##############ECHO OF PROBLEM################# ##############temp/mult2postode.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 = 0.1; 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 - expt(cos(x),2)/2.0); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 1.504983355539689 y[1] (numeric) = 1.504983355539689 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) = 1.519734751499279 y[1] (numeric) = 1.51973475149951 absolute error = 2.315925229368077e-13 relative error = 1.523900948559164e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 1.543666096272581 y[1] (numeric) = 1.543666096273025 absolute error = 4.443112544549876e-13 relative error = 2.878286020065127e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 1.575823322663209 y[1] (numeric) = 1.575823322663839 absolute error = 6.303846333821639e-13 relative error = 4.000350955060031e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 1.614924423532965 y[1] (numeric) = 1.614924423533747 absolute error = 7.818190539410352e-13 relative error = 4.841211406231953e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 1.659410561380832 y[1] (numeric) = 1.659410561381724 absolute error = 8.923972671937008e-13 relative error = 5.377796718680141e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 1.70750821427494 y[1] (numeric) = 1.707508214275898 absolute error = 9.5767838104166e-13 relative error = 5.608631179840733e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 1.757299880575323 y[1] (numeric) = 1.757299880576298 absolute error = 9.756639940405876e-13 relative error = 5.552063167051288e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 1.806800523673272 y[1] (numeric) = 1.806800523674218 absolute error = 9.454659277707833e-13 relative error = 5.232818539639488e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 1.854036709136786 y[1] (numeric) = 1.854036709137654 absolute error = 8.675282714420973e-13 relative error = 4.679132118403452e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 1.899139130433539 y[1] (numeric) = 1.899139130434279 absolute error = 7.394085344003543e-13 relative error = 3.893387917459004e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 1.936027841347897 y[1] (numeric) = 1.936027841348475 absolute error = 5.777600620149315e-13 relative error = 2.984254924829411e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 1.965500209272514 y[1] (numeric) = 1.965500209272897 absolute error = 3.825828542858289e-13 relative error = 1.946491038163936e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 1.986381263903673 y[1] (numeric) = 1.986381263903836 absolute error = 1.63202784619898e-13 relative error = 8.216085581635467e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 1.997838543487206 y[1] (numeric) = 1.997838543487134 absolute error = 7.238654120556021e-14 relative error = 3.623242801153004e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 1.999415282441655 y[1] (numeric) = 1.99941528244134 absolute error = 3.144151605738443e-13 relative error = 1.572535547442077e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 1.991048621160593 y[1] (numeric) = 1.99104862116004 absolute error = 5.535572000781031e-13 relative error = 2.780229443896912e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 1.973072112026771 y[1] (numeric) = 1.97307211202599 absolute error = 7.807088309164101e-13 relative error = 3.956818537739371e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 1.946202421731198 y[1] (numeric) = 1.946202421730212 absolute error = 9.85656001262214e-13 relative error = 5.064509170559182e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 1.911510760033748 y[1] (numeric) = 1.911510760032586 absolute error = 1.161515328362839e-12 relative error = 6.07642579182935e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 1.870380174010428 y[1] (numeric) = 1.870380174009128 absolute error = 1.300515251045908e-12 relative error = 6.953213411460473e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 1.82445041033092 y[1] (numeric) = 1.824450410329523 absolute error = 1.396882609583372e-12 relative error = 7.656456989313316e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 1.775552543733374 y[1] (numeric) = 1.775552543731926 absolute error = 1.447730824111204e-12 relative error = 8.153691813969786e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 1.725635977852893 y[1] (numeric) = 1.725635977851443 absolute error = 1.449729225555529e-12 relative error = 8.401130042266168e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 1.676690728650299 y[1] (numeric) = 1.676690728648895 absolute error = 1.403765992336048e-12 relative error = 8.372241632576153e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 1.630668088755634 y[1] (numeric) = 1.630668088754323 absolute error = 1.31161748129216e-12 relative error = 8.043436247612215e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 1.58940283558866 y[1] (numeric) = 1.589402835587483 absolute error = 1.176614361497741e-12 relative error = 