##############ECHO OF PROBLEM################# ##############temp/subpostode.ode################# diff ( y , x , 1 ) = sin ( x ) - cos ( x ); ! // BEGIN FIRST INPUT BLOCK Digits = 32; max_terms = 30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start = 0.0; 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) - sin(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y[1] (analytic) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1 y[1] (analytic) = 0.9051624180751461 y[1] (numeric) = 0.9051624180751618 absolute error = 1.576516694967722e-14 relative error = 1.741694820163027e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2000000000000001 y[1] (analytic) = 0.821264091363697 y[1] (numeric) = 0.82126409136373 absolute error = 3.297362383136715e-14 relative error = 4.014984239310272e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.7491433042130543 y[1] (numeric) = 0.7491433042131059 absolute error = 5.162537064506978e-14 relative error = 6.89125436411665e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.6895206636884644 y[1] (numeric) = 0.6895206636885356 absolute error = 7.116529587847253e-14 relative error = 1.032098088225331e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.6429918995054241 y[1] (numeric) = 0.6429918995055161 absolute error = 9.192646643896296e-14 relative error = 1.429667566724727e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.6100219116952863 y[1] (numeric) = 0.6100219116953991 absolute error = 1.127986593019159e-13 relative error = 1.84909192832831e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.5909401254778204 y[1] (numeric) = 0.5909401254779548 absolute error = 1.344480082821065e-13 relative error = 2.275154495108873e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 0.5859371997533118 y[1] (numeric) = 0.5859371997534679 absolute error = 1.56097357262297e-13 relative error = 2.664062929065031e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 0.5950631221018522 y[1] (numeric) = 0.5950631221020298 absolute error = 1.77635683940025e-13 relative error = 2.985156991624505e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 0.6182267093239641 y[1] (numeric) = 0.6182267093241628 absolute error = 1.98729921407903e-13 relative error = 3.214515296908084e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 0.6574013755977741 y[1] (numeric) = 0.6574013755979955 absolute error = 2.213784711102562e-13 relative error = 3.36747806329059e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 0.7084677342720017 y[1] (numeric) = 0.7084677342722443 absolute error = 2.425837308805967e-13 relative error = 3.424061804732263e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 0.7724386564215769 y[1] (numeric) = 0.77243865642184 absolute error = 2.630118345336996e-13 relative error = 3.404954326756979e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 0.8486749657383563 y[1] (numeric) = 0.8486749657386392 absolute error = 2.828848266744899e-13 relative error = 3.333252871767898e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 0.9364149342200202 y[1] (numeric) = 0.9364149342203221 absolute error = 3.018696403955801e-13 relative error = 3.223673922362421e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 1.034781893104477 y[1] (numeric) = 1.034781893104797 absolute error = 3.19300141882195e-13 relative error = 3.085675773899116e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 1.142792992254348 y[1] (numeric) = 1.142792992254683 absolute error = 3.352873534367973e-13 relative error = 2.933929029223285e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 1.259369020470649 y[1] (numeric) = 1.259369020470999 absolute error = 3.499422973618493e-13 relative error = 2.778711336182222e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 1.383345188614354 y[1] (numeric) = 1.383345188614718 absolute error = 3.632649736573512e-13 relative error = 2.625989352818152e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 1.513482767794446 y[1] (numeric) = 1.51348276779482 absolute error = 3.743672039036028e-13 relative error = 2.473547845207099e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 1.648481466337519 y[1] (numeric) = 1.648481466337903 absolute error = 3.841371665203042e-13 relative error = 2.330248621925688e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 1.78699242187237 y[1] (numeric) = 1.786992421872761 absolute error = 3.910205492729801e-13 relative error = 2.188148894684611e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 1.927631678716927 y[1] (numeric) = 1.927631678717324 absolute error = 3.961275751862559e-13 relative error = 2.054996188119956e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 2.068994015905959 y[1] (numeric) = 2.068994015906358 absolute error = 3.992361996552063e-13 relative error = 1.929615052464959e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 2.209666987694448 y[1] (numeric) = 2.209666987694847 absolute error = 3.992361996552063e-13 relative error = 1.80677089298314e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 2.348245036248585 y[1] (numeric) = 2.348245036248984 absolute error = 3.987921104453562e-13 