##############ECHO OF PROBLEM################# ##############temp/expt_lin_lin_newpostode.ode################# diff ( y , x , 1 ) = expt ( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln ( 2.0 * x + 1.0 ) + ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; glob_max_h=0.00001; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; glob_max_minutes=30.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(expt(2.0*x+1.0,3.0*x+2.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 900000.0000000001 step_error = 1.111111111111111e-16 est_needed_step_err = 1.111111111111111e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.059527025082972e-152 estimated_step_error = 1.059527025082972e-152 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.473230175068735e-142 estimated_step_error = 1.473230175068735e-142 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.886657497008343e-135 estimated_step_error = 9.886657497008343e-135 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.634792866711534e-127 estimated_step_error = 6.634792866711534e-127 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.45249296148839e-119 estimated_step_error = 4.45249296148839e-119 best_h = 1e-05 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.520956754552532 y[1] (numeric) = 1.520956754552532 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1100099999999961 y[1] (analytic) = 1.589416016111751 y[1] (numeric) = 1.589416016877971 absolute error = 7.66219754311237e-10 relative error = 4.820762761568678e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.1200099999999922 y[1] (analytic) = 1.661477678093273 y[1] (numeric) = 1.66147767885952 absolute error = 7.662470657976428e-10 relative error = 4.611840868527317e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.1300099999999953 y[1] (analytic) = 1.737421092673896 y[1] (numeric) = 1.737421093440119 absolute error = 7.662233070249158e-10 relative error = 4.410118596210294e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.1400000000000053 y[1] (analytic) = 1.817389968552543 y[1] (numeric) = 1.817389969318682 absolute error = 7.661395962088591e-10 relative error = 4.215603747494269e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.1500000000000153 y[1] (analytic) = 1.901784104483919 y[1] (numeric) = 1.901784105249976 absolute error = 7.66056773571222e-10 relative error = 4.028095364584531e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.1600000000000253 y[1] (analytic) = 1.990780368343364 y[1] (numeric) = 1.99078036910933 absolute error = 7.659657352832028e-10 relative error = 3.847565243576337e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.1700000000000353 y[1] (analytic) = 2.084649490500211 y[1] (numeric) = 2.084649491266079 absolute error = 7.658678136124308e-10 relative error = 3.673844534069183e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.1800000000000453 y[1] (analytic) = 2.183679149148946 y[1] (numeric) = 2.183679149914715 absolute error = 7.657687817186343e-10 relative error = 3.506782496032351e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.1900000000000553 y[1] (analytic) = 2.288175082965221 y[1] (numeric) = 2.28817508373089 absolute error = 7.656684175572082e-10 relative error = 3.346196815345908e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.2000000000000653 y[1] (analytic) = 2.39846227969988 y[1] (numeric) = 2.398462280465438 absolute error = 7.655582834331653e-10 relative error = 3.19187126648896e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.2100000000000753 y[1] (analytic) = 2.51488624608273 y[1] (numeric) = 2.514886246848175 absolute error = 7.654441525062339e-10 relative error = 3.043653181922303e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.2200000000000853 y[1] (analytic) = 2.637814364797841 y[1] (numeric) = 2.637814365563164 absolute error = 7.653233602411547e-10 relative error = 2.901354130353324e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.2300000000000953 y[1] (analytic) = 2.767637344711443 y[1] (numeric) = 2.767637345476637 absolute error = 7.651941302810883e-10 relative error = 2.764791896392294e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.2400000000001053 y[1] (analytic) = 2.904770770984286 y[1] (numeric) = 2.904770771749337 absolute error = 7.650515776447264e-10 relative error = 2.633776080669827e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.2500000000001153 y[1] (analytic) = 3.049656762184943 y[1] (numeric) = 3.049656762949841 absolute error = 7.648983668673281e-10 relative error = 2.508145757095997e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.2600000000001253 y[1] (analytic) = 3.20276574204164 y[1] (numeric) = 3.202765742806385 absolute error = 