##############ECHO OF PROBLEM################# ##############temp/cospostode.ode################# diff ( y , x , 1 ) = cos ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits = 32; max_terms = 30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start = 1.6; 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(1.0 + sin(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 1.6 y[1] (analytic) = 1.999573603041505 y[1] (numeric) = 1.999573603041505 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999998 y[1] (analytic) = 1.991008194880942 y[1] (numeric) = 1.991008194880926 absolute error = 1.576516694967722e-14 relative error = 7.918182853396012e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999996 y[1] (analytic) = 1.972699452068077 y[1] (numeric) = 1.972699452068045 absolute error = 3.108624468950438e-14 relative error = 1.575822645305404e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999994 y[1] (analytic) = 1.944671817861837 y[1] (numeric) = 1.944671817861791 absolute error = 4.662936703425657e-14 relative error = 2.397801346528767e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999991 y[1] (analytic) = 1.907205335118509 y[1] (numeric) = 1.907205335118447 absolute error = 6.17284001691587e-14 relative error = 3.236589109337987e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999989 y[1] (analytic) = 1.86067435654889 y[1] (numeric) = 1.860674356548814 absolute error = 7.616129948928574e-14 relative error = 4.093209498009468e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999987 y[1] (analytic) = 1.805543804309752 y[1] (numeric) = 1.805543804309662 absolute error = 9.015010959956271e-14 relative error = 4.992961643155841e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999985 y[1] (analytic) = 1.742364524655331 y[1] (numeric) = 1.742364524655228 absolute error = 1.034727858950646e-13 relative error = 5.938641680938334e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999983 y[1] (analytic) = 1.67176778406364 y[1] (numeric) = 1.671767784063525 absolute error = 1.156852391659413e-13 relative error = 6.919934710354332e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999981 y[1] (analytic) = 1.594458961830492 y[1] (numeric) = 1.594458961830364 absolute error = 1.27897692436818e-13 relative error = 8.021385027682819e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999979 y[1] (analytic) = 1.511210502152741 y[1] (numeric) = 1.511210502152603 absolute error = 1.378896996584444e-13 relative error = 9.124453506776094e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999977 y[1] (analytic) = 1.422854196121205 y[1] (numeric) = 1.422854196121058 absolute error = 1.472155730652958e-13 relative error = 1.034649744623273e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999974 y[1] (analytic) = 1.33027287073904 y[1] (numeric) = 1.330272870738886 absolute error = 1.543210004228968e-13 relative error = 1.160070266915711e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.904999999999972 y[1] (analytic) = 1.234391568006146 y[1] (numeric) = 1.234391568005985 absolute error = 1.609823385706477e-13 relative error = 1.304143213086547e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.00499999999997 y[1] (analytic) = 1.136168302205287 y[1] (numeric) = 1.13616830220512 absolute error = 1.663114090888484e-13 relative error = 1.463792017133732e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999968 y[1] (analytic) = 1.036584487740048 y[1] (numeric) = 1.036584487739879 absolute error = 1.694200335577989e-13 relative error = 1.634406414157006e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999966 y[1] (analytic) = 0.9366351331665349 y[1] (numeric) = 0.9366351331663633 absolute error = 1.716404796070492e-13 relative error = 1.832522329445134e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999964 y[1] (analytic) = 0.8373188993967814 y[1] (numeric) = 0.8373188993966093 absolute error = 1.720845688168993e-13 relative error = 2.055185532547658e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.404999999999962 y[1] (analytic) = 0.7396281214090329 y[1] (numeric) = 0.739628121408862 absolute error = 1.708633234898116e-13 relative error = 2.310124757889241e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999959 y[1] (analytic) = 0.6445388931646652 y[1] (numeric) = 0.6445388931644968 absolute error = 1.684208328356362e-13 relative error = 2.613043753010705e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999957 y[1] (analytic) = 0.5530013147999759 y[1] (numeric) = 0.5530013147998116 absolute error = 1.643130076445232e-13 relative error = 2.971295062905162e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999955 