##############ECHO OF PROBLEM################# ##############temp/expt_lin_cpostode.ode################# diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , 2.0); ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.1; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(5.0/3.0 * expt((0.2 * x + 0.3),3.0)) ; } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 4.9 estimated_steps = 4900000.000000001 step_error = 2.040816326530612e-17 est_needed_step_err = 2.040816326530612e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.05461333333333335 y[1] (numeric) = 0.05461333333333335 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 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] = 0.2 y[1] (analytic) = 0.06550666666666666 y[1] (numeric) = 0.06550666666666669 absolute error = 2.775557561562891e-17 relative error = 4.237061207352267e-14 % Correct digits = 16 h = 0.1 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] = 0.3 y[1] (analytic) = 0.07776 y[1] (numeric) = 0.07776000000000002 absolute error = 2.775557561562891e-17 relative error = 3.569389868265035e-14 % Correct digits = 16 h = 0.1 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] = 0.4 y[1] (analytic) = 0.09145333333333334 y[1] (numeric) = 0.09145333333333336 absolute error = 1.387778780781446e-17 relative error = 1.517472059463601e-14 % Correct digits = 16 h = 0.1 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] = 0.5 y[1] (analytic) = 0.1066666666666667 y[1] (numeric) = 0.1066666666666667 absolute error = 1.387778780781446e-17 relative error = 1.301042606982605e-14 % Correct digits = 16 h = 0.1 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] = 0.6 y[1] (analytic) = 0.12348 y[1] (numeric) = 0.12348 absolute error = 4.163336342344337e-17 relative error = 3.371668563608955e-14 % Correct digits = 16 h = 0.1 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] = 0.7 y[1] (analytic) = 0.1419733333333333 y[1] (numeric) = 0.1419733333333333 absolute error = 5.551115123125783e-17 relative error = 3.909970268918424e-14 % Correct digits = 16 h = 0.1 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] = 0.7999999999999999 y[1] (analytic) = 0.1622266666666666 y[1] (numeric) = 0.1622266666666667 absolute error = 5.551115123125783e-17 relative error = 3.421826532706779e-14 % Correct digits = 16 h = 0.1 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] = 0.8999999999999999 y[1] (analytic) = 0.18432 y[1] (numeric) = 0.18432 absolute error = 2.775557561562891e-17 relative error = 1.505836350674312e-14 % Correct digits = 16 h = 0.1 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] = 0.9999999999999999 y[1] (analytic) = 0.2083333333333333 y[1] (numeric) = 0.2083333333333333 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 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] = 1.1 y[1] (analytic) = 0.2343466666666667 y[1] (numeric) = 0.2343466666666667 absolute error = 2.775557561562891e-17 relative error = 1.184381071445248e-14 % Correct digits = 16 h = 0.1 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] = 1.2 y[1] (analytic) = 0.2624400000000001 y[1] (numeric) = 0.26244 absolute error = 5.551115123125783e-17 relative error = 2.115193996008909e-14 % Correct digits = 16 h = 0.1 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] = 1.3 y[1] (analytic) = 0.2926933333333334 y[1] (numeric) = 0.2926933333333334 absolute error = 5.551115123125783e-17 relative error = 1.896563567030036e-14 % Correct digits = 16 h = 0.1 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] = 1.4 y[1] (analytic) = 0.3251866666666668 y[1] (numeric) = 0.3251866666666667 absolute error = 1.110223024625157e-16 relative error = 3.414109920328292e-14 % Correct digits = 16 h = 0.1 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] = 1.5 y[1] (analytic) = 0.3600000000000002 y[1] (numeric) = 0.36 absolute error = 1.665334536937735e-16 relative error = 4.625929269271483e-14 % Correct digits = 16 h = 0.1 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] = 1.6 y[1] (analytic) = 0.3972133333333335 y[1] (numeric) = 0.3972133333333334 absolute error = 1.110223024625157e-16 relative error = 2.795029601117341e-14 % Correct digits = 16 h = 0.1 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] = 1.7 y[1] (analytic) = 0.4369066666666669 