7.647451560899299e-10 relative error = 2.387764880994494e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.2700000000001353 y[1] (analytic) = 3.364598334030522 y[1] (numeric) = 3.364598334795103 absolute error = 7.645808430822854e-10 relative error = 2.272428287647572e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.2800000000001453 y[1] (analytic) = 3.535687387600901 y[1] (numeric) = 3.535687388365312 absolute error = 7.644112010041226e-10 relative error = 2.161987520969169e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.2900000000001553 y[1] (analytic) = 3.716600145486073 y[1] (numeric) = 3.716600146250305 absolute error = 7.642317889633432e-10 relative error = 2.056265831802021e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.3000000000001653 y[1] (analytic) = 3.907940562245493 y[1] (numeric) = 3.907940563009538 absolute error = 7.640448274059963e-10 relative error = 1.955108618558359e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.3100000000001753 y[1] (analytic) = 4.110351784933933 y[1] (numeric) = 4.11035178569778 absolute error = 7.638476517968229e-10 relative error = 1.858351040892965e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.3200000000001853 y[1] (analytic) = 4.324518807600128 y[1] (numeric) = 4.324518808363763 absolute error = 7.636344889760949e-10 relative error = 1.765825339073668e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.3300000000001953 y[1] (analytic) = 4.551171312185456 y[1] (numeric) = 4.551171312948847 absolute error = 7.63391128089097e-10 relative error = 1.67735089655968e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.3400000000002053 y[1] (analytic) = 4.791086709327331 y[1] (numeric) = 4.791086710090489 absolute error = 7.631584253431356e-10 relative error = 1.592871245384501e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.3500000000002153 y[1] (analytic) = 5.04509339357734 y[1] (numeric) = 5.045093394340235 absolute error = 7.628946363524847e-10 relative error = 1.512151662690106e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.3600000000002253 y[1] (analytic) = 5.314074228626133 y[1] (numeric) = 5.314074229388751 absolute error = 7.626184128639579e-10 relative error = 1.435091758327058e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.3700000000002353 y[1] (analytic) = 5.598970279291816 y[1] (numeric) = 5.598970280054156 absolute error = 7.623404130185918e-10 relative error = 1.36157253028858e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.3800000000002453 y[1] (analytic) = 5.900784808282486 y[1] (numeric) = 5.900784809044534 absolute error = 7.620482023185104e-10 relative error = 1.29143533797213e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.3900000000002553 y[1] (analytic) = 6.220587557093526 y[1] (numeric) = 6.220587557855244 absolute error = 7.61717799946382e-10 relative error = 1.224511017577065e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.4000000000002653 y[1] (analytic) = 6.559519331853952 y[1] (numeric) = 6.559519332615331 absolute error = 7.613785157900566e-10 relative error = 1.160723030562156e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.4100000000002753 y[1] (analytic) = 6.918796916501542 y[1] (numeric) = 6.918796917262557 absolute error = 7.610152508163992e-10 relative error = 1.099924249837937e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.4200000000002853 y[1] (analytic) = 7.299718337352473 y[1] (numeric) = 7.299718338113109 absolute error = 7.606359986311872e-10 relative error = 1.042007326144397e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.4300000000002953 y[1] (analytic) = 7.703668504947269 y[1] (numeric) = 7.703668505707512 absolute error = 7.602425355912601e-10 relative error = 9.868578004142248e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.4400000000003053 y[1] (analytic) = 8.132125261011179 y[1] (numeric) = 8.132125261771 absolute error = 7.598206508419025e-10 relative error = 9.343444996903842e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.4500000000003153 y[1] (analytic) = 8.586665860474859 y[1] (numeric) = 8.586665861234213 absolute error = 7.593534689931403e-10 relative error = 8.843403031303545e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.4600000000003253 y[1] (analytic) = 9.068973920772217 y[1] (numeric) = 9.068973921531104 absolute error = 7.58886287144378e-10 relative error = 8.367939898979876e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.4700000000003353 y[1] (analytic) = 9.580846873079601 y[1] (numeric) = 9.580846873837988 absolute error = 7.583871308725065e-10 relative error = 7.91565861472469e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.4800000000003453 y[1] (analytic) = 10.12420395279795 y[1] (numeric) = 10.1242039535558 