relative error = 1.698255949823884e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 2.483343535515031 y[1] (numeric) = 2.483343535515427 absolute error = 3.961275751862559e-13 relative error = 1.595138044821903e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 2.613612625946741 y[1] (numeric) = 2.613612625947132 absolute error = 3.90354415458205e-13 relative error = 1.493543502135498e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 2.737750701853359 y[1] (numeric) = 2.737750701853742 absolute error = 3.82804898890754e-13 relative error = 1.398246007686561e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 2.854517416615018 y[1] (numeric) = 2.85451741661539 absolute error = 3.725908470642025e-13 relative error = 1.305267380382752e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 2.962746075815762 y[1] (numeric) = 2.962746075816123 absolute error = 3.606004383982508e-13 relative error = 1.217115571738503e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 3.061355294468497 y[1] (numeric) = 3.061355294468845 absolute error = 3.47277762102749e-13 relative error = 1.134392217493469e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 3.14935980185632 y[1] (numeric) = 3.149359801856653 absolute error = 3.33066907387547e-13 relative error = 1.057570199477456e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 3.225880286031832 y[1] (numeric) = 3.225880286032149 absolute error = 3.170796958329447e-13 relative error = 9.82924559246387e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 3.290152179611461 y[1] (numeric) = 3.29015217961176 absolute error = 2.988720382290921e-13 relative error = 9.083836306452741e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 3.341533299080024 y[1] (numeric) = 3.341533299080303 absolute error = 2.793321129956894e-13 relative error = 8.359399353362537e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 3.37951026127613 y[1] (numeric) = 3.37951026127639 absolute error = 2.597921877622866e-13 relative error = 7.687273234204859e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 3.403703612947031 y[1] (numeric) = 3.40370361294727 absolute error = 2.389199948993337e-13 relative error = 7.019412442097726e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 3.413871622120089 y[1] (numeric) = 3.413871622120307 absolute error = 2.180478020363807e-13 relative error = 6.387111941279394e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 3.409912693408744 y[1] (numeric) = 3.409912693408941 absolute error = 1.967315199635777e-13 relative error = 5.769400499427851e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 3.391866383120033 y[1] (numeric) = 3.391866383120209 absolute error = 1.754152378907747e-13 relative error = 5.171643516494235e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 3.359913004021043 y[1] (numeric) = 3.359913004021196 absolute error = 1.532107773982716e-13 relative error = 4.559962630428631e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 3.314371823713349 y[1] (numeric) = 3.31437182371348 absolute error = 1.314504061156185e-13 relative error = 3.966073002887902e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 3.255697874616671 y[1] (numeric) = 3.255697874616782 absolute error = 1.105782132526656e-13 relative error = 3.396451928626368e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 3.184477407435356 y[1] (numeric) = 3.184477407435447 absolute error = 9.103828801926284e-14 relative error = 2.858814064960857e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 3.101422033535122 y[1] (numeric) = 3.101422033535194 absolute error = 7.194245199571014e-14 relative error = 2.319660182258631e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 3.007361614757524 y[1] (numeric) = 3.007361614757578 absolute error = 5.417888360170764e-14 relative error = 1.801542033915863e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 2.903235971714747 y[1] (numeric) = 2.903235971714784 absolute error = 3.68594044175552e-14 relative error = 1.269597262388038e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 2.790085493412714 y[1] (numeric) = 2.790085493412735 absolute error = 2.176037128265307e-14 relative error = 7.799177241711224e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 2.669040742028041 y[1] (numeric) = 2.66904074202805 absolute error = 8.881784197001252e-15 relative error = 3.32770648913082e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.104999999999913 y[1] (analytic) = 2.541311156704491 y[1] (numeric) = 2.541311156704488 absolute error = 3.108624468950438e-15 relative error = 1.223236462307758e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.204999999999911 y[1] (analytic) = 2.408172969236828 y[1] (numeric) = 2.408172969236815 absolute error = 1.332267629550188e-14 relative error = 5.5322754908772e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.304999999999909 y[1] (analytic) = 2.270956452384597 y[1] (numeric) = 2.270956452384575 absolute error = 2.220446049250313e-14 relative error = 9.777580925951944e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.404999999999907 y[1] (analytic) = 2.131032628226433 y[1] (numeric) = 