-11 relative error = 2.240147815963572e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 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] = -1.559999999743098 y[1] (analytic) = 0.4109137037375317 y[1] (numeric) = 0.4109137036436019 absolute error = 9.392975286459659e-11 relative error = 2.285875404257474e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 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] = -1.54999999973726 y[1] (analytic) = 0.4162329174218947 y[1] (numeric) = 0.4162329173248561 absolute error = 9.703865488930319e-11 relative error = 2.331354653311683e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 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] = -1.539999999731421 y[1] (analytic) = 0.4216560881652535 y[1] (numeric) = 0.4216560880650536 absolute error = 1.001999039296209e-10 relative error = 2.376341922765051e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 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] = -1.529999999725582 y[1] (analytic) = 0.427185942659991 y[1] (numeric) = 0.4271859425565609 absolute error = 1.034300978197678e-10 relative error = 2.421196193295401e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 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] = -1.519999999719744 y[1] (analytic) = 0.4328252975863315 y[1] (numeric) = 0.4328252974796089 absolute error = 1.067226307327473e-10 relative error = 2.465720726766448e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 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] = -1.509999999713905 y[1] (analytic) = 0.4385770631998027 y[1] (numeric) = 0.4385770630897148 absolute error = 1.100879387649911e-10 relative error = 2.510116191708784e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 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 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; Iterations = 5000000 Total Elapsed Time = 1 Minutes 19.0 Seconds Elapsed Time(since restart) = 1 Minutes 19.0 Seconds Time to Timeout = 8 Minutes 41.0 Seconds Percent Done = 100 %