absolute error = 7.578471183933289e-10 relative error = 7.485498335737186e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.4900000000003553 y[1] (analytic) = 10.70109476942235 y[1] (numeric) = 10.70109477017963 absolute error = 7.57275131491042e-10 relative error = 7.07661363447508e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.5000000000003653 y[1] (analytic) = 11.31370849900782 y[1] (numeric) = 11.31370849976446 absolute error = 7.566445248130549e-10 relative error = 6.68785593052367e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.5100000000003198 y[1] (analytic) = 11.96438374573996 y[1] (numeric) = 11.96438374649959 absolute error = 7.596305806600867e-10 relative error = 6.349099099488185e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.5200000000002742 y[1] (analytic) = 12.6556191227032 y[1] (numeric) = 12.65561912346593 absolute error = 7.627320997016795e-10 relative error = 6.026825651961961e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.5300000000002287 y[1] (analytic) = 13.39008460572624 y[1] (numeric) = 13.39008460649232 absolute error = 7.660787559871096e-10 relative error = 5.721239100009103e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.5400000000001832 y[1] (analytic) = 14.17063371839683 y[1] (numeric) = 14.17063371916646 absolute error = 7.696296933090707e-10 relative error = 5.431159315831513e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.5500000000001377 y[1] (analytic) = 15.0003166107534 y[1] (numeric) = 15.00031661152679 absolute error = 7.73390240738081e-10 relative error = 5.155826112254553e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.5600000000000922 y[1] (analytic) = 15.88239409900061 y[1] (numeric) = 15.88239409977803 absolute error = 7.77424347120359e-10 relative error = 4.894881352738112e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.5700000000000467 y[1] (analytic) = 16.82035273879011 y[1] (numeric) = 16.82035273957185 absolute error = 7.817355651695834e-10 relative error = 4.647557499592685e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.5800000000000012 y[1] (analytic) = 17.81792101021699 y[1] (numeric) = 17.81792101100329 absolute error = 7.863043549605209e-10 relative error = 4.412997198212101e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.5900099999999556 y[1] (analytic) = 18.88018109482638 y[1] (numeric) = 18.88018109561755 absolute error = 7.911715727004776e-10 relative error = 4.190487203098266e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.6000099999999101 y[1] (analytic) = 20.00928005473505 y[1] (numeric) = 20.0092800555313 absolute error = 7.962519532611623e-10 relative error = 3.979413307640397e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.6100099999998646 y[1] (analytic) = 21.21081069338661 y[1] (numeric) = 21.21081069418829 absolute error = 8.01687605189727e-10 relative error = 3.779617935299796e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.6200099999998191 y[1] (analytic) = 22.48965669164186 y[1] (numeric) = 22.48965669244938 absolute error = 8.075140556229599e-10 relative error = 3.590601967361589e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.6300099999997736 y[1] (analytic) = 23.8510444662709 y[1] (numeric) = 23.85104446708461 absolute error = 8.137135409924667e-10 relative error = 3.411647410842677e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.6400099999997281 y[1] (analytic) = 25.30056804282567 y[1] (numeric) = 25.30056804364596 absolute error = 8.202967194392841e-10 relative error = 3.24220672852399e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.6500099999996826 y[1] (analytic) = 26.84421578655163 y[1] (numeric) = 26.84421578737897 absolute error = 8.273488560917031e-10 relative error = 3.082037719672135e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.6600099999996371 y[1] (analytic) = 28.48839913371492 y[1] (numeric) = 28.48839913454977 absolute error = 8.348450819539721e-10 relative error = 2.93047383264848e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.6700099999995915 y[1] (analytic) = 30.23998347688239 y[1] (numeric) = 30.2399834777252 absolute error = 8.428138187355216e-10 relative error = 2.787084256774905e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.680009999999546 y[1] (analytic) = 32.10632136974571 y[1] (numeric) = 32.10632137059703 absolute error = 8.513225679962488e-10 relative error = 2.651573059997037e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.6900099999995005 y[1] (analytic) = 34.09528823010088 y[1] (numeric) = 34.09528823096119 absolute error = 8.603109336036141e-10 relative error = 2.52325461453085e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.700009999999455 y[1] (analytic) = 36.21532073365865 