##############ECHO OF PROBLEM################# ##############temp/expt_lin_lin_new_sm_hpostode.ode################# diff ( y , x , 1 ) = expt ( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln ( 2.0 * x + 1.0 ) + ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.000001; glob_type_given_pole=0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(expt(2.0*x+1.0,3.0*x+2.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 900000.0000000001 step_error = 3.513641844631533e-15 est_needed_step_err = 3.513641844631533e-15 opt_iter = 1 SETTING H FOR MAX H NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.520956754552532 y[1] (numeric) = 1.520956754552532 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11000000000001 y[1] (analytic) = 1.589345825194902 y[1] (numeric) = 1.589345825194846 absolute error = 5.551115123125783e-14 relative error = 3.492704378825199e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12000000000002 y[1] (analytic) = 1.661403714019402 y[1] (numeric) = 1.661403714019279 absolute error = 1.230127111284673e-13 relative error = 7.404143260933553e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13000000000003 y[1] (analytic) = 1.737343136278465 y[1] (numeric) = 1.737343136278261 absolute error = 2.038369473211787e-13 relative error = 1.173268210894796e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14000000000004 y[1] (analytic) = 1.817389968552827 y[1] (numeric) = 1.817389968552548 absolute error = 2.793321129956894e-13 relative error = 1.536996009822368e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15000000000005 y[1] (analytic) = 1.90178410448422 y[1] (numeric) = 1.901784104483854 absolute error = 3.659295089164516e-13 relative error = 1.924138013634807e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16000000000006 y[1] (analytic) = 1.990780368343681 y[1] (numeric) = 1.990780368343223 absolute error = 4.580780199603396e-13 relative error = 2.300997273453415e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17000000000007 y[1] (analytic) = 2.084649490500545 y[1] (numeric) = 2.084649490499998 absolute error = 5.471179065352771e-13 relative error = 2.624507904222828e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18000000000008 y[1] (analytic) = 2.183679149149298 y[1] (numeric) = 2.183679149148629 absolute error = 6.696865284538944e-13 relative error = 3.06678079842813e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.19000000000009 y[1] (analytic) = 2.288175082965593 y[1] (numeric) = 2.288175082964814 absolute error = 7.789324740770098e-13 relative error = 3.404164654513557e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000001 y[1] (analytic) = 2.398462279700273 y[1] (numeric) = 2.398462279699368 absolute error = 9.046097204645775e-13 relative error = 3.771623711245621e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.21000000000011 y[1] (analytic) = 2.514886246083145 y[1] (numeric) = 2.514886246082129 absolute error = 1.016076112136943e-12 relative error = 4.040246805275783e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.22000000000012 y[1] (analytic) = 2.637814364798278 y[1] (numeric) = 2.637814364797142 absolute error = 1.13642428800631e-12 relative error = 4.308204182871739e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.23000000000013 y[1] (analytic) = 2.767637344711905 y[1] (numeric) = 2.767637344710636 absolute error = 1.269206961751479e-12 relative error = 4.58588609586635e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.24000000000014 y[1] (analytic) = 2.904770770984774 y[1] (numeric) = 2.904770770983393 absolute error = 1.381117442633695e-12 relative error = 4.754652093133907e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.25000000000015 y[1] (analytic) = 3.04965676218546 y[1] (numeric) = 3.049656762183917 absolute error = 1.543210004228968e-12 relative error = 5.060274399939569e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2600009999998824 y[1] (analytic) = 3.202781480554723 y[1] (numeric) = 3.202781480557259 absolute error = 2.536193477453708e-12 relative error = 7.918721563902755e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2700009999996149 y[1] (analytic) = 3.364614970990445 y[1] (numeric) = 3.364614970997311 absolute error = 6.865619184281968e-12 relative error = 2.040536359576659e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2800009999993473 y[1] (analytic) = 3.535704977974554 y[1] (numeric) = 3.535704977986002 absolute error = 1.144861982993461e-11 relative error = 3.238002011268772e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2900009999990797 y[1] (analytic) = 3.716618747792957 y[1] (numeric) = 3.716618747809245 absolute error = 1.628785994967075e-11 relative error = 4.382440345634854e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000009999988122 y[1] (analytic) = 3.907960238797485 y[1] (numeric) = 3.907960238818879 absolute error = 2.139310950610707e-11 relative error = 5.474239295917176e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3100009999985446 y[1] (analytic) = 4.110372602091842 y[1] (numeric) = 