##############ECHO OF PROBLEM################# ##############temp/sub_lin_linpostode.ode################# diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) - ( 0.3 * x + 0.1 ) ; ! /* 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(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(-0.2) * c(x) * c(x) / c(2.0) + c(0.1) * c(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.009000000000000001 y[1] (numeric) = 0.009000000000000001 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) = 0.016 y[1] (numeric) = 0.016 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] = 0.3 y[1] (closed_form) = 0.021 y[1] (numeric) = 0.02100000000000001 absolute error = 1.040834085586084e-17 relative error = 4.956352788505164e-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) = 0.024 y[1] (numeric) = 0.02400000000000001 absolute error = 1.040834085586084e-17 relative error = 4.336808689942018e-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] = 0.4999999999999999 y[1] (closed_form) = 0.025 y[1] (numeric) = 0.02500000000000002 absolute error = 1.387778780781446e-17 relative error = 5.551115123125783e-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] = 0.6 y[1] (closed_form) = 0.024 y[1] (numeric) = 0.02400000000000001 absolute error = 1.387778780781446e-17 relative error = 5.782411586589357e-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] = 0.7000000000000001 y[1] (closed_form) = 0.021 y[1] (numeric) = 0.02100000000000001 absolute error = 1.387778780781446e-17 relative error = 6.608470384673551e-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] = 0.8000000000000002 y[1] (closed_form) = 0.01599999999999999 y[1] (numeric) = 0.01600000000000001 absolute error = 2.081668171172169e-17 relative error = 1.301042606982606e-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] = 0.9000000000000002 y[1] (closed_form) = 0.00899999999999998 y[1] (numeric) = 0.009000000000000001 absolute error = 2.081668171172169e-17 relative error = 2.312964634635748e-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 y[1] (closed_form) = -2.775557561562891e-17 y[1] (numeric) = -6.938893903907228e-18 absolute error = 2.081668171172169e-17 relative error = -1 % Desired digits = 8 Estimated correct digits = -16 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) = -0.01100000000000004 y[1] (numeric) = -0.01100000000000001 absolute error = 3.122502256758253e-17 relative error = 2.838638415234765e-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] = 1.2 y[1] (closed_form) = -0.02400000000000005 y[1] (numeric) = -0.02400000000000001 absolute error = 4.163336342344337e-17 relative error = 1.734723475976804e-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] = 1.3 y[1] (closed_form) = -0.03900000000000009 y[1] (numeric) = -0.03900000000000001 absolute error = 8.326672684688674e-17 relative error = 2.135044278125296e-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] = 1.400000000000001 y[1] (closed_form) = -0.05600000000000011 y[1] (numeric) = -0.05600000000000001 absolute error = 9.71445146547012e-17 relative error = 1.734723475976804e-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] = 1.500000000000001 y[1] (closed_form) = -0.07500000000000015 y[1] (numeric) = -0.07500000000000002 absolute error = 1.249000902703301e-16 relative error = 1.665334536937732e-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] = 1.600000000000001 y[1] (closed_form) = -0.0960000000000002 y[1] (numeric) = -0.09600000000000004 absolute error = 1.52655665885959e-16 relative error = 1.59016318631207e-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] = 1.700000000000001 y[1] (closed_form) = -0.1190000000000002 y[1] (numeric) = -0.1190000000000001 absolute error = 1.52655665885959e-16 relative error = 1.282820721730746e-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] = 1.800000000000001 y[1] (closed_form) = -0.1440000000000002 y[1] (numeric) = -0.1440000000000001 absolute error = 1.665334536937735e-16 relative error = 1.156482317317869e-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] = 1.900000000000001 y[1] (closed_form) = -0.1710000000000003 y[1] (numeric) = -0.1710000000000001 absolute error = 2.220446049250313e-16 relative error = 1.298506461549888e-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] = 2.000000000000001 y[1] (closed_form) = -0.2000000000000003 y[1] (numeric) = -0.2000000000000001 absolute error = 1.387778780781446e-16 relative error = 6.93889390390722e-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) = -0.2310000000000002 y[1] (numeric) = -0.2310000000000001 absolute error = 5.551115123125783e-17 relative error = 2.403080139881289e-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) = -0.2640000000000001 y[1] (numeric) = -0.2640000000000001 absolute error = 5.551115123125783e-17 relative error = 2.102695122396129e-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) = -0.2989999999999999 y[1] (numeric) = -0.2990000000000001 absolute error = 1.665334536937735e-16 relative error = 5.569680725544265e-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) = -0.3359999999999997 y[1] (numeric) = -0.3360000000000001 