##############ECHO OF PROBLEM################# ##############temp/div_lin_cpostode.ode################# diff ( y , x , 1 ) = ( 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=c(-5.0); x_end=c(5.0); 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(0.05) * c(x) * c(x) + c(0.15) * c(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (closed_form) = 0.5 y[1] (numeric) = 0.5 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] = -4.9 y[1] (closed_form) = 0.4655000000000001 y[1] (numeric) = 0.4655 absolute error = 1.110223024625157e-16 relative error = 2.38501186815286e-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] = -4.800000000000001 y[1] (closed_form) = 0.4320000000000003 y[1] (numeric) = 0.432 absolute error = 2.775557561562891e-16 relative error = 6.424901762877059e-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] = -4.700000000000001 y[1] (closed_form) = 0.3995000000000003 y[1] (numeric) = 0.3995 absolute error = 3.33066907387547e-16 relative error = 8.337094052253986e-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] = -4.600000000000001 y[1] (closed_form) = 0.3680000000000005 y[1] (numeric) = 0.3679999999999999 absolute error = 6.106226635438361e-16 relative error = 1.659300716151726e-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] = -4.500000000000002 y[1] (closed_form) = 0.3375000000000006 y[1] (numeric) = 0.3374999999999999 absolute error = 6.661338147750939e-16 relative error = 1.97372982155583e-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] = -4.400000000000002 y[1] (closed_form) = 0.3080000000000007 y[1] (numeric) = 0.3079999999999999 absolute error = 8.326672684688674e-16 relative error = 2.703465157366447e-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] = -4.300000000000002 y[1] (closed_form) = 0.2795000000000007 y[1] (numeric) = 0.2794999999999999 absolute error = 8.881784197001252e-16 relative error = 3.177740320930672e-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] = -4.200000000000003 y[1] (closed_form) = 0.2520000000000008 y[1] (numeric) = 0.2519999999999998 absolute error = 9.436895709313831e-16 relative error = 3.744799884648334e-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] = -4.100000000000003 y[1] (closed_form) = 0.2255000000000009 y[1] (numeric) = 0.2254999999999998 absolute error = 1.137978600240785e-15 relative error = 5.046468293750691e-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] = -4.000000000000004 y[1] (closed_form) = 0.2000000000000008 y[1] (numeric) = 0.1999999999999997 absolute error = 1.110223024625157e-15 relative error = 5.551115123125759e-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] = -3.900000000000004 y[1] (closed_form) = 0.175500000000001 y[1] (numeric) = 0.1754999999999997 absolute error = 1.304512053934559e-15 relative error = 7.433117116436191e-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] = -3.800000000000004 y[1] (closed_form) = 0.152000000000001 y[1] (numeric) = 0.1519999999999996 absolute error = 1.387778780781446e-15 relative error = 9.130123557772607e-13 % Desired digits = 8 Estimated correct digits = 12 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] = -3.700000000000005 y[1] (closed_form) = 0.1295000000000011 y[1] (numeric) = 0.1294999999999996 absolute error = 1.471045507628332e-15 relative error = 1.135942476933066e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -3.600000000000005 y[1] (closed_form) = 0.1080000000000012 y[1] (numeric) = 0.1079999999999995 absolute error = 1.665334536937735e-15 relative error = 1.541976423090478e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -3.500000000000005 y[1] (closed_form) = 0.08750000000000102 y[1] (numeric) = 0.08749999999999949 absolute error = 1.52655665885959e-15 relative error = 1.744636181553797e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -3.400000000000006 y[1] (closed_form) = 0.06800000000000117 y[1] (numeric) = 0.06799999999999945 absolute error = 1.720845688168993e-15 relative error = 2.530655423777887e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -3.300000000000006 y[1] (closed_form) = 0.0495000000000011 y[1] (numeric) = 0.04949999999999939 absolute error = 1.706967900361178e-15 relative error = 3.448420000729576e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -3.200000000000006 y[1] (closed_form) = 0.03200000000000119 y[1] (numeric) = 0.03199999999999932 absolute error = 1.873501354054952e-15 relative error = 5.854691731421506e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -3.100000000000007 y[1] (closed_form) = 0.01550000000000118 y[1] (numeric) = 0.01549999999999925 absolute error = 1.927277781810233e-15 relative error = 