7.402870657783642e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 1.554540084573107 y[1] (numeric) = 1.554540084572103 absolute error = 1.003863658866067e-12 relative error = 6.457624790947337e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 1.527469703576193 y[1] (numeric) = 1.527469703575392 absolute error = 8.009148899645879e-13 relative error = 5.243409333026008e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 1.509270903262737 y[1] (numeric) = 1.509270903262161 absolute error = 5.762057497804562e-13 relative error = 3.81777551355967e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 1.500669212371601 y[1] (numeric) = 1.500669212371264 absolute error = 3.377298440909726e-13 relative error = 2.250528239712715e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 1.502007553174411 y[1] (numeric) = 1.502007553174315 absolute error = 9.525713551283843e-14 relative error = 6.34198778238616e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 1.513232570246735 y[1] (numeric) = 1.513232570246877 absolute error = 1.4166445794217e-13 relative error = 9.361710865043788e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 1.533896757580492 y[1] (numeric) = 1.533896757580855 absolute error = 3.632649736573512e-13 relative error = 2.368249178845329e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 1.563176299236297 y[1] (numeric) = 1.563176299236857 absolute error = 5.606626274357041e-13 relative error = 3.58668838383502e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 1.59990391228527 y[1] (numeric) = 1.599903912285997 absolute error = 7.267519919196275e-13 relative error = 4.542472746888591e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 1.642615382695835 y[1] (numeric) = 1.642615382696689 absolute error = 8.535394613318203e-13 relative error = 5.196222258256248e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 1.689607938926561 y[1] (numeric) = 1.689607938927498 absolute error = 9.372502773885572e-13 relative error = 5.547146505384021e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 1.739008136054116 y[1] (numeric) = 1.739008136055089 absolute error = 9.736655925962623e-13 relative error = 5.598970886965207e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 1.78884654411036 y[1] (numeric) = 1.788846544111322 absolute error = 9.621192731401607e-13 relative error = 5.3784338086901e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 1.837136263040283 y[1] (numeric) = 1.837136263041186 absolute error = 9.023892744153272e-13 relative error = 4.911934365292861e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 1.881952134137169 y[1] (numeric) = 1.881952134137966 absolute error = 7.966960424710123e-13 relative error = 4.233349127321342e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 1.921507490045045 y[1] (numeric) = 1.921507490045695 absolute error = 6.494804694057166e-13 relative error = 3.380056922861597e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 1.954225383548008 y[1] (numeric) = 1.954225383548475 absolute error = 4.671818487622659e-13 relative error = 2.390624196652643e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 1.978801455479377 y[1] (numeric) = 1.978801455479634 absolute error = 2.569056078982612e-13 relative error = 1.298288957625738e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 1.994255935405528 y[1] (numeric) = 1.994255935405555 absolute error = 2.686739719592879e-14 relative error = 1.347239174216892e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 1.999972701981239 y[1] (numeric) = 1.999972701981025 absolute error = 2.138289545428051e-13 relative error = 1.069159365680237e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 1.995723845763435 y[1] (numeric) = 1.995723845762979 absolute error = 4.560796185160143e-13 relative error = 2.285284206450656e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 1.981678755241479 y[1] (numeric) = 1.98167875524079 absolute error = 6.894484982922222e-13 relative error = 3.479113334937119e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 1.958397363852636 y[1] (numeric) = 1.95839736385173 absolute error = 9.052758542793526e-13 relative error = 4.622534072954729e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.104999999999913 y[1] (analytic) = 1.926807827202898 y[1] (numeric) = 1.926807827201803 absolute error = 1.095123991490254e-12 relative error = 5.683618137881556e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.204999999999911 y[1] (analytic) = 1.888169520431945 y[1] (numeric) = 1.888169520430695 absolute error = 1.250111125727926e-12 relative error = 6.620756834597912e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.304999999999909 y[1] (analytic) = 1.844022830900506 y[1] (numeric) = 1.844022830899141 absolute error = 1.364686141869242e-12 relative error = 7.400592438450532e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.404999999999907 y[1] (analytic) = 1.796127747807264 y[1] (numeric) = 1.796127747805829 absolute error = 1.434852237025552e-12 relative error = 7.988586773837431e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.504999999999905 