##############ECHO OF PROBLEM################# ##############temp/add_sub_sin_c_cos_c_tan_cpostode.ode################# diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; ! /* 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(sin(0.1)) + c(cos(0.05)) - c(tan(0.02))) *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) = -5.392905049741961 y[1] (numeric) = -5.392905049741961 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) = -5.285046948747122 y[1] (numeric) = -5.285046948747121 absolute error = 8.881784197001252e-16 relative error = 1.680549725127187e-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) = -5.177188847752283 y[1] (numeric) = -5.177188847752282 absolute error = 8.881784197001252e-16 relative error = 1.715561177734003e-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) = -5.069330746757444 y[1] (numeric) = -5.069330746757442 absolute error = 1.77635683940025e-15 relative error = 3.504124958775835e-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) = -4.961472645762606 y[1] (numeric) = -4.961472645762603 absolute error = 2.664535259100376e-15 relative error = 5.37045238247166e-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] = -4.500000000000002 y[1] (closed_form) = -4.853614544767766 y[1] (numeric) = -4.853614544767764 absolute error = 2.664535259100376e-15 relative error = 5.489795768748808e-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] = -4.400000000000002 y[1] (closed_form) = -4.745756443772928 y[1] (numeric) = -4.745756443772924 absolute error = 3.552713678800501e-15 relative error = 7.48608513920292e-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] = -4.300000000000002 y[1] (closed_form) = -4.637898342778088 y[1] (numeric) = -4.637898342778085 absolute error = 3.552713678800501e-15 relative error = 7.660180142440196e-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] = -4.200000000000003 y[1] (closed_form) = -4.53004024178325 y[1] (numeric) = -4.530040241783245 absolute error = 4.440892098500626e-15 relative error = 9.803206729908583e-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] = -4.100000000000003 y[1] (closed_form) = -4.422182140788411 y[1] (numeric) = -4.422182140788406 absolute error = 5.329070518200751e-15 relative error = 1.20507711996925e-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) = -4.314324039793572 y[1] (numeric) = -4.314324039793567 absolute error = 5.329070518200751e-15 relative error = 1.235204047968481e-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) = -4.206465938798734 y[1] (numeric) = -4.206465938798727 absolute error = 6.217248937900877e-15 relative error = 1.478021937740063e-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) = -4.098607837803895 y[1] (numeric) = -4.098607837803888 absolute error = 7.105427357601002e-15 relative error = 1.733619716446991e-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] = -3.700000000000005 y[1] (closed_form) = -3.990749736809056 y[1] (numeric) = -3.990749736809049 absolute error = 7.105427357601002e-15 relative error = 1.78047430337799e-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] = -3.600000000000005 y[1] (closed_form) = -3.882891635814217 y[1] (numeric) = -3.882891635814209 absolute error = 7.993605777301127e-15 relative error = 2.058673413280801e-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] = -3.500000000000005 y[1] (closed_form) = -3.775033534819378 y[1] (numeric) = -3.77503353481937 absolute error = 8.43769498715119e-15 relative error = 2.235131134419155e-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] = -3.400000000000006 y[1] (closed_form) = -3.667175433824539 y[1] (numeric) = -3.66717543382453 absolute error = 8.881784197001252e-15 relative error = 2.421968721506824e-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] = -3.300000000000006 y[1] (closed_form) = -3.5593173328297 y[1] (numeric) = -3.559317332829691 absolute error = 9.325873406851315e-15 relative error = 2.620129798721018e-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] = -3.200000000000006 y[1] (closed_form) = -3.451459231834862 y[1] (numeric) = -3.451459231834852 absolute error = 1.021405182655144e-14 relative error = 2.959343031591149e-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] = -3.100000000000007 y[1] (closed_form) = -3.343601130840023 y[1] (numeric) = -3.343601130840012 absolute error = 1.06581410364015e-14 