2.131032628226405 absolute error = 2.753353101070388e-14 relative error = 1.292027660487717e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.504999999999905 y[1] (analytic) = 1.989799569360659 y[1] (numeric) = 1.989799569360627 absolute error = 3.197442310920451e-14 relative error = 1.606916777023838e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.604999999999903 y[1] (analytic) = 1.84866842982602 y[1] (numeric) = 1.848668429825986 absolute error = 3.375077994860476e-14 relative error = 1.825680549528348e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.704999999999901 y[1] (analytic) = 1.709049345316992 y[1] (numeric) = 1.709049345316959 absolute error = 3.352873534367973e-14 relative error = 1.961835416604712e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.804999999999898 y[1] (analytic) = 1.572337343574058 y[1] (numeric) = 1.572337343574027 absolute error = 3.086420008457935e-14 relative error = 1.962950267047807e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.904999999999896 y[1] (analytic) = 1.439898405727652 y[1] (numeric) = 1.439898405727625 absolute error = 2.664535259100376e-14 relative error = 1.850502263563418e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.004999999999894 y[1] (analytic) = 1.313055817866243 y[1] (numeric) = 1.313055817866223 absolute error = 1.998401444325282e-14 relative error = 1.521947062062256e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.104999999999892 y[1] (analytic) = 1.193076949199159 y[1] (numeric) = 1.193076949199148 absolute error = 1.06581410364015e-14 relative error = 8.933322401003284e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.20499999999989 y[1] (analytic) = 1.081160588922379 y[1] (numeric) = 1.081160588922378 absolute error = 2.220446049250313e-16 relative error = 2.053761552170053e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.304999999999888 y[1] (analytic) = 0.9784249683131574 y[1] (numeric) = 0.9784249683131697 absolute error = 1.232347557333924e-14 relative error = 1.259521779639924e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.404999999999886 y[1] (analytic) = 0.8858965877327423 y[1] (numeric) = 0.8858965877327689 absolute error = 2.664535259100376e-14 relative error = 3.007727195247098e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.504999999999884 y[1] (analytic) = 0.8044999601740759 y[1] (numeric) = 0.8044999601741186 absolute error = 4.274358644806853e-14 relative error = 5.313062593417627e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.604999999999881 y[1] (analytic) = 0.7350483738335769 y[1] (numeric) = 0.7350483738336369 absolute error = 5.995204332975845e-14 relative error = 8.156203790654499e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.704999999999879 y[1] (analytic) = 0.6782357660043175 y[1] (numeric) = 0.6782357660043956 absolute error = 7.815970093361102e-14 relative error = 1.152397217181163e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.804999999999877 y[1] (analytic) = 0.6346297894839761 y[1] (numeric) = 0.6346297894840738 absolute error = 9.769962616701378e-14 relative error = 1.539474316931361e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.904999999999875 y[1] (analytic) = 0.6046661407757246 y[1] (numeric) = 0.6046661407758424 absolute error = 1.177946629127291e-13 relative error = 1.948094245224491e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.004999999999873 y[1] (analytic) = 0.5886442067527901 y[1] (numeric) = 0.5886442067529291 absolute error = 1.389999226830696e-13 relative error = 2.361357184671057e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.104999999999871 y[1] (analytic) = 0.5867240732837831 y[1] (numeric) = 0.5867240732839434 absolute error = 1.603162047558726e-13 relative error = 2.732395210215481e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.204999999999869 y[1] (analytic) = 0.5989249257076138 y[1] (numeric) = 0.5989249257077959 absolute error = 1.820765760385257e-13 relative error = 3.040056745399385e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.304999999999866 y[1] (analytic) = 0.6251248571399288 y[1] (numeric) = 0.6251248571401328 absolute error = 2.039479696236413e-13 relative error = 3.262515756560121e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.404999999999864 y[1] (analytic) = 0.6650620865264029 y[1] (numeric) = 0.665062086526628 absolute error = 2.251532293939817e-13 relative error = 3.385446771893878e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.504999999999862 y[1] (analytic) = 0.7183375742724984 y[1] (numeric) = 0.7183375742727446 absolute error = 2.461364445593972e-13 relative error = 3.426473198324251e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.60499999999986 y[1] (analytic) = 0.784419009315192 y[1] (numeric) = 0.7844190093154587 absolute error = 2.666755705149626e-13 relative error = 3.399657164705555e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.704999999999858 y[1] (analytic) = 0.8626461277991549 y[1] (numeric) = 0.8626461277994412 absolute error = 2.862154957483654e-13 relative error = 3.317878403727134e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.804999999999856 