y[1] (analytic) = 1.746393696973472 y[1] (numeric) = 1.746393696972015 absolute error = 1.45683465291313e-12 relative error = 8.341960094323794e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.604999999999903 y[1] (analytic) = 1.696803418061001 y[1] (numeric) = 1.69680341805957 absolute error = 1.430855434136902e-12 relative error = 8.432652945572165e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.704999999999901 y[1] (analytic) = 1.649333918998916 y[1] (numeric) = 1.649333918997558 absolute error = 1.357580714511641e-12 relative error = 8.231084675295118e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.804999999999898 y[1] (analytic) = 1.605877658916155 y[1] (numeric) = 1.605877658914916 absolute error = 1.239452984691525e-12 relative error = 7.718227959706849e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.904999999999896 y[1] (analytic) = 1.56816710176806 y[1] (numeric) = 1.568167101766978 absolute error = 1.081801315194753e-12 relative error = 6.898507907576018e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.004999999999894 y[1] (analytic) = 1.53770564846558 y[1] (numeric) = 1.53770564846469 absolute error = 8.901768211444505e-13 relative error = 5.788993634982906e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.104999999999892 y[1] (analytic) = 1.515707701025211 y[1] (numeric) = 1.515707701024537 absolute error = 6.7390537594747e-13 relative error = 4.446143379041002e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.20499999999989 y[1] (analytic) = 1.503050248192862 y[1] (numeric) = 1.503050248192422 absolute error = 4.39870362356487e-13 relative error = 2.92651801152589e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.304999999999888 y[1] (analytic) = 1.500237902670057 y[1] (numeric) = 1.500237902669859 absolute error = 1.978417429882029e-13 relative error = 1.3187357994095e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.404999999999886 y[1] (analytic) = 1.507382783797921 y[1] (numeric) = 1.507382783797964 absolute error = 4.285460875053104e-14 relative error = 2.842981173140166e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.504999999999884 y[1] (analytic) = 1.524200047712863 y[1] (numeric) = 1.524200047713135 absolute error = 2.720046410331634e-13 relative error = 1.784573104044444e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.604999999999881 y[1] (analytic) = 1.550019243172538 y[1] (numeric) = 1.550019243173019 absolute error = 4.811706588725428e-13 relative error = 3.104288291851755e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.704999999999879 y[1] (analytic) = 1.583811040331152 y[1] (numeric) = 1.583811040331813 absolute error = 6.603606550470431e-13 relative error = 4.169440913285787e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.804999999999877 y[1] (analytic) = 1.624228266872174 y[1] (numeric) = 1.624228266872979 absolute error = 8.042455590384634e-13 relative error = 4.951554996559834e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 6.904999999999875 y[1] (analytic) = 1.669659615517348 y[1] (numeric) = 1.669659615518253 absolute error = 9.059419880941277e-13 relative error = 5.42590824905003e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.004999999999873 y[1] (analytic) = 1.7182938817631 y[1] (numeric) = 1.718293881764062 absolute error = 9.623413177450857e-13 relative error = 5.600563023349943e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.104999999999871 y[1] (analytic) = 1.768192170888515 y[1] (numeric) = 1.768192170889486 absolute error = 9.710010573371619e-13 relative error = 5.491490536626653e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.204999999999869 y[1] (analytic) = 1.817365195569321 y[1] (numeric) = 1.817365195570252 absolute error = 9.314771176605063e-13 relative error = 5.125426193543368e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.304999999999866 y[1] (analytic) = 1.863852582485945 y[1] (numeric) = 1.86385258248679 absolute error = 8.446576771348191e-13 relative error = 4.53178371010567e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.404999999999864 y[1] (analytic) = 1.905801026221456 y[1] (numeric) = 1.90580102622217 absolute error = 7.145395386487507e-13 relative error = 3.74928719639445e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.504999999999862 y[1] (analytic) = 1.941538174700086 y[1] (numeric) = 1.941538174700632 absolute error = 5.46451772720502e-13 relative error = 2.814530148524707e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.60499999999986 y[1] (analytic) = 1.969639300587087 y[1] (numeric) = 1.969639300587434 absolute error = 3.466116282879739e-13 relative error = 1.759772097280248e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.704999999999858 y[1] (analytic) = 1.988984100671574 y[1] (numeric) = 1.988984100671698 absolute error = 1.236788449432424e-13 relative error = 6.218191734236722e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.804999999999856 y[1] (analytic) = 1.998801358820227 y[1] (numeric) = 1.998801358820114 