##############ECHO OF PROBLEM################# ##############temp/addpostode.ode################# diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ; ! // BEGIN FIRST INPUT BLOCK max_terms = 30; Digits = 32; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start = 0.1; x_end = 10.0 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 100; // 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(2.0 - cos(x) - cos(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.009991669443948525 y[1] (numeric) = 0.009991669443948525 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) = 0.03986684431751676 y[1] (numeric) = 0.03986684431754685 absolute error = 3.008704396734174e-14 relative error = 7.546883753255094e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.08932702174878805 y[1] (numeric) = 0.08932702174884752 absolute error = 5.946632075648495e-14 relative error = 6.657148037882698e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.1578780119942301 y[1] (numeric) = 0.157878011994318 absolute error = 8.784639682346551e-14 relative error = 5.564194514095857e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.2448348762192549 y[1] (numeric) = 0.2448348762193701 absolute error = 1.152411499560912e-13 relative error = 4.706892732589712e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.349328770180644 y[1] (numeric) = 0.349328770180785 absolute error = 1.410538352786261e-13 relative error = 4.037853372503065e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.4703156254310237 y[1] (numeric) = 0.470315625431189 absolute error = 1.653122083666858e-13 relative error = 3.514920607096232e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 0.60658658130567 y[1] (numeric) = 0.6065865813058573 absolute error = 1.872946242542639e-13 relative error = 3.087681627429255e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 0.7567800634586721 y[1] (numeric) = 0.7567800634588793 absolute error = 2.071676163950542e-13 relative error = 2.737487764255403e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 0.9193953882637217 y[1] (numeric) = 0.9193953882639468 absolute error = 2.251532293939817e-13 relative error = 2.448927113058329e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 1.101731133495274 y[1] (numeric) = 1.101731133495519 absolute error = 2.449151992323095e-13 relative error = 2.223003342524314e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 1.284613901996394 y[1] (numeric) = 1.284613901996655 absolute error = 2.611244553918368e-13 relative error = 2.032707687391739e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 1.474644571913562 y[1] (numeric) = 1.474644571913836 absolute error = 2.742250870824137e-13 relative error = 1.859601237514254e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 1.669924419608753 y[1] (numeric) = 1.669924419609038 absolute error = 2.848832281188152e-13 relative error = 1.705964801601982e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 1.868502273394733 y[1] (numeric) = 1.868502273395026 absolute error = 2.928768338961163e-13 relative error = 1.56744167810945e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 2.068394008997584 y[1] (numeric) = 2.068394008997881 absolute error = 2.97539770599542e-13 relative error = 1.4385062483513e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 2.267602374270584 y[1] (numeric) = 2.267602374270882 absolute error = 2.984279490192421e-13 relative error = 1.316050611012599e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 2.464136945077456 y[1] (numeric) = 2.464136945077754 absolute error = 2.97539770599542e-13 relative error = 1.207480660496283e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 2.656034012952391 y[1] (numeric) = 2.656034012952684 absolute error = 2.930988785010413e-13 relative error = 1.103520802338065e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 2.841376205825919 y[1] (numeric) = 2.841376205826205 absolute error = 2.855493619335903e-13 relative error = 1.004968512610557e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 3.018311645772831 y[1] (numeric) = 3.018311645773106 absolute error = 2.748912208971888e-13 relative error = 9.107449897765726e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 3.185072452364259 y[1] (numeric) = 3.18507245236452 absolute error = 2.615685446016869e-13 relative error = 8.212326360347823e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 3.339992406744534 y[1] (numeric) = 3.33999240674478 absolute error = 2.460254222569347e-13 relative error = 7.366047352686465e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 3.481523599939217 y[1] (numeric) = 3.481523599939444 absolute error = 2.26929586233382e-13 relative error = 6.518111387708069e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 3.6082518990499 y[1] (numeric) = 3.608251899050105 absolute error = 2.05613304160579e-13 relative error = 5.698418788741432e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 3.718911076802674 y[1] (numeric) = 3.718911076802856 absolute error = 1.820765760385257e-13 relative error = 4.89596476705933e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 