relative error = 3.187623349596077e-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] = -3.000000000000007 y[1] (closed_form) = -3.235743029845184 y[1] (numeric) = -3.235743029845173 absolute error = 1.110223024625157e-14 relative error = 3.431122355467999e-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] = -2.900000000000007 y[1] (closed_form) = -3.127884928850345 y[1] (numeric) = -3.127884928850333 absolute error = 1.199040866595169e-14 relative error = 3.833391873005625e-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] = -2.800000000000008 y[1] (closed_form) = -3.020026827855506 y[1] (numeric) = -3.020026827855494 absolute error = 1.243449787580175e-14 relative error = 4.117346826561596e-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] = -2.700000000000008 y[1] (closed_form) = -2.912168726860668 y[1] (numeric) = -2.912168726860655 absolute error = 1.287858708565182e-14 relative error = 4.422335480380973e-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] = -2.600000000000009 y[1] (closed_form) = -2.804310625865829 y[1] (numeric) = -2.804310625865815 absolute error = 1.332267629550188e-14 relative error = 4.750784799878762e-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] = -2.500000000000009 y[1] (closed_form) = -2.69645252487099 y[1] (numeric) = -2.696452524870976 absolute error = 1.4210854715202e-14 relative error = 5.270203937998839e-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] = -2.400000000000009 y[1] (closed_form) = -2.588594423876151 y[1] (numeric) = -2.588594423876136 absolute error = 1.465494392505207e-14 relative error = 5.661351886522189e-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] = -2.30000000000001 y[1] (closed_form) = -2.480736322881312 y[1] (numeric) = -2.480736322881297 absolute error = 1.509903313490213e-14 relative error = 6.086512700134525e-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] = -2.20000000000001 y[1] (closed_form) = -2.372878221886473 y[1] (numeric) = -2.372878221886458 absolute error = 1.554312234475219e-14 relative error = 6.550324496802529e-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] = -2.10000000000001 y[1] (closed_form) = -2.265020120891635 y[1] (numeric) = -2.265020120891618 absolute error = 1.643130076445232e-14 relative error = 7.254372980132321e-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] = -2.000000000000011 y[1] (closed_form) = -2.157162019896796 y[1] (numeric) = -2.157162019896779 absolute error = 1.687538997430238e-14 relative error = 7.822958970467013e-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] = -1.900000000000011 y[1] (closed_form) = -2.049303918901956 y[1] (numeric) = -2.04930391890194 absolute error = 1.687538997430238e-14 relative error = 8.23469365312317e-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] = -1.80000000000001 y[1] (closed_form) = -1.941445817907117 y[1] (numeric) = -1.9414458179071 absolute error = 1.709743457922741e-14 relative error = 8.806547379034498e-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] = -1.70000000000001 y[1] (closed_form) = -1.833587716912278 y[1] (numeric) = -1.833587716912261 absolute error = 1.709743457922741e-14 relative error = 9.324579577801231e-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] = -1.60000000000001 y[1] (closed_form) = -1.725729615917438 y[1] (numeric) = -1.725729615917421 absolute error = 1.709743457922741e-14 relative error = 9.907365801413806e-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] = -1.50000000000001 y[1] (closed_form) = -1.617871514922599 y[1] (numeric) = -1.617871514922582 absolute error = 1.731947918415244e-14 relative error = 1.070510174906011e-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) = -1.51001341392776 y[1] (numeric) = -1.510013413927743 absolute error = 1.731947918415244e-14 relative error = 1.146975187399297e-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) = -1.402155312932921 y[1] (numeric) = -1.402155312932903 absolute error = 1.731947918415244e-14 relative error = 1.235204047968473e-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) = -1.294297211938081 y[1] (numeric) = -1.294297211938064 absolute error = 1.754152378907747e-14 relative error = 1.355293330409851e-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) = -1.186439110943242 y[1] (numeric) = -1.186439110943224 absolute error = 1.754152378907747e-14 relative error = 1.478501814992564e-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) = -1.078581009948403 y[1] (numeric) = -1.078581009948385 absolute error = 1.754152378907747e-14 relative error = 1.626351996491819e-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) = -0.9707229089535634 y[1] (numeric) = -0.9707229089535457 absolute error = 1.765254609153999e-14 relative error = 1.818494848398024e-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) = -0.862864807958724 y[1] (numeric) = -0.8628648079587066 absolute error = 1.743050148661496e-14 relative error = 2.020073286781765e-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) = -0.7550067069638847 y[1] (numeric) = -0.7550067069638674 absolute error = 1.731947918415244e-14 relative error = 2.293950374798579e-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) = -0.6471486059690454 y[1] (numeric) = -0.6471486059690282 absolute error = 1.720845688168993e-14 relative error = 2.659119825487663e-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) = -0.5392905049742062 y[1] (numeric) = -0.5392905049741891 absolute error = 1.709743457922741e-14 relative error = 3.170357056452378e-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) = -0.4314324039793669 y[1] (numeric) = -0.4314324039793499 absolute error = 1.704192342799615e-14 relative error = 3.95007961173245e-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) = -0.3235743029845277 y[1] (numeric) = -0.3235743029845107 absolute error = 1.69864122767649e-14 relative error = 5.249617203865886e-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] = -0.2000000000000094 y[1] (closed_form) = -0.2157162019896885 y[1] (numeric) = -0.2157162019896715 absolute error = 1.701416785238052e-14 relative error = 7.887292514631709e-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) = -0.1078581009948494 y[1] (numeric) = -0.1078581009948323 absolute error = 1.704192342799615e-14 relative error = 1.580031844692868e-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) = -1.013355154976055e-14 y[1] (numeric) = 6.911138328291599e-15 absolute error = 1.704468987805215e-14 relative error = 168.2005543106445 % 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] = 0.09999999999999061 y[1] (closed_form) = 0.1078581009948291 y[1] (numeric) = 0.1078581009948461 absolute error = 1.705580121580397e-14 relative error = 1.581318515576466e-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) = 0.2157162019896683 y[1] (numeric) = 0.2157162019896854 absolute error = 1.704192342799615e-14 relative error = 7.900159223465454e-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) = 0.3235743029845075 y[1] (numeric) = 0.3235743029845246 absolute error = 1.709743457922741e-14 relative error = 5.283928427420896e-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] = 0.3999999999999906 y[1] (closed_form) = 0.4314324039793467 y[1] (numeric) = 0.4314324039793638 absolute error = 1.709743457922741e-14 relative error = 3.962946320565641e-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] = 0.4999999999999906 y[1] (closed_form) = 0.5392905049741858 y[1] (numeric) = 0.5392905049742029 absolute error = 1.709743457922741e-14 relative error = 3.170357056452498e-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) = 0.6471486059690252 y[1] (numeric) = 0.6471486059690421 absolute error = 1.687538997430238e-14 relative error = 2.607652990155725e-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) = 0.7550067069638645 y[1] (numeric) = 0.7550067069638813 absolute error = 1.676436767183986e-14 relative error = 2.220426324324325e-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) = 0.8628648079587038 y[1] (numeric) = 0.8628648079587204 absolute error = 1.665334536937735e-14 relative error = 1.930006324950776e-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) = 0.9707229089535431 y[1] (numeric) = 0.9707229089535596 absolute error = 1.654232306691483e-14 relative error = 1.704124103215794e-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) = 1.078581009948382 y[1] (numeric) = 1.078581009948399 absolute error = 1.665334536937735e-14 relative error = 1.544005059960617e-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) = 1.186439110943222 y[1] (numeric) = 1.186439110943238 absolute error = 1.687538997430238e-14 relative error = 1.422356176448567e-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) = 