absolute error = 1.13686837721616e-13 relative error = 5.687750672168772e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 7.904999999999854 y[1] (analytic) = 1.998699691930808 y[1] (numeric) = 1.998699691930452 absolute error = 3.561595462997502e-13 relative error = 1.781956277562082e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.004999999999852 y[1] (analytic) = 1.988683153141369 y[1] (numeric) = 1.988683153140775 absolute error = 5.941913627793838e-13 relative error = 2.987863410220908e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.104999999999867 y[1] (analytic) = 1.969151070244425 y[1] (numeric) = 1.969151070243611 absolute error = 8.144596108650148e-13 relative error = 4.136095108050385e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.204999999999883 y[1] (analytic) = 1.940882125748027 y[1] (numeric) = 1.940882125747017 absolute error = 1.010524997013817e-12 relative error = 5.206524309787001e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.304999999999898 y[1] (analytic) = 1.905003313261433 y[1] (numeric) = 1.905003313260259 absolute error = 1.173949826238641e-12 relative error = 6.16245556144885e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.404999999999914 y[1] (analytic) = 1.862945007816345 y[1] (numeric) = 1.862945007815046 absolute error = 1.298516849601583e-12 relative error = 6.970237146847628e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.50499999999993 y[1] (analytic) = 1.8163839413282 y[1] (numeric) = 1.816383941326821 absolute error = 1.379119041189369e-12 relative error = 7.592662596328132e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.604999999999945 y[1] (analytic) = 1.76717635658594 y[1] (numeric) = 1.767176356584527 absolute error = 1.412647776533049e-12 relative error = 7.993813244888502e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.704999999999961 y[1] (analytic) = 1.717284004709726 y[1] (numeric) = 1.717284004708327 absolute error = 1.398214877212922e-12 relative error = 8.142013047220248e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.804999999999977 y[1] (analytic) = 1.668695936324442 y[1] (numeric) = 1.668695936323106 absolute error = 1.335154209414213e-12 relative error = 8.001183321361079e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 8.899999999999991 y[1] (analytic) = 1.6255109493029 y[1] (numeric) = 1.625510949301666 absolute error = 1.234568003383174e-12 relative error = 7.594953475475623e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.000000000000007 y[1] (analytic) = 1.584920822938977 y[1] (numeric) = 1.58492082293789 absolute error = 1.087574474922803e-12 relative error = 6.862011396292174e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.100000000000023 y[1] (analytic) = 1.550911882427012 y[1] (numeric) = 1.550911882426108 absolute error = 9.043876758596525e-13 relative error = 5.831328562937967e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.200000000000038 y[1] (analytic) = 1.524839956903799 y[1] (numeric) = 1.524839956903106 absolute error = 6.934453011808728e-13 relative error = 4.547659562836479e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.300000000000054 y[1] (analytic) = 1.507744451765231 y[1] (numeric) = 1.507744451764768 absolute error = 4.629630012686903e-13 relative error = 3.070566770958198e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.40000000000007 y[1] (analytic) = 1.500306910853196 y[1] (numeric) = 1.500306910852974 absolute error = 2.218225603201063e-13 relative error = 1.478514554025216e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.500000000000085 y[1] (analytic) = 1.502823845453339 y[1] (numeric) = 1.502823845453359 absolute error = 2.020605904817785e-14 relative error = 1.344539422189067e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.600000000000101 y[1] (analytic) = 1.5151949133258 y[1] (numeric) = 1.515194913326052 absolute error = 2.529088050096107e-13 relative error = 1.669150303933404e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.700000000000117 y[1] (analytic) = 1.536926919033665 y[1] (numeric) = 1.536926919034133 absolute error = 4.68292071786891e-13 relative error = 3.04693779507309e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.800000000000132 y[1] (analytic) = 1.567153476088671 y[1] (numeric) = 1.567153476089328 absolute error = 6.574740751830177e-13 relative error = 4.195339417706255e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 9.900000000000148 y[1] (analytic) = 1.604669547046451 y[1] (numeric) = 1.604669547047263 absolute error = 8.120171202108395e-13 relative error = 5.060338570676033e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 10.00000000000016 y[1] (analytic) = 1.647979484546727 y[1] (numeric) = 1.647979484547653 absolute error = 9.263700917472306e-13 relative error = 5.621247718396366e-11 % Correct digits = 12 h = 0.005 Finished! diff ( y , x , 1 ) = sin(x) * cos(x) ; Iterations = 1980 Total Elapsed Time Unknown Elapsed Time(since restart) Unknown Time to Timeout = 22 Minutes 41 Seconds Percent Done = 100.1 %