4.110372602118603 absolute error = 2.676081578556477e-11 relative error = 6.510557162614823e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3200009999982771 y[1] (analytic) = 4.324540836048243 y[1] (numeric) = 4.324540836080687 absolute error = 3.244426949322587e-11 relative error = 7.502361689541447e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3300009999980095 y[1] (analytic) = 4.551194627225389 y[1] (numeric) = 4.551194627263887 absolute error = 3.849809360190193e-11 relative error = 8.458898543166036e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.340000999997742 y[1] (analytic) = 4.791111391192567 y[1] (numeric) = 4.791111391237499 absolute error = 4.493205807420964e-11 relative error = 9.378211944061164e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500009999974744 y[1] (analytic) = 5.045119527769986 y[1] (numeric) = 5.045119527821707 absolute error = 5.172129391439739e-11 relative error = 1.025174797736833e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3600009999972069 y[1] (analytic) = 5.31410190627748 y[1] (numeric) = 5.314101906336403 absolute error = 5.892353271974571e-11 relative error = 1.108814504481747e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3700009999969393 y[1] (analytic) = 5.59899959754846 y[1] (numeric) = 5.59899959761503 absolute error = 6.657074891336379e-11 relative error = 1.188975776003128e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3800009999966718 y[1] (analytic) = 5.900815870719871 y[1] (numeric) = 5.900815870794475 absolute error = 7.460432271955142e-11 relative error = 1.264305213957643e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3900009999964042 y[1] (analytic) = 6.220620474158913 y[1] (numeric) = 6.220620474242053 absolute error = 8.313971733286962e-11 relative error = 1.336518080121435e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000009999961366 y[1] (analytic) = 6.559554221340978 y[1] (numeric) = 6.559554221433181 absolute error = 9.22035781059094e-11 relative error = 1.405637867980915e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4100009999958691 y[1] (analytic) = 6.91883390405868 y[1] (numeric) = 6.918833904160521 absolute error = 1.018412021380755e-10 relative error = 1.471941710847171e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4200009999956015 y[1] (analytic) = 7.299757557027896 y[1] (numeric) = 7.299757557139932 absolute error = 1.120357140393935e-10 relative error = 1.534786781124399e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.430000999995334 y[1] (analytic) = 7.703710099772802 y[1] (numeric) = 7.703710099895629 absolute error = 1.2282708183875e-10 relative error = 1.594388680882117e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4400009999950664 y[1] (analytic) = 8.132169383628218 y[1] (numeric) = 8.132169383762474 absolute error = 1.342552735650315e-10 relative error = 1.650915853220124e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4500009999947989 y[1] (analytic) = 8.586712673805366 y[1] (numeric) = 8.58671267395184 absolute error = 1.464748322632659e-10 relative error = 1.705831298048462e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4600009999945313 y[1] (analytic) = 9.069023598738138 y[1] (numeric) = 9.069023598897489 absolute error = 1.593516429920783e-10 relative error = 1.75709811819489e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4700009999942638 y[1] (analytic) = 9.58089960137429 y[1] (numeric) = 9.58089960154741 absolute error = 1.731201848542696e-10 relative error = 1.806930372482321e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4800009999939962 y[1] (analytic) = 10.12425992971348 y[1] (numeric) = 10.12425992990114 absolute error = 1.876543365142425e-10 relative error = 1.853511642500403e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900009999937286 y[1] (analytic) = 10.70115420673688 y[1] (numeric) = 10.70115420693998 absolute error = 2.031033119465064e-10 relative error = 1.897957061665773e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5000009999934611 y[1] (analytic) = 11.31377162293743 y[1] (numeric) = 11.31377162315696 absolute error = 2.1953105999728e-10 relative error = 1.940387938821435e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5100009999937487 y[1] (analytic) = 11.96445079800088 y[1] (numeric) = 11.9644507982017 absolute error = 2.008242461215559e-10 relative error = 1.678507852237658e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5200009999940363 y[1] (analytic) = 12.65569036153078 y[1] (numeric) = 12.6556903617117 absolute error = 1.809254968065943e-10 relative error = 1.429598004045276e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5300009999943238 y[1] (analytic) = 13.39016030708721 y[1] (numeric) = 13.39016030724711 absolute error = 1.598969845417741e-10 relative error = 1.194137940657387e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5400009999946114 y[1] (analytic) = 14.17071417725143 y[1] (numeric) = 14.17071417738889 absolute error = 1.374651503738278e-10 relative error = 9.700650839073708e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5500009999948989 