##############ECHO OF PROBLEM################# ##############temp/multpostode.ode################# diff ( y , x , 1 ) = x * x ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(10.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(20.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.11); glob_lower_ratio_limit=c(0.99); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(1.0) + c(x) * c(x) * c(x) / c(3.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 1.000333333333333 y[1] (numeric) = 1.000333333333333 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 NO POLE (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] (closed_form) = 1.002666666666667 y[1] (numeric) = 1.002666666666667 absolute error = 2.220446049250313e-16 relative error = 2.214540607629967e-14 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 NO POLE (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] (closed_form) = 1.009 y[1] (numeric) = 1.009 absolute error = 2.220446049250313e-16 relative error = 2.200640286670281e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] (closed_form) = 1.021333333333333 y[1] (numeric) = 1.021333333333333 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 0.4999999999999999 y[1] (closed_form) = 1.041666666666667 y[1] (numeric) = 1.041666666666667 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] (closed_form) = 1.072 y[1] (numeric) = 1.072 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 0.7000000000000001 y[1] (closed_form) = 1.114333333333333 y[1] (numeric) = 1.114333333333333 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 0.8000000000000002 y[1] (closed_form) = 1.170666666666667 y[1] (numeric) = 1.170666666666667 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 0.9000000000000002 y[1] (closed_form) = 1.243 y[1] (numeric) = 1.243 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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 y[1] (closed_form) = 1.333333333333333 y[1] (numeric) = 1.333333333333333 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] (closed_form) = 1.443666666666667 y[1] (numeric) = 1.443666666666667 absolute error = 2.220446049250313e-16 relative error = 1.538060066439838e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] (closed_form) = 1.576000000000001 y[1] (numeric) = 1.576 absolute error = 2.220446049250313e-16 relative error = 1.408912467798422e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] (closed_form) = 1.732333333333334 y[1] (numeric) = 1.732333333333334 absolute error = 2.220446049250313e-16 relative error = 1.281766047287077e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 1.400000000000001 y[1] (closed_form) = 1.914666666666668 y[1] (numeric) = 1.914666666666667 absolute error = 4.440892098500626e-16 relative error = 2.319407433060911e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 1.500000000000001 y[1] (closed_form) = 2.125000000000002 y[1] (numeric) = 2.125000000000001 absolute error = 8.881784197001252e-16 relative error = 4.179663151529998e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 1.600000000000001 y[1] (closed_form) = 2.365333333333335 y[1] (numeric) = 2.365333333333334 absolute error = 4.440892098500626e-16 relative error = 1.877491022477716e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 1.700000000000001 y[1] (closed_form) = 2.637666666666669 y[1] (numeric) = 2.637666666666668 absolute error = 8.881784197001252e-16 relative error = 3.367288334513299e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 1.800000000000001 y[1] (closed_form) = 2.944000000000003 y[1] (numeric) = 2.944000000000002 absolute error = 8.881784197001252e-16 relative error = 3.01691039300314e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] (closed_form) = 3.286333333333337 y[1] (numeric) = 3.286333333333336 absolute error = 1.332267629550188e-15 relative error = 4.05396377791922e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 2.000000000000001 y[1] (closed_form) = 3.66666666666667 y[1] (numeric) = 3.66666666666667 absolute error = 4.440892098500626e-16 relative error = 1.21115239050017e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] (closed_form) = 4.087000000000002 y[1] (numeric) = 4.087000000000003 absolute error = 1.77635683940025e-15 relative error = 4.346358794715561e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 2.2 y[1] (closed_form) = 4.549333333333335 y[1] (numeric) = 4.549333333333337 absolute error = 1.77635683940025e-15 relative error = 3.904653076055649e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 2.3 y[1] (closed_form) = 5.055666666666665 y[1] (numeric) = 5.05566666666667 absolute error = 4.440892098500626e-15 relative error = 8.78398911815249e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 2.399999999999999 y[1] (closed_form) = 5.607999999999996 y[1] (numeric) = 5.608000000000002 absolute error = 6.217248937900877e-15 relative error = 1.108639254261926e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 2.499999999999999 y[1] (closed_form) = 6.208333333333328 y[1] (numeric) = 6.208333333333336 absolute error = 7.993605777301127e-15 relative error = 1.287560662115619e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 2.599999999999999 y[1] (closed_form) = 6.858666666666658 y[1] (numeric) = 6.858666666666669 absolute error = 1.06581410364015e-14 relative error = 1.553966908495555e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 