1.294297211938061 y[1] (numeric) = 1.294297211938078 absolute error = 1.687538997430238e-14 relative error = 1.303826495077852e-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] = 1.299999999999991 y[1] (closed_form) = 1.4021553129329 y[1] (numeric) = 1.402155312932917 absolute error = 1.687538997430238e-14 relative error = 1.203532149302632e-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] = 1.399999999999991 y[1] (closed_form) = 1.510013413927739 y[1] (numeric) = 1.510013413927757 absolute error = 1.709743457922741e-14 relative error = 1.132270377304449e-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] = 1.499999999999991 y[1] (closed_form) = 1.617871514922579 y[1] (numeric) = 1.617871514922596 absolute error = 1.709743457922741e-14 relative error = 1.056785685484152e-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] = 1.599999999999991 y[1] (closed_form) = 1.725729615917418 y[1] (numeric) = 1.725729615917435 absolute error = 1.709743457922741e-14 relative error = 9.907365801413921e-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) = 1.833587716912257 y[1] (numeric) = 1.833587716912275 absolute error = 1.731947918415244e-14 relative error = 9.445678013876676e-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] = 1.799999999999992 y[1] (closed_form) = 1.941445817907097 y[1] (numeric) = 1.941445817907114 absolute error = 1.731947918415244e-14 relative error = 8.920918124216859e-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] = 1.899999999999992 y[1] (closed_form) = 2.049303918901936 y[1] (numeric) = 2.049303918901953 absolute error = 1.731947918415244e-14 relative error = 8.451396117679127e-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] = 1.999999999999992 y[1] (closed_form) = 2.157162019896775 y[1] (numeric) = 2.157162019896793 absolute error = 1.731947918415244e-14 relative error = 8.028826311795168e-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] = 2.099999999999992 y[1] (closed_form) = 2.265020120891614 y[1] (numeric) = 2.265020120891632 absolute error = 1.77635683940025e-14 relative error = 7.842565383926904e-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] = 2.199999999999991 y[1] (closed_form) = 2.372878221886453 y[1] (numeric) = 2.372878221886471 absolute error = 1.820765760385257e-14 relative error = 7.673237267683027e-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] = 2.299999999999991 y[1] (closed_form) = 2.480736322881292 y[1] (numeric) = 2.480736322881311 absolute error = 1.865174681370263e-14 relative error = 7.518633335460357e-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] = 2.399999999999991 y[1] (closed_form) = 2.588594423876131 y[1] (numeric) = 2.58859442387615 absolute error = 1.909583602355269e-14 relative error = 7.376913064256242e-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] = 2.49999999999999 y[1] (closed_form) = 2.69645252487097 y[1] (numeric) = 2.69645252487099 absolute error = 1.998401444325282e-14 relative error = 7.411224287810923e-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] = 2.59999999999999 y[1] (closed_form) = 2.804310625865809 y[1] (numeric) = 2.804310625865829 absolute error = 2.042810365310288e-14 relative error = 7.284536693147489e-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] = 2.69999999999999 y[1] (closed_form) = 2.912168726860648 y[1] (numeric) = 2.912168726860668 absolute error = 2.087219286295294e-14 relative error = 7.167233364755419e-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] = 2.799999999999989 y[1] (closed_form) = 3.020026827855486 y[1] (numeric) = 3.020026827855508 absolute error = 2.176037128265307e-14 relative error = 7.205356946482842e-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] = 2.899999999999989 y[1] (closed_form) = 3.127884928850325 y[1] (numeric) = 3.127884928850347 absolute error = 2.220446049250313e-14 relative error = 7.098873838899351e-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] = 2.999999999999988 y[1] (closed_form) = 3.235743029845164 y[1] (numeric) = 3.235743029845187 absolute error = 2.264854970235319e-14 relative error = 6.99948960515476e-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] = 3.099999999999988 y[1] (closed_form) = 3.343601130840003 y[1] (numeric) = 3.343601130840026 absolute error = 2.309263891220326e-14 relative error = 6.906517257458207e-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] = 