y[1] (analytic) = 15.00040214241016 y[1] (numeric) = 15.00040214252368 absolute error = 1.135198601787124e-10 relative error = 7.567787790019395e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5600009999951865 y[1] (analytic) = 15.88248504057076 y[1] (numeric) = 15.88248504065887 absolute error = 8.811795737528882e-11 relative error = 5.548121540816651e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.570000999995474 y[1] (analytic) = 16.82044945074918 y[1] (numeric) = 16.8204494508104 absolute error = 6.122746754044783e-11 relative error = 3.640061326525421e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5800009999957616 y[1] (analytic) = 17.81802387808166 y[1] (numeric) = 17.81802387811429 absolute error = 3.26352278534614e-11 relative error = 1.831585145286886e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5900009999960492 y[1] (analytic) = 18.87919613486195 y[1] (numeric) = 18.87919613486396 absolute error = 2.017941369558685e-12 relative error = 1.068870387882879e-11 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 13 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6000009999963367 y[1] (analytic) = 20.00823200823642 y[1] (numeric) = 20.00823200820595 absolute error = 3.04680725093931e-11 relative error = 1.522776849891128e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6100009999966243 y[1] (analytic) = 21.20969531233682 y[1] (numeric) = 21.20969531227195 absolute error = 6.486899906121835e-11 relative error = 3.058459732964042e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6200009999969118 y[1] (analytic) = 22.48846943023691 y[1] (numeric) = 22.48846943013533 absolute error = 1.015791895042639e-10 relative error = 4.516945442613602e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6300009999971994 y[1] (analytic) = 23.84978045933066 y[1] (numeric) = 23.84978045918993 absolute error = 1.407336469583242e-10 relative error = 5.900836160664344e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6400009999974869 y[1] (analytic) = 25.29922208259354 y[1] (numeric) = 25.29922208241106 absolute error = 1.824780326842301e-10 relative error = 7.212792238769243e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6500009999977745 y[1] (analytic) = 26.84278229775954 y[1] (numeric) = 26.84278229753279 absolute error = 2.267555032631208e-10 relative error = 8.447540972011949e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6600009999980621 y[1] (analytic) = 28.48687214678071 y[1] (numeric) = 28.48687214650665 absolute error = 2.740634386100282e-10 relative error = 9.620692549111611e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6700009999983496 y[1] (analytic) = 30.238356599096 y[1] (numeric) = 30.2383565987716 absolute error = 3.244018387249525e-10 relative error = 1.072815705648007e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6800009999986372 y[1] (analytic) = 32.10458775428961 y[1] (numeric) = 32.10458775391156 absolute error = 3.780513679885189e-10 relative error = 1.177561820391249e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6900009999989247 y[1] (analytic) = 34.09344054273762 y[1] (numeric) = 34.0934405423025 absolute error = 4.351150550974126e-10 relative error = 1.276242726374233e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000009999992123 y[1] (analytic) = 36.21335111690568 y[1] (numeric) = 36.21335111640937 absolute error = 4.963069955010724e-10 relative error = 1.370508335168624e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7100009999994998 y[1] (analytic) = 38.47335814115377 y[1] (numeric) = 38.47335814059277 absolute error = 5.610019115920295e-10 relative error = 1.458156861519044e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7200009999997874 y[1] (analytic) = 40.88314720432074 y[1] (numeric) = 40.88314720369029 absolute error = 6.304432531578641e-10 relative error = 1.542061451402244e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7300000000000749 y[1] (analytic) = 43.4528332303076 y[1] (numeric) = 43.45283322960346 absolute error = 7.041478511382593e-10 relative error = 1.62048777672598e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7400000000003625 y[1] (analytic) = 46.19405563722965 y[1] (numeric) = 46.19405563644641 absolute error = 7.832454684830736e-10 relative error = 1.695554671869565e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.75000000000065 y[1] (analytic) = 49.11849334718602 y[1] (numeric) = 49.11849334631864 absolute error = 8.673879392517847e-10 relative error = 1.765909090738584e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7600000000009376 y[1] (analytic) = 52.23893502309783 y[1] (numeric) = 52.23893502214064 absolute error = 9.571934356245038e-10 relative error = 1.832337192941e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7700000000012251 y[1] (analytic) = 55.56909432512941 y[1] (numeric) = 55.56909432407613 absolute error = 1.053280129781342e-09 relative error = 1.895442318384212e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7800000000015127 y[1] (analytic) = 