2.699999999999998 y[1] (closed_form) = 7.560999999999988 y[1] (numeric) = 7.561000000000002 absolute error = 1.332267629550188e-14 relative error = 1.762025697064132e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 2.799999999999998 y[1] (closed_form) = 8.31733333333332 y[1] (numeric) = 8.317333333333334 absolute error = 1.4210854715202e-14 relative error = 1.708583045271164e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 2.899999999999998 y[1] (closed_form) = 9.129666666666646 y[1] (numeric) = 9.129666666666665 absolute error = 1.953992523340276e-14 relative error = 2.140267103589339e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 2.999999999999997 y[1] (closed_form) = 9.999999999999977 y[1] (numeric) = 9.999999999999996 absolute error = 1.953992523340276e-14 relative error = 1.95399252334028e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 3.099999999999997 y[1] (closed_form) = 10.93033333333331 y[1] (numeric) = 10.93033333333333 absolute error = 2.309263891220326e-14 relative error = 2.112711315196546e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 3.199999999999997 y[1] (closed_form) = 11.92266666666663 y[1] (numeric) = 11.92266666666666 absolute error = 2.486899575160351e-14 relative error = 2.085858511932753e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 3.299999999999996 y[1] (closed_form) = 12.97899999999996 y[1] (numeric) = 12.97899999999999 absolute error = 3.197442310920451e-14 relative error = 2.463550590122861e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 3.399999999999996 y[1] (closed_form) = 14.10133333333329 y[1] (numeric) = 14.10133333333332 absolute error = 3.552713678800501e-14 relative error = 2.519416848619879e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 3.499999999999996 y[1] (closed_form) = 15.29166666666661 y[1] (numeric) = 15.29166666666665 absolute error = 4.085620730620576e-14 relative error = 2.671795573157879e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 3.599999999999995 y[1] (closed_form) = 16.55199999999994 y[1] (numeric) = 16.55199999999998 absolute error = 4.618527782440651e-14 relative error = 2.790314029990738e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 3.699999999999995 y[1] (closed_form) = 17.88433333333326 y[1] (numeric) = 17.88433333333331 absolute error = 4.973799150320701e-14 relative error = 2.781092846804869e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 3.799999999999994 y[1] (closed_form) = 19.29066666666659 y[1] (numeric) = 19.29066666666664 absolute error = 5.329070518200751e-14 relative error = 2.762512364287102e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 3.899999999999994 y[1] (closed_form) = 20.77299999999991 y[1] (numeric) = 20.77299999999997 absolute error = 6.039613253960852e-14 relative error = 2.907434291609723e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 3.999999999999994 y[1] (closed_form) = 22.33333333333323 y[1] (numeric) = 22.3333333333333 absolute error = 6.750155989720952e-14 relative error = 3.022457905845216e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 4.099999999999993 y[1] (closed_form) = 23.97366666666656 y[1] (numeric) = 23.97366666666663 absolute error = 7.105427357601002e-14 relative error = 2.963846730830092e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 4.199999999999993 y[1] (closed_form) = 25.69599999999987 y[1] (numeric) = 25.69599999999996 absolute error = 8.171241461241152e-14 relative error = 3.179966322089505e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 4.299999999999993 y[1] (closed_form) = 27.5023333333332 y[1] (numeric) = 27.50233333333328 absolute error = 8.526512829121202e-14 relative error = 3.10028706502039e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 4.399999999999992 y[1] (closed_form) = 29.39466666666652 y[1] (numeric) = 29.39466666666661 absolute error = 8.881784197001252e-14 relative error = 3.021563162365496e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 4.499999999999992 y[1] (closed_form) = 31.37499999999984 y[1] (numeric) = 31.37499999999994 absolute error = 9.592326932761353e-14 relative error = 3.057315357055427e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 4.599999999999992 y[1] (closed_form) = 33.44533333333315 y[1] (numeric) = 33.44533333333326 absolute error = 1.06581410364015e-13 relative error = 3.186734881717896e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 4.699999999999991 y[1] (closed_form) = 35.60766666666647 y[1] (numeric) = 35.60766666666659 absolute error = 1.13686837721616e-13 relative error = 3.192762917769113e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 4.799999999999991 y[1] (closed_form) = 37.86399999999979 y[1] (numeric) = 37.86399999999991 absolute error = 1.20792265079217e-13 relative error = 3.190161237038287e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 4.899999999999991 y[1] (closed_form) = 40.21633333333311 y[1] (numeric) = 40.21633333333324 absolute error = 1.27897692436818e-13 relative error = 3.180242499402865e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 4.99999999999999 y[1] (closed_form) = 42.66666666666642 y[1] (numeric) = 42.66666666666656 absolute error = 1.4210854715202e-13 relative error = 3.330669073875489e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 5.09999999999999 y[1] (closed_form) = 45.21699999999974 y[1] (numeric) = 