y[1] (numeric) = 36.21532073452863 absolute error = 8.699814202373091e-10 relative error = 2.402246901623448e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.7100099999994095 y[1] (analytic) = 38.47545810655649 y[1] (numeric) = 38.47545810743684 absolute error = 8.803553441794065e-10 relative error = 2.288095808349551e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.720009999999364 y[1] (analytic) = 40.88538654085972 y[1] (numeric) = 40.88538654175098 absolute error = 8.912621751733241e-10 relative error = 2.179903996462456e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.7300099999993185 y[1] (analytic) = 43.4554869750801 y[1] (numeric) = 43.45548697598307 absolute error = 9.029719194586505e-10 relative error = 2.077923830370298e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.740009999999273 y[1] (analytic) = 46.19688650091138 y[1] (numeric) = 46.19688650182671 absolute error = 9.153282576335187e-10 relative error = 1.981363522443143e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.7500099999992275 y[1] (analytic) = 49.12151367810231 y[1] (numeric) = 49.12151367903087 absolute error = 9.285585633733717e-10 relative error = 1.890329702497157e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.760009999999182 y[1] (analytic) = 52.24215806178464 y[1] (numeric) = 52.2421580627273 absolute error = 9.426628366782097e-10 relative error = 1.804410215143412e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 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] = 0.7700099999991364 y[1] (analytic) = 55.57253427078553 y[1] (numeric) = 55.57253427174334 absolute error = 9.578116078046151e-10 relative error = 1.723534152928017e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.202 Order of pole (ratio test) = 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] = 0.7800099999990909 y[1] (analytic) = 59.12735095162966 y[1] (numeric) = 59.12735095260361 absolute error = 9.739551387610845e-10 relative error = 1.647215921372578e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.19 Order of pole (ratio test) = 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] = 0.7900099999990454 y[1] (analytic) = 62.92238502123912 y[1] (numeric) = 62.92238502223034 absolute error = 9.91221327240055e-10 relative error = 1.575307939941363e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.182 Order of pole (ratio test) = 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] = 0.8000099999989999 y[1] (analytic) = 66.9745616019439 y[1] (numeric) = 66.97456160295363 absolute error = 1.009723860079248e-09 relative error = 1.507622948068601e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.176 Order of pole (ratio test) = 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] = 0.8100099999989544 y[1] (analytic) = 71.30204009551397 y[1] (numeric) = 71.30204009654338 absolute error = 1.029405893859803e-09 relative error = 1.443725722967874e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.173 Order of pole (ratio test) = 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] = 0.8200099999989089 y[1] (analytic) = 75.92430687872115 y[1] (numeric) = 75.92430687977161 absolute error = 1.050452169693017e-09 relative error = 1.383551872750017e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.172 Order of pole (ratio test) = 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] = 0.8300099999988634 y[1] (analytic) = 80.86227514166106 y[1] (numeric) = 80.86227514273413 absolute error = 1.073075850399619e-09 relative error = 1.327041378095926e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.172 Order of pole (ratio test) = 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] = 0.8400099999988179 y[1] (analytic) = 86.13839243195277 y[1] (numeric) = 86.13839243304976 absolute error = 1.096992718885303e-09 relative error = 1.273523556585875e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.173 Order of pole (ratio test) = 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] = 0.8500099999987724 y[1] (analytic) = 91.77675651325319 y[1] (numeric) = 91.77675651437583 absolute error = 1.122643311646243e-09 relative error = 1.223232716318675e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.175 Order of pole (ratio test) = 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] = 0.8600099999987268 y[1] (analytic) = 97.80324019555707 y[1] (numeric) = 97.80324019670728 absolute error = 1.150212369793735e-09 relative error = 1.17604730425484e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.178 Order of pole (ratio test) = 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] = 0.8700099999986813 y[1] (analytic) = 104.2456258478148 y[1] (numeric) = 104.2456258489945 absolute error = 1.179671471618349e-09 