3.812395463272495 y[1] (numeric) = 3.812395463272652 absolute error = 1.576516694967722e-13 relative error = 4.135239143355993e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 3.887770993371586 y[1] (numeric) = 3.887770993371717 absolute error = 1.310063169057685e-13 relative error = 3.369702514091656e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 3.944284539719034 y[1] (numeric) = 3.944284539719137 absolute error = 1.025846074753645e-13 relative error = 2.600841963665023e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 3.981371437640632 y[1] (numeric) = 3.981371437640706 absolute error = 7.371880883511039e-14 relative error = 1.851593351430589e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 3.998661127111645 y[1] (numeric) = 3.998661127111689 absolute error = 4.39648317751562e-14 relative error = 1.099488813319706e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 3.995980855270089 y[1] (numeric) = 3.995980855270103 absolute error = 1.376676550535194e-14 relative error = 3.445153018487483e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 3.973357402506226 y[1] (numeric) = 3.973357402506208 absolute error = 1.820765760385257e-14 relative error = 4.582436403120431e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 3.931016814881752 y[1] (numeric) = 3.931016814881702 absolute error = 4.973799150320701e-14 relative error = 1.265270382841218e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 3.869382145552275 y[1] (numeric) = 3.869382145552196 absolute error = 7.949196856316121e-14 relative error = 2.054384022382864e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 3.789069227760021 y[1] (numeric) = 3.789069227759913 absolute error = 1.083577672034153e-13 relative error = 2.859746304172779e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 3.69088052163165 y[1] (numeric) = 3.690880521631514 absolute error = 1.358912982141192e-13 relative error = 3.681812440627173e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 3.575797096261924 y[1] (numeric) = 3.575797096261761 absolute error = 1.63424829224823e-13 relative error = 4.570304880991835e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 3.444968827195616 y[1] (numeric) = 3.444968827195428 absolute error = 1.882938249764265e-13 relative error = 5.465762810100883e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 3.29970290725116 y[1] (numeric) = 3.299702907250949 absolute error = 2.113864638886298e-13 relative error = 6.406227161363649e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 3.141450785482113 y[1] (numeric) = 3.141450785481879 absolute error = 2.335909243811329e-13 relative error = 7.435765839803985e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 2.971793664777993 y[1] (numeric) = 2.97179366477774 absolute error = 2.531308496145357e-13 relative error = 8.517780107504392e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 2.79242670300769 y[1] (numeric) = 2.792426703007418 absolute error = 2.717825964282383e-13 relative error = 9.732846206330303e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 2.605142075562375 y[1] (numeric) = 2.60514207556209 absolute error = 2.851052727237402e-13 relative error = 1.094394334183076e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 2.411811068531417 y[1] (numeric) = 2.411811068531119 absolute error = 2.97983859809392e-13 relative error = 1.235519082308708e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 2.214365381430333 y[1] (numeric) = 2.214365381430027 absolute error = 3.064215547965432e-13 relative error = 1.383789492764808e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 2.014777826297772 y[1] (numeric) = 2.01477782629746 absolute error = 3.12194714524594e-13 relative error = 1.549524272352467e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 1.815042616009744 y[1] (numeric) = 1.815042616009429 absolute error = 3.150812943886194e-13 relative error = 1.735944333259269e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 1.617155438763763 y[1] (numeric) = 1.617155438763449 absolute error = 3.148592497836944e-13 relative error = 1.946994347212467e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 1.423093517822068 y[1] (numeric) = 1.423093517821757 absolute error = 3.115285807098189e-13 relative error = 2.189094228934362e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.104999999999913 y[1] (analytic) = 1.234795855750367 y[1] (numeric) = 1.234795855750062 absolute error = 3.05089287166993e-13 relative error = 2.47076701582866e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.204999999999911 y[1] (analytic) = 1.054143860545146 y[1] (numeric) = 1.05414386054485 absolute error = 2.959854583650667e-13 relative error = 2.807827939271961e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.304999999999909 y[1] (analytic) = 0.8829425472268876 y[1] (numeric) = 0.8829425472266035 absolute error = 2.841060720015776e-13 relative error = 3.217718671434366e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.404999999999907 y[1] (analytic) = 0.7229025027266363 y[1] (numeric) = 0.7229025027263672 absolute error = 2.690070388666754e-13 