y[1] (analytic) = 0.9522373102149432 y[1] (numeric) = 0.952237310215248 absolute error = 3.04867242562068e-13 relative error = 3.201588924227848e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.904999999999854 y[1] (analytic) = 1.052297391082765 y[1] (numeric) = 1.052297391083088 absolute error = 3.224087663511455e-13 relative error = 3.063855988651666e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.004999999999852 y[1] (analytic) = 1.161826603150056 y[1] (numeric) = 1.161826603150394 absolute error = 3.379518886958977e-13 relative error = 2.908797989128584e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.104999999999867 y[1] (analytic) = 1.279730566735404 y[1] (numeric) = 1.279730566735736 absolute error = 3.319566843629218e-13 relative error = 2.593957611012951e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.204999999999883 y[1] (analytic) = 1.404831224408514 y[1] (numeric) = 1.404831224408836 absolute error = 3.217426325363704e-13 relative error = 2.290258266944742e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.304999999999898 y[1] (analytic) = 1.535878611750696 y[1] (numeric) = 1.535878611751005 absolute error = 3.093081346605686e-13 relative error = 2.013883989881198e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.404999999999914 y[1] (analytic) = 1.671563346586132 y[1] (numeric) = 1.671563346586427 absolute error = 2.944311461305915e-13 relative error = 1.761411834806705e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.50499999999993 y[1] (analytic) = 1.810529711895758 y[1] (numeric) = 1.810529711896034 absolute error = 2.76445533131664e-13 relative error = 1.526876534062538e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.604999999999945 y[1] (analytic) = 1.951389201693571 y[1] (numeric) = 1.951389201693828 absolute error = 2.569056078982612e-13 relative error = 1.316526747587298e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.704999999999961 y[1] (analytic) = 2.092734394519469 y[1] (numeric) = 2.092734394519704 absolute error = 2.344791028008331e-13 relative error = 1.120443680836401e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.804999999999977 y[1] (analytic) = 2.233153015929243 y[1] (numeric) = 2.233153015929453 absolute error = 2.100541962590796e-13 relative error = 9.406171218933396e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.899999999999991 y[1] (analytic) = 2.364414352783216 y[1] (numeric) = 2.364414352783399 absolute error = 1.838529328779259e-13 relative error = 7.775833904133923e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.000000000000007 y[1] (analytic) = 2.49901177664293 y[1] (numeric) = 2.499011776643086 absolute error = 1.55875312657372e-13 relative error = 6.23747811491983e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.100000000000023 y[1] (analytic) = 2.628623239781789 y[1] (numeric) = 2.628623239781916 absolute error = 1.270095140171179e-13 relative error = 4.831788447083098e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.200000000000038 y[1] (analytic) = 2.751953707303963 y[1] (numeric) = 2.751953707304059 absolute error = 9.592326932761353e-14 relative error = 3.485642548165817e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.300000000000054 y[1] (analytic) = 2.867770901945601 y[1] (numeric) = 2.867770901945667 absolute error = 6.52811138479592e-14 relative error = 2.276371303009947e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.40000000000007 y[1] (analytic) = 2.97491761658192 y[1] (numeric) = 2.974917616581954 absolute error = 3.375077994860476e-14 relative error = 1.134511415055025e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.500000000000085 y[1] (analytic) = 3.072323276658266 y[1] (numeric) = 3.07232327665827 absolute error = 3.996802888650564e-15 relative error = 1.300905708398578e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.600000000000101 y[1] (analytic) = 3.159014637017189 y[1] (numeric) = 3.159014637017162 absolute error = 2.664535259100376e-14 relative error = 8.434703745520751e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.700000000000117 y[1] (analytic) = 3.234125506242334 y[1] (numeric) = 3.234125506242278 absolute error = 5.595524044110789e-14 relative error = 1.730150556405622e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.800000000000132 y[1] (analytic) = 3.296905401356756 y[1] (numeric) = 3.296905401356672 absolute error = 8.43769498715119e-14 relative error = 2.559277249410576e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.900000000000148 y[1] (analytic) = 3.346727046400746 y[1] (numeric) = 3.346727046400634 absolute error = 1.119104808822158e-13 relative error = 3.343878342351536e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 10.00000000000016 y[1] (analytic) = 3.383092639965871 y[1] (numeric) = 3.383092639965733 absolute error = 1.376676550535194e-13 relative error = 4.069284223174812e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = sin ( x ) - cos ( x ); Iterations = 2000 Total Elapsed Time = 1 Minutes 45 Seconds Elapsed Time(since restart) = 1 Minutes 44 Seconds Time to Timeout = 8 Minutes 15 Seconds Percent Done = 100.1 %