y[1] (numeric) = 0.4369066666666668 absolute error = 1.665334536937735e-16 relative error = 3.811648262644349e-14 % Correct digits = 16 h = 0.1 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] = 1.8 y[1] (analytic) = 0.4791600000000004 y[1] (numeric) = 0.4791600000000001 absolute error = 2.220446049250313e-16 relative error = 4.634038837236646e-14 % Correct digits = 16 h = 0.1 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] = 1.900000000000001 y[1] (analytic) = 0.5240533333333337 y[1] (numeric) = 0.5240533333333335 absolute error = 2.220446049250313e-16 relative error = 4.237061207352264e-14 % Correct digits = 16 h = 0.1 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] = 2 y[1] (analytic) = 0.5716666666666671 y[1] (numeric) = 0.5716666666666669 absolute error = 2.220446049250313e-16 relative error = 3.884162185277513e-14 % Correct digits = 16 h = 0.1 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] = 2.100000000000001 y[1] (analytic) = 0.6220800000000005 y[1] (numeric) = 0.6220800000000002 absolute error = 3.33066907387547e-16 relative error = 5.354084802397548e-14 % Correct digits = 16 h = 0.1 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] = 2.200000000000001 y[1] (analytic) = 0.6753733333333339 y[1] (numeric) = 0.6753733333333336 absolute error = 3.33066907387547e-16 relative error = 4.931596954586303e-14 % Correct digits = 16 h = 0.1 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] = 2.300000000000001 y[1] (analytic) = 0.7316266666666674 y[1] (numeric) = 0.731626666666667 absolute error = 4.440892098500626e-16 relative error = 6.0698882378544e-14 % Correct digits = 16 h = 0.1 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] = 2.400000000000001 y[1] (analytic) = 0.7909200000000008 y[1] (numeric) = 0.7909200000000003 absolute error = 5.551115123125783e-16 relative error = 7.018554497453316e-14 % Correct digits = 16 h = 0.1 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] = 2.500000000000001 y[1] (analytic) = 0.8533333333333343 y[1] (numeric) = 0.8533333333333337 absolute error = 5.551115123125783e-16 relative error = 6.505213034913019e-14 % Correct digits = 16 h = 0.1 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] = 2.600000000000001 y[1] (analytic) = 0.9189466666666676 y[1] (numeric) = 0.9189466666666671 absolute error = 4.440892098500626e-16 relative error = 4.832589593702161e-14 % Correct digits = 16 h = 0.1 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] = 2.700000000000001 y[1] (analytic) = 0.9878400000000012 y[1] (numeric) = 0.9878400000000005 absolute error = 6.661338147750939e-16 relative error = 6.743337127217901e-14 % Correct digits = 16 h = 0.1 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] = 2.800000000000001 y[1] (analytic) = 1.060093333333335 y[1] (numeric) = 1.060093333333334 absolute error = 6.661338147750939e-16 relative error = 6.283727987237851e-14 % Correct digits = 16 h = 0.1 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] = 2.900000000000001 y[1] (analytic) = 1.135786666666668 y[1] (numeric) = 1.135786666666667 absolute error = 6.661338147750939e-16 relative error = 5.864955403377627e-14 % Correct digits = 16 h = 0.1 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] = 3.000000000000001 y[1] (analytic) = 1.215000000000001 y[1] (numeric) = 1.215000000000001 absolute error = 6.661338147750939e-16 relative error = 5.482582837655087e-14 % Correct digits = 16 h = 0.1 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] = 3.100000000000001 y[1] (analytic) = 1.297813333333335 y[1] (numeric) = 1.297813333333334 absolute error = 8.881784197001252e-16 relative error = 6.843653065413547e-14 % Correct digits = 16 h = 0.1 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] = 3.200000000000002 y[1] (analytic) = 1.384306666666668 y[1] (numeric) = 1.384306666666667 absolute error = 8.881784197001252e-16 relative error = 6.416052462123933e-14 % Correct digits = 16 h = 0.1 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] = 3.300000000000002 y[1] (analytic) = 1.474560000000002 y[1] (numeric) = 1.474560000000001 absolute error = 1.110223024625157e-15 relative error = 7.529181753371549e-14 % Correct digits = 16 h = 0.1 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] = 3.400000000000002 y[1] (analytic) = 1.568653333333335 