relative error = 3.721207740352779e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.504999999999905 y[1] (analytic) = 0.5756227942668338 y[1] (numeric) = 0.5756227942665819 absolute error = 2.51909604287448e-13 relative error = 4.376296539964218e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.604999999999903 y[1] (analytic) = 0.4425749920102117 y[1] (numeric) = 0.4425749920099796 absolute error = 2.32092123297889e-13 relative error = 5.244130994471866e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.704999999999901 y[1] (analytic) = 0.3250884656171616 y[1] (numeric) = 0.3250884656169515 absolute error = 2.101097074103109e-13 relative error = 6.463154791155993e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.804999999999898 y[1] (analytic) = 0.2243371016235205 y[1] (numeric) = 0.2243371016233346 absolute error = 1.858790898978668e-13 relative error = 8.285704350848154e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.904999999999896 y[1] (analytic) = 0.1413275743543401 y[1] (numeric) = 0.14132757435418 absolute error = 1.600386489997163e-13 relative error = 1.132395073861972e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.004999999999894 y[1] (analytic) = 0.07688928756679213 y[1] (numeric) = 0.07688928756665944 absolute error = 1.32685529230514e-13 relative error = 1.725669900572988e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.104999999999892 y[1] (analytic) = 0.03166608732199223 y[1] (numeric) = 0.03166608732188814 absolute error = 1.040903474525123e-13 relative error = 3.287123742004626e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.20499999999989 y[1] (analytic) = 0.006109828887983869 y[1] (numeric) = 0.00610982888790933 absolute error = 7.453933303924742e-14 relative error = 1.21999051701502e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.304999999999888 y[1] (analytic) = 0.0004758619512635727 y[1] (numeric) = 0.0004758619512194541 absolute error = 4.411868006343189e-14 relative error = 9.271319118135424e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.404999999999886 y[1] (analytic) = 0.01482047924712174 y[1] (numeric) = 0.01482047924710805 absolute error = 1.368523350198103e-14 relative error = 9.234002000737474e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.504999999999884 y[1] (analytic) = 0.04900035410123759 y[1] (numeric) = 0.04900035410125466 absolute error = 1.706967900361178e-14 relative error = 3.483582785615146e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.604999999999881 y[1] (analytic) = 0.1026739725024336 y[1] (numeric) = 0.1026739725024811 absolute error = 4.755917881738014e-14 relative error = 4.632057926486959e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.704999999999879 y[1] (analytic) = 0.1753050453977845 y[1] (numeric) = 0.1753050453978618 absolute error = 7.735478924075778e-14 relative error = 4.412582026103819e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.804999999999877 y[1] (analytic) = 0.2661678671155605 y[1] (numeric) = 0.2661678671156668 absolute error = 1.0635936575909e-13 relative error = 3.995950634901868e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.904999999999875 y[1] (analytic) = 0.3743545663764131 y[1] (numeric) = 0.3743545663765473 absolute error = 1.342259636771814e-13 relative error = 3.585530289544201e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.004999999999873 y[1] (analytic) = 0.498784177443096 y[1] (numeric) = 0.4987841774432568 absolute error = 1.607602939657227e-13 relative error = 3.223043176506197e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.104999999999871 y[1] (analytic) = 0.6382134407727924 y[1] (numeric) = 0.6382134407729778 absolute error = 1.854072451124011e-13 relative error = 2.905097781831379e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.204999999999869 y[1] (analytic) = 0.7912492252554982 y[1] (numeric) = 0.7912492252557067 absolute error = 2.084998840246044e-13 relative error = 2.635072204428115e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.304999999999866 y[1] (analytic) = 0.9563624479195673 y[1] (numeric) = 0.9563624479197964 absolute error = 2.291500322826323e-13 relative error = 2.396058448145012e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.404999999999864 y[1] (analytic) = 1.131903352023315 y[1] (numeric) = 1.131903352023563 absolute error = 2.473576898864849e-13 relative error = 2.185325182086657e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.504999999999862 y[1] (analytic) = 1.316117990879045 y[1] (numeric) = 1.316117990879308 absolute error = 2.631228568361621e-13 relative error = 1.999234556929203e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.60499999999986 y[1] (analytic) = 1.507165752708575 y[1] (numeric) = 1.507165752708851 absolute error = 2.762234885267389e-13 relative error = 1.832734641364621e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.704999999999858 y[1] (analytic) = 1.703137751427698 y[1] (numeric) = 1.703137751427984 absolute error = 2.866595849582154e-13 relative error = 1.683126245765593e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.804999999999856 y[1] (analytic) = 