45.21699999999989 absolute error = 1.56319401867222e-13 relative error = 3.457093612296768e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 5.19999999999999 y[1] (closed_form) = 47.86933333333305 y[1] (numeric) = 47.86933333333322 absolute error = 1.63424829224823e-13 relative error = 3.413977547730433e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 5.299999999999989 y[1] (closed_form) = 50.62566666666637 y[1] (numeric) = 50.62566666666654 absolute error = 1.70530256582424e-13 relative error = 3.36845453720626e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 5.399999999999989 y[1] (closed_form) = 53.48799999999968 y[1] (numeric) = 53.48799999999986 absolute error = 1.77635683940025e-13 relative error = 3.321038063491365e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 5.499999999999988 y[1] (closed_form) = 56.45833333333298 y[1] (numeric) = 56.45833333333318 absolute error = 1.989519660128281e-13 relative error = 3.52387246074384e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 5.599999999999988 y[1] (closed_form) = 59.53866666666629 y[1] (numeric) = 59.5386666666665 absolute error = 2.060573933704291e-13 relative error = 3.460900367891404e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 5.699999999999988 y[1] (closed_form) = 62.7309999999996 y[1] (numeric) = 62.73099999999982 absolute error = 2.273736754432321e-13 relative error = 3.624582350723462e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 5.799999999999987 y[1] (closed_form) = 66.03733333333291 y[1] (numeric) = 66.03733333333315 absolute error = 2.415845301584341e-13 relative error = 3.658302326337157e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 5.899999999999987 y[1] (closed_form) = 69.45966666666621 y[1] (numeric) = 69.45966666666648 absolute error = 2.700062395888381e-13 relative error = 3.887237767560644e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 5.999999999999987 y[1] (closed_form) = 72.99999999999953 y[1] (numeric) = 72.9999999999998 absolute error = 2.700062395888381e-13 relative error = 3.698715610806025e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 6.099999999999986 y[1] (closed_form) = 76.66033333333282 y[1] (numeric) = 76.66033333333311 absolute error = 2.984279490192421e-13 relative error = 3.892860049559452e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 6.199999999999986 y[1] (closed_form) = 80.44266666666613 y[1] (numeric) = 80.44266666666643 absolute error = 2.984279490192421e-13 relative error = 3.709821682762598e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 6.299999999999986 y[1] (closed_form) = 84.34899999999944 y[1] (numeric) = 84.34899999999975 absolute error = 3.126388037344441e-13 relative error = 3.706490933318074e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 6.399999999999985 y[1] (closed_form) = 88.38133333333273 y[1] (numeric) = 88.38133333333306 absolute error = 3.268496584496461e-13 relative error = 3.698175238168486e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 6.499999999999985 y[1] (closed_form) = 92.54166666666602 y[1] (numeric) = 92.54166666666637 absolute error = 3.552713678800501e-13 relative error = 3.839042246340055e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 6.599999999999985 y[1] (closed_form) = 96.83199999999933 y[1] (numeric) = 96.83199999999968 absolute error = 3.552713678800501e-13 relative error = 3.668945884418917e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 6.699999999999984 y[1] (closed_form) = 101.2543333333326 y[1] (numeric) = 101.254333333333 absolute error = 3.694822225952521e-13 relative error = 3.649050963368692e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 6.799999999999984 y[1] (closed_form) = 105.8106666666659 y[1] (numeric) = 105.8106666666663 absolute error = 3.979039320256561e-13 relative error = 3.760527596704103e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 6.899999999999983 y[1] (closed_form) = 110.5029999999992 y[1] (numeric) = 110.5029999999996 absolute error = 4.121147867408581e-13 relative error = 3.72944432948301e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 6.999999999999983 y[1] (closed_form) = 115.3333333333325 y[1] (numeric) = 115.3333333333329 absolute error = 3.979039320256561e-13 relative error = 3.450034092708025e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 7.099999999999983 y[1] (closed_form) = 120.3036666666658 y[1] (numeric) = 120.3036666666662 absolute error = 4.405364961712621e-13 relative error = 3.661870900343287e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 7.199999999999982 y[1] (closed_form) = 125.4159999999991 y[1] (numeric) = 125.4159999999995 absolute error = 4.547473508864641e-13 relative error = 3.625911772712154e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 7.299999999999982 y[1] (closed_form) = 130.6723333333324 y[1] (numeric) = 130.6723333333329 absolute error = 4.831690603168681e-13 relative error = 3.697562046928105e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 7.399999999999982 y[1] (closed_form) = 136.0746666666656 y[1] (numeric) = 136.0746666666662 absolute error = 5.115907697472721e-13 relative error = 3.759632724293103e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 7.499999999999981 y[1] (closed_form) = 141.6249999999989 y[1] (numeric) = 141.6249999999995 absolute error = 5.400124791776761e-13 relative error = 