1.243405020522636e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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] = -3.000000000000007 y[1] (closed_form) = 1.054711873393899e-15 y[1] (numeric) = -8.205242041370298e-16 absolute error = 1.875236077530928e-15 relative error = 177.796052631579 % Desired digits = 8 Estimated correct digits = -1 Correct digits = 1 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] = -2.900000000000007 y[1] (closed_form) = -0.0144999999999989 y[1] (numeric) = -0.01450000000000089 absolute error = 1.991462550421375e-15 relative error = 1.373422448566569e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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] = -2.800000000000008 y[1] (closed_form) = -0.02799999999999891 y[1] (numeric) = -0.02800000000000097 absolute error = 2.05391259555654e-15 relative error = 7.335402126987925e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -2.700000000000008 y[1] (closed_form) = -0.04049999999999893 y[1] (numeric) = -0.04050000000000105 absolute error = 2.123301534595612e-15 relative error = 5.242719838507823e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -2.600000000000009 y[1] (closed_form) = -0.0519999999999991 y[1] (numeric) = -0.05200000000000114 absolute error = 2.040034807748725e-15 relative error = 3.923143861055308e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -2.500000000000009 y[1] (closed_form) = -0.06249999999999911 y[1] (numeric) = -0.06250000000000124 absolute error = 2.123301534595612e-15 relative error = 3.397282455353027e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -2.400000000000009 y[1] (closed_form) = -0.07199999999999912 y[1] (numeric) = -0.07200000000000133 absolute error = 2.206568261442499e-15 relative error = 3.064678140892396e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -2.30000000000001 y[1] (closed_form) = -0.08049999999999918 y[1] (numeric) = -0.08050000000000142 absolute error = 2.234323837058128e-15 relative error = 2.77555756156292e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -2.20000000000001 y[1] (closed_form) = -0.08799999999999927 y[1] (numeric) = -0.08800000000000151 absolute error = 2.234323837058128e-15 relative error = 2.539004360293348e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -2.10000000000001 y[1] (closed_form) = -0.09449999999999936 y[1] (numeric) = -0.09450000000000161 absolute error = 2.248201624865942e-15 relative error = 2.379049338482494e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -2.000000000000011 y[1] (closed_form) = -0.09999999999999948 y[1] (numeric) = -0.1000000000000017 absolute error = 2.248201624865942e-15 relative error = 2.248201624865954e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -1.900000000000011 y[1] (closed_form) = -0.1044999999999996 y[1] (numeric) = -0.1045000000000018 absolute error = 2.275957200481571e-15 relative error = 2.177949474145053e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -1.80000000000001 y[1] (closed_form) = -0.1079999999999997 y[1] (numeric) = -0.108000000000002 absolute error = 2.275957200481571e-15 relative error = 2.107367778223683e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -1.70000000000001 y[1] (closed_form) = -0.1104999999999998 y[1] (numeric) = -0.1105000000000021 absolute error = 2.275957200481571e-15 relative error = 2.059689774191471e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -1.60000000000001 y[1] (closed_form) = -0.1119999999999999 y[1] (numeric) = -0.1120000000000022 absolute error = 2.275957200481571e-15 relative error = 2.032104643287119e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -1.50000000000001 y[1] (closed_form) = -0.1125 y[1] (numeric) = -0.1125000000000023 absolute error = 2.289834988289385e-15 relative error = 2.035408878479454e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -1.40000000000001 y[1] (closed_form) = -0.1120000000000001 y[1] (numeric) = -0.1120000000000024 absolute error = 2.3037127760972e-15 relative error = 2.056886407229641e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -1.30000000000001 y[1] (closed_form) = -0.1105000000000002 y[1] (numeric) = -0.1105000000000025 absolute error = 2.317590563905014e-15 relative error = 2.09736702615838e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -1.20000000000001 y[1] (closed_form) = -0.1080000000000003 y[1] (numeric) = -0.1080000000000026 absolute error = 2.317590563905014e-15 relative error = 2.145917188800933e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -1.10000000000001 y[1] (closed_form) = -0.1045000000000004 y[1] (numeric) = -0.1045000000000027 absolute error = 2.331468351712829e-15 relative error = 2.231070193026622e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -1.00000000000001 