relative error = 1.131626830405831e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.181 Order of pole (ratio test) = 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] = 0.8800099999986358 y[1] (analytic) = 111.1337503608235 y[1] (numeric) = 111.1337503620349 absolute error = 1.211361677633249e-09 relative error = 1.090003418133789e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.185 Order of pole (ratio test) = 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] = 0.8900099999985903 y[1] (analytic) = 118.4996613904961 y[1] (numeric) = 118.4996613917408 absolute error = 1.244700342795113e-09 relative error = 1.050383037545912e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.189 Order of pole (ratio test) = 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] = 0.9000099999985448 y[1] (analytic) = 126.3777857788888 y[1] (numeric) = 126.377785780169 absolute error = 1.280227479583118e-09 relative error = 1.013016228835509e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.193 Order of pole (ratio test) = 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] = 0.9100099999984993 y[1] (analytic) = 134.8051111231914 y[1] (numeric) = 134.8051111245093 absolute error = 1.317886244578403e-09 relative error = 9.77623350923286e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.197 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.056 Order of pole (three term test) = 22.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9200099999984538 y[1] (analytic) = 143.8213815417301 y[1] (numeric) = 143.8213815430887 absolute error = 1.358586132482742e-09 relative error = 9.446343220451857e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.202 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.139 Order of pole (three term test) = 23.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9300099999984083 y[1] (analytic) = 153.4693087714019 y[1] (numeric) = 153.4693087728041 absolute error = 1.402185034748982e-09 relative error = 9.136582721158843e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.206 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.216 Order of pole (three term test) = 23.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9400099999983628 y[1] (analytic) = 163.7947998234018 y[1] (numeric) = 163.7947998248511 absolute error = 1.449251385565731e-09 relative error = 8.847969454025807e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.211 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.286 Order of pole (three term test) = 24.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9500099999983173 y[1] (analytic) = 174.8472025242149 y[1] (numeric) = 174.8472025257144 absolute error = 1.499500967838685e-09 relative error = 8.576064965243105e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.216 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.352 Order of pole (three term test) = 25.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9600099999982717 y[1] (analytic) = 186.6795703772734 y[1] (numeric) = 186.6795703788268 absolute error = 1.553445372337592e-09 relative error = 8.32145354308524e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.22 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.413 Order of pole (three term test) = 25.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9700099999982262 y[1] (analytic) = 199.3489482981245 y[1] (numeric) = 199.3489482997355 absolute error = 1.61097091222473e-09 relative error = 8.081160828676845e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.225 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.471 Order of pole (three term test) = 26.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9800099999981807 y[1] (analytic) = 212.916680903181 y[1] (numeric) = 212.9166809048536 absolute error = 1.672560756560415e-09 relative error = 7.855470738438637e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.23 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.526 Order of pole (three term test) = 26.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9900099999981352 y[1] (analytic) = 227.4487451699604 y[1] (numeric) = 227.4487451716994 absolute error = 1.7390107132087e-09 relative error = 7.645725686062717e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.234 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.579 Order of pole (three term test) = 27.28 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = expt ( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln ( 2.0 * x + 1.0 ) + ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0 ) ) ; Iterations = 90001 Total Elapsed Time = 2.0 Seconds Elapsed Time(since restart) = 2.0 Seconds Time to Timeout = 29 Minutes 58.0 Seconds Percent Done = 100 %