y[1] (analytic) = 0.4659299995396847 y[1] (numeric) = 0.4659299995395261 absolute error = 1.585953590677036e-13 relative error = 3.403845196153667e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999953 y[1] (analytic) = 0.3841949351839222 y[1] (numeric) = 0.3841949351837706 absolute error = 1.516564651637964e-13 relative error = 3.947383249370407e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999951 y[1] (analytic) = 0.3086127914777109 y[1] (numeric) = 0.3086127914775675 absolute error = 1.43385303630339e-13 relative error = 4.646123154642303e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999949 y[1] (analytic) = 0.239938760216828 y[1] (numeric) = 0.2399387602166946 absolute error = 1.334765631355594e-13 relative error = 5.562942936561782e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999947 y[1] (analytic) = 0.1788590096210163 y[1] (numeric) = 0.1788590096208935 absolute error = 1.227629109479267e-13 relative error = 6.86366939009942e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999945 y[1] (analytic) = 0.1259838283679474 y[1] (numeric) = 0.1259838283678364 absolute error = 1.110223024625157e-13 relative error = 8.81242488823762e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.304999999999943 y[1] (analytic) = 0.08184152779049099 y[1] (numeric) = 0.08184152779039262 absolute error = 9.836575998178887e-14 relative error = 1.201905226324695e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999941 y[1] (analytic) = 0.04687316316451234 y[1] (numeric) = 0.04687316316442745 absolute error = 8.488348912649712e-14 relative error = 1.810918730374109e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999939 y[1] (analytic) = 0.02142812683034967 y[1] (numeric) = 0.02142812683027893 absolute error = 7.074202335033419e-14 relative error = 3.301362919419485e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999936 y[1] (analytic) = 0.005760657180043207 y[1] (numeric) = 0.005760657179987133 absolute error = 5.60740689992123e-14 relative error = 9.733970838166024e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999934 y[1] (analytic) = 2.729839136188488e-05 y[1] (numeric) = 2.729839132085176e-05 absolute error = 4.103312199570108e-14 relative error = 1.503133333086915e-07 % Correct digits = 8 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.804999999999932 y[1] (analytic) = 0.004285336290125765 y[1] (numeric) = 0.0042853362901 absolute error = 2.576498042694553e-14 relative error = 6.012359050166722e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.90499999999993 y[1] (analytic) = 0.0184922259691706 y[1] (numeric) = 0.01849222596916017 absolute error = 1.042221864366866e-14 relative error = 5.636000047286957e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999928 y[1] (analytic) = 0.04250601688299672 y[1] (numeric) = 0.04250601688300157 absolute error = 4.843347944927245e-15 relative error = 1.139449964991823e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.104999999999926 y[1] (analytic) = 0.07608677117069712 y[1] (numeric) = 0.07608677117071699 absolute error = 1.98729921407903e-14 relative error = 2.611885329738355e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.204999999999924 y[1] (analytic) = 0.1188989610357506 y[1] (numeric) = 0.1188989610357852 absolute error = 3.451405827803455e-14 relative error = 2.902805708088302e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.304999999999922 y[1] (analytic) = 0.1705148212288541 y[1] (numeric) = 0.1705148212289027 absolute error = 4.862776847858186e-14 relative error = 2.851820629323287e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.404999999999919 y[1] (analytic) = 0.230418623136893 y[1] (numeric) = 0.2304186231369551 absolute error = 6.208922265216188e-14 relative error = 2.694626927584508e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.504999999999917 y[1] (analytic) = 0.2980118277727665 y[1] (numeric) = 0.2980118277728414 absolute error = 7.482903185973555e-14 relative error = 2.510941677012651e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.604999999999915 y[1] (analytic) = 0.3726190661790958 y[1] (numeric) = 0.3726190661791823 absolute error = 8.648637361829969e-14 relative error = 2.321039943155535e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.704999999999913 y[1] (analytic) = 0.453494887491599 y[1] (numeric) = 0.4534948874916962 absolute error = 9.720002580593246e-14 relative error = 2.143354390246198e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.804999999999911 y[1] (analytic) = 0.5398312072377137 y[1] (numeric) = 0.5398312072378204 absolute error = 1.066924326664775e-13 relative error = 