3.199999999999988 y[1] (closed_form) = 3.451459231834841 y[1] (numeric) = 3.451459231834865 absolute error = 2.398081733190338e-14 relative error = 6.94802276982274e-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] = 3.299999999999987 y[1] (closed_form) = 3.55931733282968 y[1] (numeric) = 3.559317332829705 absolute error = 2.442490654175344e-14 relative error = 6.86224471093604e-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] = 3.399999999999987 y[1] (closed_form) = 3.667175433824519 y[1] (numeric) = 3.667175433824544 absolute error = 2.486899575160351e-14 relative error = 6.781512420219145e-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] = 3.499999999999987 y[1] (closed_form) = 3.775033534819358 y[1] (numeric) = 3.775033534819384 absolute error = 2.531308496145357e-14 relative error = 6.705393403257501e-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] = 3.599999999999986 y[1] (closed_form) = 3.882891635814197 y[1] (numeric) = 3.882891635814223 absolute error = 2.620126338115369e-14 relative error = 6.747873965753772e-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] = 3.699999999999986 y[1] (closed_form) = 3.990749736809036 y[1] (numeric) = 3.990749736809062 absolute error = 2.664535259100376e-14 relative error = 6.676778637667498e-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] = 3.799999999999986 y[1] (closed_form) = 4.098607837803875 y[1] (numeric) = 4.098607837803901 absolute error = 2.664535259100376e-14 relative error = 6.501073936676247e-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] = 3.899999999999985 y[1] (closed_form) = 4.206465938798713 y[1] (numeric) = 4.206465938798741 absolute error = 2.753353101070388e-14 relative error = 6.545525724277453e-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] = 3.999999999999985 y[1] (closed_form) = 4.314324039793553 y[1] (numeric) = 4.31432403979358 absolute error = 2.753353101070388e-14 relative error = 6.381887581170516e-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] = 4.099999999999985 y[1] (closed_form) = 4.422182140788391 y[1] (numeric) = 4.422182140788419 absolute error = 2.842170943040401e-14 relative error = 6.427077973169363e-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] = 4.199999999999984 y[1] (closed_form) = 4.53004024178323 y[1] (numeric) = 4.530040241783259 absolute error = 2.930988785010413e-14 relative error = 6.470116441739694e-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] = 4.299999999999984 y[1] (closed_form) = 4.637898342778069 y[1] (numeric) = 4.637898342778098 absolute error = 2.930988785010413e-14 relative error = 6.319648617513189e-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] = 4.399999999999983 y[1] (closed_form) = 4.745756443772907 y[1] (numeric) = 4.745756443772938 absolute error = 3.019806626980426e-14 relative error = 6.363172368322509e-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] = 4.499999999999983 y[1] (closed_form) = 4.853614544767747 y[1] (numeric) = 4.853614544767777 absolute error = 3.019806626980426e-14 relative error = 6.221768537915341e-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] = 4.599999999999983 y[1] (closed_form) = 4.961472645762585 y[1] (numeric) = 4.961472645762616 absolute error = 3.108624468950438e-14 relative error = 6.265527779550296e-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] = 4.699999999999982 y[1] (closed_form) = 5.069330746757424 y[1] (numeric) = 5.069330746757456 absolute error = 3.197442310920451e-14 relative error = 6.30742492579653e-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] = 4.799999999999982 y[1] (closed_form) = 5.177188847752263 y[1] (numeric) = 5.177188847752295 absolute error = 3.197442310920451e-14 relative error = 6.176020239842434e-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] = 4.899999999999982 y[1] (closed_form) = 5.285046948747102 y[1] (numeric) = 5.285046948747135 absolute error = 3.286260152890463e-14 relative error = 6.218033982970615e-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] = 4.999999999999981 y[1] (closed_form) = 5.39290504974194 y[1] (numeric) = 5.392905049741974 absolute error = 3.375077994860476e-14 relative error = 6.258367176373668e-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 Finished! diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; 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 %