absolute error = 3.33066907387547e-16 relative error = 9.912705577010334e-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] = 2.499999999999999 y[1] (closed_form) = -0.3749999999999997 y[1] (numeric) = -0.3750000000000001 absolute error = 3.885780586188048e-16 relative error = 1.036208156316814e-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) = -0.4159999999999995 y[1] (numeric) = -0.416 absolute error = 5.551115123125783e-16 relative error = 1.334402673828315e-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) = -0.4589999999999994 y[1] (numeric) = -0.459 absolute error = 6.661338147750939e-16 relative error = 1.451271927614586e-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) = -0.5039999999999991 y[1] (numeric) = -0.504 absolute error = 8.881784197001252e-16 relative error = 1.762258769246283e-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) = -0.5509999999999988 y[1] (numeric) = -0.5509999999999999 absolute error = 1.110223024625157e-15 relative error = 2.014923819646386e-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) = -0.5999999999999988 y[1] (numeric) = -0.5999999999999999 absolute error = 1.110223024625157e-15 relative error = 1.850371707708598e-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) = -0.6509999999999985 y[1] (numeric) = -0.6509999999999998 absolute error = 1.332267629550188e-15 relative error = 2.046494054608588e-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) = -0.7039999999999982 y[1] (numeric) = -0.7039999999999997 absolute error = 1.554312234475219e-15 relative error = 2.207829878515942e-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) = -0.7589999999999979 y[1] (numeric) = -0.7589999999999997 absolute error = 1.77635683940025e-15 relative error = 2.340391092753959e-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) = -0.8159999999999978 y[1] (numeric) = -0.8159999999999996 absolute error = 1.77635683940025e-15 relative error = 2.176907891421881e-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) = -0.8749999999999973 y[1] (numeric) = -0.8749999999999996 absolute error = 2.220446049250313e-15 relative error = 2.537652627714651e-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) = -0.9359999999999972 y[1] (numeric) = -0.9359999999999995 absolute error = 2.331468351712829e-15 relative error = 2.490884991146192e-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) = -0.9989999999999968 y[1] (numeric) = -0.9989999999999994 absolute error = 2.664535259100376e-15 relative error = 2.667202461561946e-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) = -1.063999999999996 y[1] (numeric) = -1.063999999999999 absolute error = 3.108624468950438e-15 relative error = 2.921639538487264e-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) = -1.130999999999996 y[1] (numeric) = -1.130999999999999 absolute error = 3.108624468950438e-15 relative error = 2.748562748850971e-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) = -1.199999999999996 y[1] (numeric) = -1.199999999999999 absolute error = 3.33066907387547e-15 relative error = 2.775557561562901e-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) = -1.270999999999995 y[1] (numeric) = -1.270999999999999 absolute error = 3.552713678800501e-15 relative error = 2.795211391660514e-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) = -1.343999999999995 y[1] (numeric) = -1.343999999999999 absolute error = 3.774758283725532e-15 relative error = 2.80859991348627e-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) = -1.418999999999994 y[1] (numeric) = -1.418999999999999 absolute error = 4.218847493575595e-15 relative error = 2.973113103295005e-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) = -1.495999999999994 y[1] (numeric) = -1.495999999999998 absolute error = 4.218847493575595e-15 relative error = 2.82008522297835e-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) = -1.574999999999994 y[1] (numeric) = -1.574999999999998 absolute error = 4.884981308350689e-15 relative error = 3.101575433873466e-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) = -1.655999999999993 y[1] (numeric) = -1.655999999999998 absolute error = 4.662936703425657e-15 relative error = 2.815783033469611e-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) = -1.738999999999993 y[1] (numeric) = -1.738999999999998 absolute error = 5.10702591327572e-15 relative error = 2.936760157145337e-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) = -1.823999999999992 y[1] (numeric) = -1.823999999999998 absolute error = 5.551115123125783e-15 relative error = 3.043374519257569e-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) = -1.910999999999992 y[1] (numeric) = -1.910999999999998 absolute error = 5.995204332975845e-15 relative error = 3.137207918878007e-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) = -1.999999999999991 y[1] (numeric) = -1.999999999999998 absolute error = 6.439293542825908e-15 relative error = 3.219646771412968e-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 ) = ( 0.1 * x + 0.2 ) - ( 0.3 * x + 0.1 ) ; Iterations = 99 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 102 %