##############ECHO OF PROBLEM################# ##############temp/tan_sqrt_new_sm_hpostode.ode################# diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=1.4; x_end=2.1; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.01; glob_max_h=0.000001; glob_type_given_pole=1; array_given_rad_poles[1][1]=-2.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.5; array_given_ord_poles[1][2]=0.0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(tan(sqrt(2.0*x + 1.0))); } /* 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 = 0.01 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.7000000000000002 estimated_steps = 70.00000000000001 step_error = 2.988071523335984e-13 est_needed_step_err = 2.988071523335984e-13 opt_iter = 1 SETTING H FOR MAX H Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = -2.514161640922489 y[1] (numeric) = -2.514161640922489 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 1e-06 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.410000999999177 y[1] (analytic) = -2.47712793326297 y[1] (numeric) = -2.477127885909682 absolute error = 4.735328795746341e-08 relative error = 1.91162060390994e-06 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 8 h = 1e-06 Radius of convergence (given) for eq 1 = 3.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.420000999998354 y[1] (analytic) = -2.441119290637556 y[1] (numeric) = -2.441119198034037 absolute error = 9.260351863105143e-08 relative error = 3.793486003990646e-06 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 8 h = 1e-06 Radius of convergence (given) for eq 1 = 3.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.430000999997532 y[1] (analytic) = -2.406088121902944 y[1] (numeric) = -2.406087986026185 absolute error = 1.358767582892995e-07 relative error = 5.647206228749274e-06 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 8 h = 1e-06 Radius of convergence (given) for eq 1 = 3.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.440000999996709 y[1] (analytic) = -2.371993071094924 y[1] (numeric) = -2.371992893809279 absolute error = 1.772856452753047e-07 relative error = 7.474121549329345e-06 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 8 h = 1e-06 Radius of convergence (given) for eq 1 = 3.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.450000999995886 y[1] (analytic) = -2.3387950887979 y[1] (numeric) = -2.338794871863019 absolute error = 2.169348811698057e-07 relative error = 9.275497550377811e-06 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 8 h = 1e-06 Radius of convergence (given) for eq 1 = 3.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.460000999995064 y[1] (analytic) = -2.30645727340097 y[1] (numeric) = -2.306457018478976 absolute error = 2.549219941805347e-07 relative error = 1.10525348602986e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.470000999994241 y[1] (analytic) = -2.274944725288824 y[1] (numeric) = -2.274944433950949 absolute error = 2.91337874713804e-07 relative error = 1.280637157796509e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.480000999993418 y[1] (analytic) = -2.244224412754213 y[1] (numeric) = -2.244224086486945 absolute error = 3.2626726786944e-07 relative error = 1.453808567517676e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.490000999992596 y[1] (analytic) = -2.214265048547148 y[1] (numeric) = -2.214264688757809 absolute error = 3.597893387663476e-07 relative error = 1.624870243074185e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.500000999991773 y[1] (analytic) = -2.185036976089186 y[1] (numeric) = -2.185036584111128 absolute error = 3.919780584560328e-07 relative error = 1.793919566329726e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.51000099999095 y[1] (analytic) = -2.156512064481325 y[1] (numeric) = -2.156511641578683 absolute error = 4.229026422386539e-07 relative error = 1.96104927583778e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.51 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.520000999990128 y[1] (analytic) = -2.128663611522688 y[1] (numeric) = -2.128663158894849 absolute error = 4.526278396532746e-07 relative error = 2.126347428514072e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.52 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.530000999989305 y[1] (analytic) = -2.101466254035802 y[1] (numeric) = -2.101465772821481 absolute error = 4.812143208354769e-07 relative error = 2.289897922040478e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.53 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.540000999988482 y[1] (analytic) = -2.074895884864169 y[1] (numeric) = -2.074895376145165 absolute error = 5.087190038111089e-07 relative error = 2.451780870173212e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.54 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.55000099998766 y[1] (analytic) = -2.04892957597 y[1] (numeric) = -2.048929040774677 absolute error = 5.351953231702566e-07 relative error = 2.612072808392575e-05 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.55 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.560000999986837 y[1] (analytic) = -2.023545507115303 y[1] (numeric) = -2.023544946421882 absolute error = 5.606934201374258e-07 relative error = 2.770846606443417e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.56 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.570000999986015 y[1] (analytic) = -1.998722899659076 y[1] (numeric) = -1.99872231439861 absolute error = 5.85260466312576e-07 relative error = 2.928172116366927e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.57 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.580000999985192 y[1] (analytic) = -1.974441955047403 y[1] (numeric) = -1.974441346106581 absolute error = 6.08940821766879e-07 relative error = 3.084116097767278e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.58 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.590000999984369 y[1] (analytic) = -1.950683797612835 y[1] (numeric) = -1.950683165836601 absolute error = 6.317762335505961e-07 relative error = 3.238742405733504e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.59 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.600000999983547 y[1] (analytic) = -1.927430421334927 y[1] (numeric) = -1.9274297675289 absolute error = 6.538060264293932e-07 relative error = 3.39211220904447e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.610000999982724 y[1] (analytic) = -1.90466464024544 y[1] (numeric) = -1.904663965178134 absolute error = 6.750673060551549e-07 relative error = 3.544284341668484e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.61 