y[1] (numeric) = 1.568653333333334 absolute error = 1.332267629550188e-15 relative error = 8.49306600279339e-14 % Correct digits = 16 h = 0.1 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] = 3.500000000000002 y[1] (analytic) = 1.666666666666669 y[1] (numeric) = 1.666666666666668 absolute error = 1.332267629550188e-15 relative error = 7.993605777301116e-14 % Correct digits = 16 h = 0.1 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] = 3.600000000000002 y[1] (analytic) = 1.768680000000002 y[1] (numeric) = 1.768680000000001 absolute error = 1.332267629550188e-15 relative error = 7.532553257515129e-14 % Correct digits = 16 h = 0.1 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] = 3.700000000000002 y[1] (analytic) = 1.874773333333336 y[1] (numeric) = 1.874773333333335 absolute error = 1.554312234475219e-15 relative error = 8.290667500116726e-14 % Correct digits = 16 h = 0.1 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] = 3.800000000000002 y[1] (analytic) = 1.985026666666669 y[1] (numeric) = 1.985026666666668 absolute error = 1.332267629550188e-15 relative error = 6.711585551580429e-14 % Correct digits = 16 h = 0.1 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] = 3.900000000000002 y[1] (analytic) = 2.099520000000003 y[1] (numeric) = 2.099520000000001 absolute error = 1.77635683940025e-15 relative error = 8.460775984035627e-14 % Correct digits = 16 h = 0.1 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] = 4.000000000000002 y[1] (analytic) = 2.218333333333335 y[1] (numeric) = 2.218333333333335 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 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] = 4.100000000000001 y[1] (analytic) = 2.341546666666669 y[1] (numeric) = 2.341546666666669 absolute error = 4.440892098500626e-16 relative error = 1.896563567030035e-14 % Correct digits = 16 h = 0.1 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] = 4.200000000000001 y[1] (analytic) = 2.469240000000002 y[1] (numeric) = 2.469240000000002 absolute error = 4.440892098500626e-16 relative error = 1.798485403808711e-14 % Correct digits = 16 h = 0.1 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] = 4.300000000000001 y[1] (analytic) = 2.601493333333334 y[1] (numeric) = 2.601493333333335 absolute error = 8.881784197001252e-16 relative error = 3.414109920328292e-14 % Correct digits = 16 h = 0.1 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] = 4.4 y[1] (analytic) = 2.738386666666668 y[1] (numeric) = 2.738386666666669 absolute error = 8.881784197001252e-16 relative error = 3.243436840062001e-14 % Correct digits = 16 h = 0.1 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] = 4.5 y[1] (analytic) = 2.88 y[1] (numeric) = 2.880000000000002 absolute error = 2.220446049250313e-15 relative error = 7.709882115452476e-14 % Correct digits = 16 h = 0.1 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] = 4.6 y[1] (analytic) = 3.026413333333333 y[1] (numeric) = 3.026413333333335 absolute error = 2.220446049250313e-15 relative error = 7.336889594008903e-14 % Correct digits = 16 h = 0.1 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] = 4.699999999999999 y[1] (analytic) = 3.177706666666666 y[1] (numeric) = 3.177706666666669 absolute error = 2.220446049250313e-15 relative error = 6.987574002793356e-14 % Correct digits = 16 h = 0.1 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] = 4.799999999999999 y[1] (analytic) = 3.333959999999998 y[1] (numeric) = 3.333960000000002 absolute error = 3.996802888650564e-15 relative error = 1.198815489283185e-13 % Correct digits = 15 h = 0.1 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] = 4.899999999999999 y[1] (analytic) = 3.495253333333332 y[1] (numeric) = 3.495253333333335 absolute error = 3.108624468950438e-15 relative error = 8.893845946170157e-14 % Correct digits = 16 h = 0.1 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] = 4.999999999999998 y[1] (analytic) = 3.661666666666663 y[1] (numeric) = 3.661666666666668 absolute error = 5.329070518200751e-15 relative error = 1.455367460591923e-13 % Correct digits = 15 h = 0.1 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 Finished! diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , 2.0); Iterations = 50 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 104.1 %