y[1] (closed_form) = -0.1000000000000005 y[1] (numeric) = -0.1000000000000028 absolute error = 2.345346139520643e-15 relative error = 2.345346139520631e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -0.9000000000000097 y[1] (closed_form) = -0.09450000000000058 y[1] (numeric) = -0.09450000000000294 absolute error = 2.359223927328458e-15 relative error = 2.496533256432215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -0.8000000000000096 y[1] (closed_form) = -0.08800000000000067 y[1] (numeric) = -0.08800000000000305 absolute error = 2.373101715136272e-15 relative error = 2.696706494473016e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -0.7000000000000095 y[1] (closed_form) = -0.08050000000000077 y[1] (numeric) = -0.08050000000000315 absolute error = 2.386979502944087e-15 relative error = 2.965191929123061e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -0.6000000000000094 y[1] (closed_form) = -0.07200000000000084 y[1] (numeric) = -0.07200000000000326 absolute error = 2.414735078559715e-15 relative error = 3.353798720221788e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -0.5000000000000093 y[1] (closed_form) = -0.06250000000000093 y[1] (numeric) = -0.06250000000000336 absolute error = 2.42861286636753e-15 relative error = 3.88578058618799e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -0.4000000000000093 y[1] (closed_form) = -0.05200000000000102 y[1] (numeric) = -0.05200000000000345 absolute error = 2.421673972463623e-15 relative error = 4.657065331660721e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -0.3000000000000094 y[1] (closed_form) = -0.04050000000000113 y[1] (numeric) = -0.04050000000000355 absolute error = 2.421673972463623e-15 relative error = 5.979441907317421e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = -0.2000000000000094 y[1] (closed_form) = -0.02800000000000122 y[1] (numeric) = -0.02800000000000364 absolute error = 2.425143419415576e-15 relative error = 8.661226497912396e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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] = -0.1000000000000094 y[1] (closed_form) = -0.01450000000000132 y[1] (numeric) = -0.01450000000000374 absolute error = 2.419939248987646e-15 relative error = 1.668923619991329e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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] = -9.395262345890387e-15 y[1] (closed_form) = -1.409289351883554e-15 y[1] (numeric) = -3.83026943495679e-15 absolute error = 2.420980083073237e-15 relative error = 171.7872968980806 % Desired digits = 8 Estimated correct digits = 0 Correct digits = 1 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] = 0.09999999999999061 y[1] (closed_form) = 0.0154999999999985 y[1] (numeric) = 0.01549999999999608 absolute error = 2.421673972463623e-15 relative error = 1.562370304815392e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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] = 0.1999999999999906 y[1] (closed_form) = 0.0319999999999984 y[1] (numeric) = 0.03199999999999598 absolute error = 2.421673972463623e-15 relative error = 7.567731163949199e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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] = 0.2999999999999906 y[1] (closed_form) = 0.04949999999999831 y[1] (numeric) = 0.04949999999999589 absolute error = 2.421673972463623e-15 relative error = 4.892270651441829e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = 0.3999999999999906 y[1] (closed_form) = 0.0679999999999982 y[1] (numeric) = 0.06799999999999579 absolute error = 2.414735078559715e-15 relative error = 3.551080997882028e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = 0.4999999999999906 y[1] (closed_form) = 0.08749999999999811 y[1] (numeric) = 0.08749999999999569 absolute error = 2.414735078559715e-15 relative error = 2.759697232639734e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = 0.5999999999999907 y[1] (closed_form) = 0.107999999999998 y[1] (numeric) = 0.1079999999999956 absolute error = 2.442490654175344e-15 relative error = 2.261565420532767e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = 0.6999999999999907 y[1] (closed_form) = 0.129499999999998 y[1] (numeric) = 0.1294999999999955 absolute error = 2.442490654175344e-15 relative error = 1.8860931692474e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = 0.7999999999999908 y[1] (closed_form) = 0.1519999999999979 y[1] (numeric) = 0.1519999999999954 absolute error = 2.470246229790973e-15 relative error = 1.625161993283558e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = 0.8999999999999909 y[1] (closed_form) = 0.1754999999999978 y[1] (numeric) = 0.1754999999999953 