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.620000999981901 y[1] (analytic) = -1.88237004219044 y[1] (numeric) = -1.882369346595399 absolute error = 6.95595040900443e-07 relative error = 3.695315083165085e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.62 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.630000999981079 y[1] (analytic) = -1.86053094568709 y[1] (numeric) = -1.860530230264863 absolute error = 7.154222267935495e-07 relative error = 3.845258411057204e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.63 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.640000999980256 y[1] (analytic) = -1.839132359636145 y[1] (numeric) = -1.839131625056098 absolute error = 7.3458004767879e-07 relative error = 3.994166291675275e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.64 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.650000999979433 y[1] (analytic) = -1.818159945672005 y[1] (numeric) = -1.818159192574008 absolute error = 7.530979972969476e-07 relative error = 4.142088813966237e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.65 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.660000999978611 y[1] (analytic) = -1.797599982951008 y[1] (numeric) = -1.797599211947065 absolute error = 7.710039429120741e-07 relative error = 4.28907404441763e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.66 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.670000999977788 y[1] (analytic) = -1.777439335195692 y[1] (numeric) = -1.777438546871438 absolute error = 7.883242538753166e-07 relative error = 4.435168268561605e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.67 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.680000999976965 y[1] (analytic) = -1.757665419828164 y[1] (numeric) = -1.757664614744245 absolute error = 8.050839188644687e-07 relative error = 4.580416214498757e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.68 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.690000999976143 y[1] (analytic) = -1.738266179039655 y[1] (numeric) = -1.738265357733063 absolute error = 8.213065916251594e-07 relative error = 4.724860907544719e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.69 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.70000099997532 y[1] (analytic) = -1.71923005265602 y[1] (numeric) = -1.719229215641303 absolute error = 8.370147170921882e-07 relative error = 4.868544007819623e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.710000999974497 y[1] (analytic) = -1.700545952670428 y[1] (numeric) = -1.700545100440874 absolute error = 8.522295547042091e-07 relative error = 5.011505589519192e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.71 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.720000999973675 y[1] (analytic) = -1.682203239324906 y[1] (numeric) = -1.682202372353618 absolute error = 8.669712885378544e-07 relative error = 5.153784443345759e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.72 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.730000999972852 y[1] (analytic) = -1.664191698631967 y[1] (numeric) = -1.664190817372875 absolute error = 8.812590914786256e-07 relative error = 5.295418143252705e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.73 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.740000999972029 y[1] (analytic) = -1.646501521236101 y[1] (numeric) = -1.646500626124887 absolute error = 8.95111213594646e-07 relative error = 5.436443283226649e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.74 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.750000999971207 y[1] (analytic) = -1.629123282522899 y[1] (numeric) = -1.629122373977987 absolute error = 9.085449121926104e-07 relative error = 5.57689477487312e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.75 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.760000999970384 y[1] (analytic) = -1.612047923890696 y[1] (numeric) = -1.612047002314028 absolute error = 9.215766678671855e-07 relative error = 5.716806890225384e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.76 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.770000999969561 y[1] (analytic) = -1.595266735106215 y[1] (numeric) = -1.595265800884067 absolute error = 9.342221485297841e-07 relative error = 5.856212807368431e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.77 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.780000999968739 y[1] (analytic) = -1.578771337671723 y[1] (numeric) = -1.578770391175472 absolute error = 9.464962513749953e-07 relative error = 5.995144634249763e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.78 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.790000999967916 y[1] (analytic) = -1.562553669136632 y[1] (numeric) = -1.562552710723452 absolute error = 9.584131801521067e-07 relative error = 6.133633673406333e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.79 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.800000999967093 y[1] (analytic) = -1.54660596829159 y[1] (numeric) = -1.546604998305118 absolute error = 9.69986472254547e-07 relative error = 6.271710391277051e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.810000999966271 y[1] (analytic) = -1.530920761187656 y[1] (numeric) = -1.53091977995866 absolute error = 9.812289964994392e-07 relative error = 6.409404205467971e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.81 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.820000999965448 y[1] (analytic) = -1.515490847927403 y[1] (numeric) = -1.515489855774337 absolute error = 9.921530654821709e-07 relative error = 6.546744025798949e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.830000999964625 y[1] (analytic) = -1.500309290178649 y[1] (numeric) = -1.500308287408235 absolute error = 1.002770413816023e-06 relative error = 6.683757944980922e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.83 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.840000999963803 y[1] (analytic) = -1.485369399365143 y[1] (numeric) = -1.48536838627292 absolute error = 1.013092222779122e-06 relative error = 6.820473231858179e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.84 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.85000099996298 y[1] (analytic) = -1.470664725491703 y[1] (numeric) = -1.470663702362497 absolute error = 1.023129205801609e-06 relative error = 6.956916747014082e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.85 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.860000999962157 y[1] (analytic) = -1.456189046564426 y[1] (numeric) = -1.456188013672862 absolute error = 1.032891564278771e-06 relative error = 