59.12367886960834 y[1] (numeric) = 59.12367886845276 absolute error = 1.155584072876081e-09 relative error = 1.954519906355307e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7900000000018003 y[1] (analytic) = 62.91846446624539 y[1] (numeric) = 62.91846446498105 absolute error = 1.264339744011522e-09 relative error = 2.009489193255531e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000000000020878 y[1] (analytic) = 66.97037504723529 y[1] (numeric) = 66.97037504585425 absolute error = 1.381039282932761e-09 relative error = 2.062164474902062e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8100000000023754 y[1] (analytic) = 71.29756873491498 y[1] (numeric) = 71.29756873340948 absolute error = 1.5054979485285e-09 relative error = 2.111569826631755e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8200000000026629 y[1] (analytic) = 75.91953053045033 y[1] (numeric) = 75.9195305288121 absolute error = 1.638227331568487e-09 relative error = 2.157847025820866e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8300000000029505 y[1] (analytic) = 80.85717214474134 y[1] (numeric) = 80.85717214296102 absolute error = 1.780321667865792e-09 relative error = 2.201810452483871e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.840000000003238 y[1] (analytic) = 86.13293953461992 y[1] (numeric) = 86.13293953268732 absolute error = 1.932605186993896e-09 relative error = 2.243746930542308e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8500000000035256 y[1] (analytic) = 91.77092875272994 y[1] (numeric) = 91.77092875063531 absolute error = 2.09463735245663e-09 relative error = 2.282462846268535e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8600000000038132 y[1] (analytic) = 97.79701076850991 y[1] (numeric) = 97.79701076624234 absolute error = 2.267569243485923e-09 relative error = 2.318648827471184e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8700000000041007 y[1] (analytic) = 104.2389659707548 y[1] (numeric) = 104.2389659683016 absolute error = 2.453205638630607e-09 relative error = 2.353443950431047e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8800000000043883 y[1] (analytic) = 111.1266291196528 y[1] (numeric) = 111.1266291170012 absolute error = 2.651574959600111e-09 relative error = 2.386084218162593e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8900000000046758 y[1] (analytic) = 118.4920455783379 y[1] (numeric) = 118.4920455754744 absolute error = 2.863416170839628e-09 relative error = 2.416547167249768e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000000000049634 y[1] (analytic) = 126.3696397212673 y[1] (numeric) = 126.3696397181771 absolute error = 3.090192990384821e-09 relative error = 2.44536029160235e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9100000000052509 y[1] (analytic) = 134.7963964895536 y[1] (numeric) = 134.7963964862202 absolute error = 3.333440190544934e-09 relative error = 2.472944587063399e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9200000000055385 y[1] (analytic) = 143.8120571422188 y[1] (numeric) = 143.812057138626 absolute error = 3.592788289097371e-09 relative error = 2.498252483478756e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9300000000058261 y[1] (analytic) = 153.4593303377005 y[1] (numeric) = 153.4593303338307 absolute error = 3.869814690915518e-09 relative error = 2.52172004295839e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9400000000061136 y[1] (analytic) = 163.7841197723753 y[1] (numeric) = 163.7841197682101 absolute error = 4.165144673606846e-09 relative error = 2.543069913857035e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9500000000064012 y[1] (analytic) = 174.8357697029675 y[1] (numeric) = 174.8357696984847 absolute error = 4.482757276491611e-09 relative error = 2.563981777932211e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9600000000066887 y[1] (analytic) = 186.6673297881306 y[1] (numeric) = 186.6673297833077 absolute error = 4.822936716664117e-09 relative error = 2.583706919758375e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9700000000069763 y[1] (analytic) = 199.3358408019241 y[1] (numeric) = 199.3358407967366 absolute error = 5.187530405237339e-09 relative error = 2.602407266233713e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9800000000072638 y[1] (analytic) = 212.9026428991266 y[1] (numeric) = 212.9026428935483 absolute error = 5.578357331614825e-09 relative error = 2.620144708235422e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9900000000075514 y[1] (analytic) = 227.433708250147 y[1] (numeric) = 227.4337082441512 absolute error = 5.995843821438029e-09 relative error = 2.636303944375472e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 1e-06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = expt ( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln ( 2.0 * x + 1.0 ) + ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0 ) ) ; Iterations = 900000 Total Elapsed Time = 24.0 Seconds Elapsed Time(since restart) = 24.0 Seconds Time to Timeout = 9 Minutes 36.0 Seconds Percent Done = 100 %