3.812974257212217e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 7.599999999999981 y[1] (closed_form) = 147.3253333333322 y[1] (numeric) = 147.3253333333328 absolute error = 5.684341886080801e-13 relative error = 3.858360105128453e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 7.699999999999981 y[1] (closed_form) = 153.1776666666655 y[1] (numeric) = 153.1776666666661 absolute error = 5.968558980384842e-13 relative error = 3.896494254200386e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 7.79999999999998 y[1] (closed_form) = 159.1839999999988 y[1] (numeric) = 159.1839999999994 absolute error = 6.252776074688882e-13 relative error = 3.928017938165223e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 7.89999999999998 y[1] (closed_form) = 165.3463333333321 y[1] (numeric) = 165.3463333333327 absolute error = 6.536993168992922e-13 relative error = 3.953515652394049e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 7.99999999999998 y[1] (closed_form) = 171.6666666666653 y[1] (numeric) = 171.666666666666 absolute error = 6.821210263296962e-13 relative error = 3.973520541726416e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 8.09999999999998 y[1] (closed_form) = 178.1469999999987 y[1] (numeric) = 178.1469999999993 absolute error = 6.536993168992922e-13 relative error = 3.669437694147513e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 8.199999999999982 y[1] (closed_form) = 184.7893333333321 y[1] (numeric) = 184.7893333333326 absolute error = 5.115907697472721e-13 relative error = 2.768508119591727e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 8.299999999999983 y[1] (closed_form) = 191.5956666666655 y[1] (numeric) = 191.5956666666659 absolute error = 4.263256414560601e-13 relative error = 2.225131960827556e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 8.399999999999984 y[1] (closed_form) = 198.5679999999989 y[1] (numeric) = 198.5679999999992 absolute error = 3.410605131648481e-13 relative error = 1.717600586020154e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 8.499999999999986 y[1] (closed_form) = 205.7083333333323 y[1] (numeric) = 205.7083333333325 absolute error = 1.989519660128281e-13 relative error = 9.671555973886767e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 8.599999999999987 y[1] (closed_form) = 213.0186666666657 y[1] (numeric) = 213.0186666666658 absolute error = 1.13686837721616e-13 relative error = 5.336942508400666e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 8.699999999999989 y[1] (closed_form) = 220.5009999999992 y[1] (numeric) = 220.5009999999992 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 8.79999999999999 y[1] (closed_form) = 228.1573333333326 y[1] (numeric) = 228.1573333333325 absolute error = 8.526512829121202e-14 relative error = 3.737119778071812e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 8.899999999999991 y[1] (closed_form) = 235.989666666666 y[1] (numeric) = 235.9896666666658 absolute error = 2.273736754432321e-13 relative error = 9.634899640092971e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = 8.999999999999993 y[1] (closed_form) = 243.9999999999994 y[1] (numeric) = 243.9999999999991 absolute error = 3.410605131648481e-13 relative error = 1.397788988380528e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 9.099999999999994 y[1] (closed_form) = 252.1903333333329 y[1] (numeric) = 252.1903333333324 absolute error = 4.547473508864641e-13 relative error = 1.803191045730533e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 9.199999999999996 y[1] (closed_form) = 260.5626666666663 y[1] (numeric) = 260.5626666666658 absolute error = 5.115907697472721e-13 relative error = 1.963407790885646e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 9.299999999999997 y[1] (closed_form) = 269.1189999999997 y[1] (numeric) = 269.1189999999991 absolute error = 6.252776074688882e-13 relative error = 2.323424237860905e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 9.399999999999999 y[1] (closed_form) = 277.8613333333332 y[1] (numeric) = 277.8613333333324 absolute error = 7.958078640513122e-13 relative error = 2.864046805305689e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 9.5 y[1] (closed_form) = 286.7916666666667 y[1] (numeric) = 286.7916666666657 absolute error = 9.663381206337363e-13 relative error = 3.369477683453388e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 9.600000000000001 y[1] (closed_form) = 295.9120000000001 y[1] (numeric) = 295.9119999999991 absolute error = 1.023181539494544e-12 relative error = 3.457722361697207e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 9.700000000000003 y[1] (closed_form) = 305.2243333333336 y[1] (numeric) = 305.2243333333324 absolute error = 1.193711796076968e-12 relative error = 3.910932601737631e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 9.800000000000004 y[1] (closed_form) = 314.730666666667 y[1] (numeric) = 314.7306666666657 absolute error = 1.307398633798584e-12 relative error = 4.154023653447337e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = 9.900000000000006 y[1] (closed_form) = 324.4330000000006 y[1] (numeric) = 324.4329999999991 absolute error = 1.477928890381008e-12 relative error = 4.555420966365955e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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 ) = x * x ; Iterations = 198 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 100.5 %