1.902075899604942 y[1] (numeric) = 1.902075899605236 absolute error = 2.935429677108914e-13 relative error = 1.543276836491434e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.904999999999854 y[1] (analytic) = 2.101992473023929 y[1] (numeric) = 2.101992473024228 absolute error = 2.988720382290921e-13 relative error = 1.421851134410269e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.004999999999852 y[1] (analytic) = 2.300889971366692 y[1] (numeric) = 2.300889971366992 absolute error = 3.002043058586423e-13 relative error = 1.304731254403816e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.104999999999867 y[1] (analytic) = 2.496781076576593 y[1] (numeric) = 2.496781076576857 absolute error = 2.646771690706373e-13 relative error = 1.060073594572191e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.204999999999883 y[1] (analytic) = 2.68770850948333 y[1] (numeric) = 2.687708509483555 absolute error = 2.251532293939817e-13 relative error = 8.377144641971012e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.304999999999898 y[1] (analytic) = 2.871764586289518 y[1] (numeric) = 2.871764586289702 absolute error = 1.84297022087776e-13 relative error = 6.417553269082483e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.404999999999914 y[1] (analytic) = 3.047110279516557 y[1] (numeric) = 3.0471102795167 absolute error = 1.4210854715202e-13 relative error = 4.663715261876456e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.50499999999993 y[1] (analytic) = 3.211993592959304 y[1] (numeric) = 3.211993592959404 absolute error = 1.003641614261142e-13 relative error = 3.124668792805583e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.604999999999945 y[1] (analytic) = 3.364767067053013 y[1] (numeric) = 3.364767067053069 absolute error = 5.684341886080801e-14 relative error = 1.689371588821261e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.704999999999961 y[1] (analytic) = 3.503904239744737 y[1] (numeric) = 3.503904239744751 absolute error = 1.376676550535194e-14 relative error = 3.928978808608897e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.804999999999977 y[1] (analytic) = 3.628014898397575 y[1] (numeric) = 3.628014898397546 absolute error = 2.886579864025407e-14 relative error = 7.956361660202536e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.899999999999991 y[1] (analytic) = 3.730870418482215 y[1] (numeric) = 3.730870418482147 absolute error = 6.838973831690964e-14 relative error = 1.833077288830948e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.000000000000007 y[1] (analytic) = 3.822260523769359 y[1] (numeric) = 3.822260523769251 absolute error = 1.088018564132653e-13 relative error = 2.846531672466149e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.100000000000023 y[1] (analytic) = 3.895443204262238 y[1] (numeric) = 3.895443204262089 absolute error = 1.49213974509621e-13 relative error = 3.830474908384162e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.200000000000038 y[1] (analytic) = 3.949687242808345 y[1] (numeric) = 3.949687242808158 absolute error = 1.865174681370263e-13 relative error = 4.722335128601394e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.300000000000054 y[1] (analytic) = 3.98445065090522 y[1] (numeric) = 3.984450650905 absolute error = 2.207123372954811e-13 relative error = 5.539341721934437e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.40000000000007 y[1] (analytic) = 3.999386084070417 y[1] (numeric) = 3.999386084070162 absolute error = 2.544631172440859e-13 relative error = 6.362554449484492e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.500000000000085 y[1] (analytic) = 3.994344312392744 y[1] (numeric) = 3.99434431239246 absolute error = 2.842170943040401e-13 relative error = 7.115488102070616e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.600000000000101 y[1] (analytic) = 3.969375711588219 y[1] (numeric) = 3.969375711587909 absolute error = 3.099742684753437e-13 relative error = 7.809144082037964e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.700000000000117 y[1] (analytic) = 3.924729759662557 y[1] (numeric) = 3.924729759662224 absolute error = 3.326228181776969e-13 relative error = 8.475050221197786e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.800000000000132 y[1] (analytic) = 3.86085254420941 y[1] (numeric) = 3.860852544209059 absolute error = 3.512745649913995e-13 relative error = 9.098367807862765e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.900000000000148 y[1] (analytic) = 3.778382305250587 y[1] (numeric) = 3.778382305250221 absolute error = 3.663735981263017e-13 relative error = 9.6965729914936e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 10.00000000000016 y[1] (analytic) = 3.678143058152727 y[1] (numeric) = 3.67814305815235 absolute error = 3.774758283725532e-13 relative error = 1.026267392008762e-11 % Correct digits = 12 h = 0.005 Finished! diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ; Iterations = 1980 Total Elapsed Time = 1 Minutes 53 Seconds Elapsed Time(since restart) = 1 Minutes 52 Seconds Time to Timeout = 8 Minutes 7 Seconds Percent Done = 100.1 %