##############ECHO OF PROBLEM################# ##############temp/sub_lin_sinpostode.ode################# diff ( y , x , 1 ) = (0.1 * x + 1.0) - sin(x); ! /* BEGIN FIRST INPUT BLOCK */ Digits = 32; max_terms = 30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start = 0.1; x_end = 5.0 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.05; glob_look_poles = true; glob_max_iter = 1000000; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_h = 0.005 ; glob_display_interval = 0.1; glob_look_poles = true; glob_max_iter = 10000; glob_max_minutes = 10; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(cos(x) + (0.05 * x * x) + x) ; } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 1.095504165278026 y[1] (numeric) = 1.095504165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2000000000000001 y[1] (analytic) = 1.182066577841242 y[1] (numeric) = 1.182066577841226 absolute error = 1.554312234475219e-14 relative error = 1.314910905707015e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 1.259836489125606 y[1] (numeric) = 1.259836489125576 absolute error = 3.019806626980426e-14 relative error = 2.396982983939712e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 1.329060994002885 y[1] (numeric) = 1.329060994002841 absolute error = 4.39648317751562e-14 relative error = 3.307961935045756e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 1.390082561890373 y[1] (numeric) = 1.390082561890315 absolute error = 5.773159728050814e-14 relative error = 4.153105640142623e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 1.443335614909679 y[1] (numeric) = 1.443335614909608 absolute error = 7.061018436615996e-14 relative error = 4.892152846278834e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 1.489342187284489 y[1] (numeric) = 1.489342187284406 absolute error = 8.237854842718662e-14 relative error = 5.53120358306556e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 1.528706709347166 y[1] (numeric) = 1.528706709347072 absolute error = 9.348077867343818e-14 relative error = 6.115023771522476e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 1.562109968270665 y[1] (numeric) = 1.562109968270561 absolute error = 1.036948304999896e-13 relative error = 6.638126163088574e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 1.59030230586814 y[1] (numeric) = 1.590302305868028 absolute error = 1.121325254871408e-13 relative error = 7.051019486884797e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 1.615185683252361 y[1] (numeric) = 1.615185683252242 absolute error = 1.196820420545919e-13 relative error = 7.409800823246426e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 1.635294299001799 y[1] (numeric) = 1.635294299001673 absolute error = 1.256772463875677e-13 relative error = 7.685298387225006e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 1.652828964043213 y[1] (numeric) = 1.652828964043083 absolute error = 1.294520046712933e-13 relative error = 7.832147638230085e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 1.668739040195614 y[1] (numeric) = 1.668739040195482 absolute error = 1.325606291402437e-13 relative error = 7.943760285293292e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 1.684000113302622 y[1] (numeric) = 1.684000113302488 absolute error = 1.336708521648688e-13 relative error = 7.937698525608568e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 1.699604245501194 y[1] (numeric) = 1.699604245501061 absolute error = 1.332267629550188e-13 relative error = 7.838693231537069e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 1.716550062864691 y[1] (numeric) = 1.71655006286456 absolute error = 1.316724507205436e-13 relative error = 7.670760880740055e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 1.735832777461253 y[1] (numeric) = 1.735832777461124 absolute error = 1.285638262515931e-13 relative error = 7.40646379771815e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 1.758434243523782 y[1] (numeric) = 1.758434243523658 absolute error = 1.241229341530925e-13 relative error = 7.058719119593497e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 1.785313147087016 y[1] (numeric) = 1.785313147086897 absolute error = 1.181277298201167e-13 relative error = 6.616639216087011e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 1.817395427113557 y[1] (numeric) = 1.817395427113446 absolute error = 1.103561686477406e-13 relative error = 6.07221560048776e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 1.85556502381784 y[1] (numeric) = 1.855565023817739 absolute error = 1.012523398458143e-13 relative error = 5.456685082233699e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 1.9006550466277 y[1] (numeric) = 1.900655046627609 absolute error = 9.059419880941277e-14 relative error = 4.766472431183792e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 1.953439450030356 y[1] (numeric) = 1.953439450030277 absolute error = 7.860379014346108e-14 relative error = 