1.976403572746689e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.904999999999909 y[1] (analytic) = 0.6307653814495299 y[1] (numeric) = 0.6307653814496449 absolute error = 1.150191053511662e-13 relative error = 1.823484749382515e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.004999999999907 y[1] (analytic) = 0.7253888259171646 y[1] (numeric) = 0.7253888259172866 absolute error = 1.220135104063047e-13 relative error = 1.682042872000871e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.104999999999905 y[1] (analytic) = 0.8227560944618495 y[1] (numeric) = 0.8227560944619768 absolute error = 1.273425809245055e-13 relative error = 1.547756154973219e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.204999999999902 y[1] (analytic) = 0.9218943255216259 y[1] (numeric) = 0.9218943255217574 absolute error = 1.315614284180811e-13 relative error = 1.427077103914714e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.3049999999999 y[1] (analytic) = 1.021812962662487 y[1] (numeric) = 1.021812962662621 absolute error = 1.343369859796439e-13 relative error = 1.314692520924855e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.404999999999898 y[1] (analytic) = 1.121513651890831 y[1] (numeric) = 1.121513651890966 absolute error = 1.352251643993441e-13 relative error = 1.205738014614083e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.504999999999896 y[1] (analytic) = 1.220000216876555 y[1] (numeric) = 1.22000021687669 absolute error = 1.35003119794419e-13 relative error = 1.106582752419947e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.604999999999894 y[1] (analytic) = 1.316288612417652 y[1] (numeric) = 1.316288612417785 absolute error = 1.330047183500938e-13 relative error = 1.010452548896564e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.704999999999892 y[1] (analytic) = 1.409416756694586 y[1] (numeric) = 1.409416756694716 absolute error = 1.294520046712933e-13 relative error = 9.184792507709974e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.80499999999989 y[1] (analytic) = 1.498454144073815 y[1] (numeric) = 1.49845414407394 absolute error = 1.247890679678676e-13 relative error = 8.327853639124802e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.904999999999887 y[1] (analytic) = 1.582511142412492 y[1] (numeric) = 1.58251114241261 absolute error = 1.179056852151916e-13 relative error = 7.450543762709174e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.004999999999885 y[1] (analytic) = 1.660747881968767 y[1] (numeric) = 1.660747881968878 absolute error = 1.103561686477406e-13 relative error = 6.644968200526416e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.104999999999883 y[1] (analytic) = 1.732382647102622 y[1] (numeric) = 1.732382647102723 absolute error = 1.014743844507393e-13 relative error = 5.85750409243901e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.204999999999881 y[1] (analytic) = 1.796699686920143 y[1] (numeric) = 1.796699686920234 absolute error = 9.103828801926284e-14 relative error = 5.066972999551103e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.304999999999879 y[1] (analytic) = 1.853056366819861 y[1] (numeric) = 1.853056366819941 absolute error = 7.971401316808624e-14 relative error = 4.301758683406276e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.404999999999877 y[1] (analytic) = 1.90088958948526 y[1] (numeric) = 1.900889589485328 absolute error = 6.750155989720952e-14 relative error = 3.551051058966986e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.504999999999875 y[1] (analytic) = 1.939721421167028 y[1] (numeric) = 1.939721421167083 absolute error = 5.506706202140776e-14 relative error = 2.838916012397121e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.604999999999873 y[1] (analytic) = 1.969163867039099 y[1] (numeric) = 1.969163867039139 absolute error = 4.085620730620576e-14 relative error = 2.074799766036665e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.70499999999987 y[1] (analytic) = 1.988922747914696 y[1] (numeric) = 1.988922747914722 absolute error = 2.597921877622866e-14 relative error = 1.306195467041986e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.804999999999868 y[1] (analytic) = 1.998800639587528 y[1] (numeric) = 1.99880063958754 absolute error = 1.13242748511766e-14 relative error = 5.665534934746403e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.904999999999866 y[1] (analytic) = 1.998698845429199 y[1] (numeric) = 1.998698845429195 absolute error = 3.552713678800501e-15 relative error = 1.777513249144643e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.004999999999864 y[1] (analytic) = 1.988618382533288 