absolute error = 2.470246229790973e-15 relative error = 1.407547709282624e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = 0.999999999999991 y[1] (closed_form) = 0.1999999999999977 y[1] (numeric) = 0.1999999999999952 absolute error = 2.498001805406602e-15 relative error = 1.249000902703315e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = 1.099999999999991 y[1] (closed_form) = 0.2254999999999976 y[1] (numeric) = 0.2254999999999951 absolute error = 2.498001805406602e-15 relative error = 1.107761332774558e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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] = 1.199999999999991 y[1] (closed_form) = 0.2519999999999976 y[1] (numeric) = 0.2519999999999951 absolute error = 2.498001805406602e-15 relative error = 9.912705577010422e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.299999999999991 y[1] (closed_form) = 0.2794999999999975 y[1] (numeric) = 0.279499999999995 absolute error = 2.55351295663786e-15 relative error = 9.136003422675787e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.399999999999991 y[1] (closed_form) = 0.3079999999999974 y[1] (numeric) = 0.3079999999999949 absolute error = 2.55351295663786e-15 relative error = 8.290626482590523e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.499999999999991 y[1] (closed_form) = 0.3374999999999974 y[1] (numeric) = 0.3374999999999948 absolute error = 2.609024107869118e-15 relative error = 7.730441801093742e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.599999999999991 y[1] (closed_form) = 0.3679999999999973 y[1] (numeric) = 0.3679999999999947 absolute error = 2.609024107869118e-15 relative error = 7.089739423557437e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.699999999999992 y[1] (closed_form) = 0.3994999999999973 y[1] (numeric) = 0.3994999999999946 absolute error = 2.664535259100376e-15 relative error = 6.669675241803238e-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] = 1.799999999999992 y[1] (closed_form) = 0.4319999999999972 y[1] (numeric) = 0.4319999999999946 absolute error = 2.664535259100376e-15 relative error = 6.16790569236202e-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] = 1.899999999999992 y[1] (closed_form) = 0.4654999999999971 y[1] (numeric) = 0.4654999999999945 absolute error = 2.664535259100376e-15 relative error = 5.7240284835669e-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] = 1.999999999999992 y[1] (closed_form) = 0.4999999999999971 y[1] (numeric) = 0.4999999999999944 absolute error = 2.720046410331634e-15 relative error = 5.440092820663298e-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] = 2.099999999999992 y[1] (closed_form) = 0.535499999999997 y[1] (numeric) = 0.5354999999999943 absolute error = 2.664535259100376e-15 relative error = 4.975789466107172e-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] = 2.199999999999991 y[1] (closed_form) = 0.5719999999999967 y[1] (numeric) = 0.5719999999999942 absolute error = 2.55351295663786e-15 relative error = 4.464183490625655e-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] = 2.299999999999991 y[1] (closed_form) = 0.6094999999999966 y[1] (numeric) = 0.6094999999999942 absolute error = 2.442490654175344e-15 relative error = 4.007367767309857e-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] = 2.399999999999991 y[1] (closed_form) = 0.6479999999999964 y[1] (numeric) = 0.647999999999994 absolute error = 2.331468351712829e-15 relative error = 3.597944987211176e-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] = 2.49999999999999 y[1] (closed_form) = 0.687499999999996 y[1] (numeric) = 0.687499999999994 absolute error = 1.998401444325282e-15 relative error = 2.906765737200427e-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] = 2.59999999999999 y[1] (closed_form) = 0.7279999999999959 y[1] (numeric) = 0.7279999999999939 absolute error = 1.998401444325282e-15 relative error = 2.74505692901826e-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] = 2.69999999999999 y[1] (closed_form) = 0.7694999999999956 y[1] (numeric) = 0.7694999999999939 absolute error = 1.77635683940025e-15 relative error = 2.308455931644263e-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] = 2.799999999999989 y[1] (closed_form) = 0.8119999999999954 y[1] (numeric) = 0.8119999999999937 absolute error = 1.665334536937735e-15 relative error = 2.050904602140079e-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] = 2.899999999999989 y[1] (closed_form) = 0.855499999999995 y[1] (numeric) = 0.8554999999999936 absolute error = 1.443289932012704e-15 relative error = 1.687071808314099e-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] = 2.999999999999988 y[1] (closed_form) = 