4.023866219259553e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 2.014625300475011 y[1] (numeric) = 2.014625300474946 absolute error = 6.52811138479592e-14 relative error = 3.240360072543869e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 2.084845711598621 y[1] (numeric) = 2.084845711598569 absolute error = 5.240252676230739e-14 relative error = 2.513496632905564e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 2.164653518363708 y[1] (numeric) = 2.16465351836367 absolute error = 3.774758283725532e-14 relative error = 1.743816389876069e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 2.254515753314159 y[1] (numeric) = 2.254515753314138 absolute error = 2.087219286295294e-14 relative error = 9.257949443143444e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 2.354808980140431 y[1] (numeric) = 2.354808980140427 absolute error = 3.996802888650564e-15 relative error = 1.697293887681798e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 2.465815531179629 y[1] (numeric) = 2.465815531179642 absolute error = 1.287858708565182e-14 relative error = 5.222850988975151e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 2.58772068644412 y[1] (numeric) = 2.58772068644415 absolute error = 2.97539770599542e-14 relative error = 1.149814089898559e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 2.720610822364895 y[1] (numeric) = 2.720610822364943 absolute error = 4.796163466380676e-14 relative error = 1.7628995029181e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 2.864472548746823 y[1] (numeric) = 2.864472548746889 absolute error = 6.572520305780927e-14 relative error = 2.294495825647321e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 3.019192842559057 y[1] (numeric) = 3.01919284255914 absolute error = 8.304468224196171e-14 relative error = 2.750559059075317e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 3.184560177223792 y[1] (numeric) = 3.184560177223894 absolute error = 1.021405182655144e-13 relative error = 3.207366561826367e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 3.360266636119915 y[1] (numeric) = 3.360266636120036 absolute error = 1.20348175869367e-13 relative error = 3.58150673448737e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 3.545910989184097 y[1] (numeric) = 3.545910989184236 absolute error = 1.381117442633695e-13 relative error = 3.894958014587629e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 3.741002701868957 y[1] (numeric) = 3.741002701869112 absolute error = 1.549871342376719e-13 relative error = 4.142930294069082e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 3.944966836402107 y[1] (numeric) = 3.944966836402277 absolute error = 1.70086167372574e-13 relative error = 4.311472679646051e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 4.157149796374331 y[1] (numeric) = 4.157149796374517 absolute error = 1.856292897173262e-13 relative error = 4.465301921023467e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 4.376825857258852 y[1] (numeric) = 4.376825857259051 absolute error = 1.989519660128281e-13 relative error = 4.545576463428888e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 4.603204417610907 y[1] (numeric) = 4.60320441761112 absolute error = 2.122746423083299e-13 relative error = 4.611453740707475e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 4.835437898496056 y[1] (numeric) = 4.83543789849628 absolute error = 2.238209617644316e-13 relative error = 4.628763029591292e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 5.072630212218709 y[1] (numeric) = 5.072630212218941 absolute error = 2.318145675417327e-13 relative error = 4.569908663622845e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 5.313845715734185 y[1] (numeric) = 5.313845715734428 absolute error = 2.433608869978343e-13 relative error = 4.579750711941973e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 5.558118559284723 y[1] (numeric) = 5.558118559284973 absolute error = 2.504663143554353e-13 relative error = 4.506314712143671e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 5.804462336850999 y[1] (numeric) = 5.804462336851255 absolute error = 2.566835632933362e-13 relative error = 4.422176394594208e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 6.05187994199501 y[1] (numeric) = 6.05187994199527 absolute error = 2.602362769721367e-13 relative error = 4.300089880605752e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 6.299373530617996 y[1] (numeric) = 6.299373530618259 absolute error = 2.629008122312371e-13 relative error = 4.173443771089493e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 6.545954491088839 y[1] (numeric) = 6.545954491089105 absolute error = 2.664535259100376e-13 relative error = 4.070506849272585e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = (0.1 * x + 1.0) - sin(x); Iterations = 981 Total Elapsed Time = 49 Seconds Elapsed Time(since restart) = 48 Seconds Time to Timeout = 9 Minutes 11 Seconds Percent Done = 100.2 %