y[1] (numeric) = 1.988618382533269 absolute error = 1.865174681370263e-14 relative error = 9.379248918509087e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.10499999999988 y[1] (analytic) = 1.968659971552889 y[1] (numeric) = 1.968659971552858 absolute error = 3.108624468950438e-14 relative error = 1.579056065481099e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.204999999999895 y[1] (analytic) = 1.939023030333147 y[1] (numeric) = 1.939023030333106 absolute error = 4.107825191113079e-14 relative error = 2.118502527743215e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.304999999999911 y[1] (analytic) = 1.900003681394058 y[1] (numeric) = 1.900003681394009 absolute error = 4.884981308350689e-14 relative error = 2.571037812288087e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.404999999999927 y[1] (analytic) = 1.85199179317214 y[1] (numeric) = 1.851991793172085 absolute error = 5.484501741648273e-14 relative error = 2.961407151947621e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.504999999999942 y[1] (analytic) = 1.795467084583886 y[1] (numeric) = 1.795467084583828 absolute error = 5.795364188543317e-14 relative error = 3.227775233699947e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.604999999999958 y[1] (analytic) = 1.730994331832927 y[1] (numeric) = 1.730994331832867 absolute error = 5.972999872483342e-14 relative error = 3.450617811185212e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.704999999999973 y[1] (analytic) = 1.65921772535289 y[1] (numeric) = 1.659217725352831 absolute error = 5.906386491005833e-14 relative error = 3.559741678717683e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.799999999999988 y[1] (analytic) = 1.584917192891772 y[1] (numeric) = 1.584917192891715 absolute error = 5.639932965095795e-14 relative error = 3.558503239406102e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.900000000000004 y[1] (analytic) = 1.501020856457882 y[1] (numeric) = 1.50102085645783 absolute error = 5.151434834260726e-14 relative error = 3.431954201100919e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.00000000000002 y[1] (analytic) = 1.412118485241739 y[1] (numeric) = 1.412118485241694 absolute error = 4.507505479978136e-14 relative error = 3.192016482389225e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.100000000000035 y[1] (analytic) = 1.319098362349318 y[1] (numeric) = 1.319098362349282 absolute error = 3.61932706027801e-14 relative error = 2.743788608631109e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.200000000000051 y[1] (analytic) = 1.222889914100197 y[1] (numeric) = 1.222889914100172 absolute error = 2.531308496145357e-14 relative error = 2.069939793401513e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.300000000000066 y[1] (analytic) = 1.124454423506996 y[1] (numeric) = 1.124454423506984 absolute error = 1.265654248072678e-14 relative error = 1.125571852103442e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.400000000000082 y[1] (analytic) = 1.024775425453276 y[1] (numeric) = 1.024775425453277 absolute error = 1.110223024625157e-15 relative error = 1.083381780094976e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.500000000000098 y[1] (analytic) = 0.9248488795380932 y[1] (numeric) = 0.9248488795381105 absolute error = 1.720845688168993e-14 relative error = 1.860677702316569e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.600000000000113 y[1] (analytic) = 0.8256732187769085 y[1] (numeric) = 0.8256732187769429 absolute error = 3.441691376337985e-14 relative error = 4.168345657905986e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.700000000000129 y[1] (analytic) = 0.7282393735889328 y[1] (numeric) = 0.7282393735889859 absolute error = 5.3179682879545e-14 relative error = 7.30250036021304e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.800000000000145 y[1] (analytic) = 0.6335208707479377 y[1] (numeric) = 0.6335208707480103 absolute error = 7.260858581048524e-14 relative error = 1.146111977727951e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.90000000000016 y[1] (analytic) = 0.5424641062245364 y[1] (numeric) = 0.5424641062246293 absolute error = 9.281464485866309e-14 relative error = 1.710982234467792e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 10.00000000000018 y[1] (analytic) = 0.4559788891104826 y[1] (numeric) = 0.4559788891105968 absolute error = 1.141309269314661e-13 relative error = 2.50298708245268e-11 % Correct digits = 12 h = 0.005 Finished! diff ( y , x , 1 ) = cos ( x ) ; Iterations = 1680 Total Elapsed Time = 36 Seconds Elapsed Time(since restart) = 36 Seconds Time to Timeout = 9 Minutes 24 Seconds Percent Done = 100.1 %