0.8999999999999948 y[1] (numeric) = 0.8999999999999935 absolute error = 1.332267629550188e-15 relative error = 1.480297366166884e-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] = 3.099999999999988 y[1] (closed_form) = 0.9454999999999945 y[1] (numeric) = 0.9454999999999933 absolute error = 1.110223024625157e-15 relative error = 1.17421790018526e-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] = 3.199999999999988 y[1] (closed_form) = 0.9919999999999942 y[1] (numeric) = 0.9919999999999932 absolute error = 9.992007221626409e-16 relative error = 1.007258792502668e-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] = 3.299999999999987 y[1] (closed_form) = 1.039499999999994 y[1] (numeric) = 1.039499999999993 absolute error = 1.110223024625157e-15 relative error = 1.068035617725024e-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] = 3.399999999999987 y[1] (closed_form) = 1.087999999999994 y[1] (numeric) = 1.087999999999993 absolute error = 6.661338147750939e-16 relative error = 6.122553444624061e-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] = 3.499999999999987 y[1] (closed_form) = 1.137499999999994 y[1] (numeric) = 1.137499999999993 absolute error = 6.661338147750939e-16 relative error = 5.856121448572288e-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] = 3.599999999999986 y[1] (closed_form) = 1.187999999999993 y[1] (numeric) = 1.187999999999993 absolute error = 4.440892098500626e-16 relative error = 3.738124662037586e-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] = 3.699999999999986 y[1] (closed_form) = 1.239499999999992 y[1] (numeric) = 1.239499999999992 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] = 3.799999999999986 y[1] (closed_form) = 1.291999999999992 y[1] (numeric) = 1.291999999999992 absolute error = 2.220446049250313e-16 relative error = 1.718611493227807e-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] = 3.899999999999985 y[1] (closed_form) = 1.345499999999992 y[1] (numeric) = 1.345499999999992 absolute error = 4.440892098500626e-16 relative error = 3.300551541063287e-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] = 3.999999999999985 y[1] (closed_form) = 1.399999999999992 y[1] (numeric) = 1.399999999999992 absolute error = 2.220446049250313e-16 relative error = 1.586032892321661e-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] = 4.099999999999985 y[1] (closed_form) = 1.455499999999991 y[1] (numeric) = 1.455499999999992 absolute error = 6.661338147750939e-16 relative error = 4.576666539162472e-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] = 4.199999999999984 y[1] (closed_form) = 1.511999999999991 y[1] (numeric) = 1.511999999999992 absolute error = 1.110223024625157e-15 relative error = 7.342744871859545e-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] = 4.299999999999984 y[1] (closed_form) = 1.569499999999991 y[1] (numeric) = 1.569499999999992 absolute error = 1.332267629550188e-15 relative error = 8.488484418924471e-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] = 4.399999999999983 y[1] (closed_form) = 1.62799999999999 y[1] (numeric) = 1.627999999999992 absolute error = 1.332267629550188e-15 relative error = 8.183462097974176e-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] = 4.499999999999983 y[1] (closed_form) = 1.68749999999999 y[1] (numeric) = 1.687499999999992 absolute error = 1.77635683940025e-15 relative error = 1.052655904829784e-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] = 4.599999999999983 y[1] (closed_form) = 1.74799999999999 y[1] (numeric) = 1.747999999999991 absolute error = 1.77635683940025e-15 relative error = 1.016222448169486e-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] = 4.699999999999982 y[1] (closed_form) = 1.809499999999989 y[1] (numeric) = 1.809499999999991 absolute error = 1.998401444325282e-15 relative error = 1.104394277051834e-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] = 4.799999999999982 y[1] (closed_form) = 1.871999999999989 y[1] (numeric) = 1.871999999999991 absolute error = 2.220446049250313e-15 relative error = 1.186135710069619e-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] = 4.899999999999982 y[1] (closed_form) = 1.935499999999988 y[1] (numeric) = 1.935499999999991 absolute error = 2.442490654175344e-15 relative error = 1.261942988465698e-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] = 4.999999999999981 y[1] (closed_form) = 1.999999999999988 y[1] (numeric) = 1.999999999999991 absolute error = 2.664535259100376e-15 relative error = 1.332267629550196e-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 ) = ( 0.2 * x + 0.3 ) / 2.0 ; Iterations = 201 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 101 %