7.093114501277582e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.86 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.870000999961335 y[1] (analytic) = -1.441936358569306 y[1] (numeric) = -1.44193531618025 absolute error = 1.042389055294635e-06 relative error = 7.229091971360627e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.87 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.880000999960512 y[1] (analytic) = -1.427900865975144 y[1] (numeric) = -1.427899814344116 absolute error = 1.051631028481381e-06 relative error = 7.364874225797179e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.88 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.890000999959689 y[1] (analytic) = -1.414076972729048 y[1] (numeric) = -1.414075912102649 absolute error = 1.060626398707853e-06 relative error = 7.500485611196504e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.89 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.900000999958867 y[1] (analytic) = -1.400459273714933 y[1] (numeric) = -1.40045820433122 absolute error = 1.069383713137029e-06 relative error = 7.635950100143393e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.910000999958044 y[1] (analytic) = -1.387042546647502 y[1] (numeric) = -1.387041468736365 absolute error = 1.07791113634903e-06 relative error = 7.771291075060055e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.91 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.920000999957221 y[1] (analytic) = -1.373821744375991 y[1] (numeric) = -1.3738206581595 absolute error = 1.086216491197334e-06 relative error = 7.906531510685241e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.92 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.930000999956399 y[1] (analytic) = -1.360791987573719 y[1] (numeric) = -1.360790893266436 absolute error = 1.094307282345497e-06 relative error = 8.041694045367199e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.93 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.940000999955576 y[1] (analytic) = -1.347948557791061 y[1] (numeric) = -1.347947455600364 absolute error = 1.102190696933292e-06 relative error = 8.176800891715756e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.94 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.950000999954753 y[1] (analytic) = -1.335286890850918 y[1] (numeric) = -1.335285780977303 absolute error = 1.109873614790757e-06 relative error = 8.311873818243548e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.95 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.960000999953931 y[1] (analytic) = -1.322802570567158 y[1] (numeric) = -1.322801453204514 absolute error = 1.11736264463147e-06 relative error = 8.446934330891081e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.96 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.970000999953108 y[1] (analytic) = -1.310491322767729 y[1] (numeric) = -1.310490198103612 absolute error = 1.124664117169161e-06 relative error = 8.582003540427073e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.97 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.980000999952285 y[1] (analytic) = -1.298349009605339 y[1] (numeric) = -1.298347877821246 absolute error = 1.131784092889276e-06 relative error = 8.717102139072038e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.98 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.990000999951463 y[1] (analytic) = -1.286371624139695 y[1] (numeric) = -1.286370485411262 absolute error = 1.138728433325298e-06 relative error = 8.852250873357544e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 3.99 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.00000099995064 y[1] (analytic) = -1.274555285176266 y[1] (numeric) = -1.274554139673541 absolute error = 1.145502725119485e-06 relative error = 8.987469891987196e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.010000999952038 y[1] (analytic) = -1.262896232344972 y[1] (numeric) = -1.262895080235205 absolute error = 1.152109767144083e-06 relative error = 9.122758763836212e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 4.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.020000999953436 y[1] (analytic) = -1.251390821418484 y[1] (numeric) = -1.251389662861141 absolute error = 1.158557342950672e-06 relative error = 9.258157588509538e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 4.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.030000999954833 y[1] (analytic) = -1.240035519831819 y[1] (numeric) = -1.240034354981395 absolute error = 1.164850423895913e-06 relative error = 9.393685949043601e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 4.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.040000999956231 y[1] (analytic) = -1.228826902417688 y[1] (numeric) = -1.228825731423908 absolute error = 1.170993779942009e-06 relative error = 9.52936314820343e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 4.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.050000999957629 y[1] (analytic) = -1.217761647333597 y[1] (numeric) = -1.217760470341585 absolute error = 1.176992012741351e-06 relative error = 9.665208420042502e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 4.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.060000999959027 y[1] (analytic) = -1.206836532173043 y[1] (numeric) = -1.206835349323501 absolute error = 1.182849542535891e-06 relative error = 9.801240772899364e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 4.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.070000999960425 y[1] (analytic) = -1.196048430251193 y[1] (numeric) = -1.196047241680586 absolute error = 1.188570607046913e-06 relative error = 9.937478926311456e-05 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 7 h = 1e-06 Radius of convergence (given) for eq 1 = 4.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.080000999961822 y[1] (analytic) = -1.18539430705596 y[1] (numeric) = -1.185393112896655 absolute error = 1.194159304995779e-06 relative error = 0.0001007394162337077 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 6 h = 1e-06 Radius of convergence (given) for eq 1 = 4.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.09000099996322 y[1] (analytic) = -1.174871216855956 y[1] (numeric) = -1.174870017236395 absolute error = 1.199619560576792e-06 relative error = 0.0001021064728938602 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 6 h = 1e-06 Radius of convergence (given) for eq 1 = 4.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; Iterations = 700001 Total Elapsed Time = 1 Minutes 56.0 Seconds Elapsed Time(since restart) = 1 Minutes 56.0 Seconds Time to Timeout = 8 Minutes 4.0 Seconds Percent Done = 100 %