##############ECHO OF PROBLEM################# ##############temp/h2sinpostode.ode################# diff ( y , x , 2 ) = sin(x); ! // BEGIN FIRST INPUT BLOCK Digits = 32; max_terms = 30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start = 0.1; x_end = 5.0 ; array_y_init[0 + 1] = exact_soln_y(x_start); array_y_init[1 + 1] = exact_soln_yp(x_start); glob_h = 0.00001; glob_look_poles = true; glob_max_iter = 100; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 100; glob_max_minutes = 1; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(2.0 - cos(x)); } double exact_soln_yp (double x) { return(sin(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 1.004995834721974 y[1] (numeric) = 1.004995834721974 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10001 y[1] (analytic) = 1.004996833105891 y[1] (numeric) = 1.004996833061133 absolute error = 4.475841919315826e-11 relative error = 4.453588082942975e-09 % Correct digits = 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10002 y[1] (analytic) = 1.004997831589308 y[1] (numeric) = 1.004997831410275 absolute error = 1.790325665496084e-10 relative error = 1.781422416270148e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10003 y[1] (analytic) = 1.004998830172225 y[1] (numeric) = 1.004998829769403 absolute error = 4.028217759355357e-10 relative error = 4.008181540534776e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10004 y[1] (analytic) = 1.004999828854642 y[1] (numeric) = 1.004999828138518 absolute error = 7.161249371279155e-10 relative error = 7.12562247840434e-08 % Correct digits = 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10005 y[1] (analytic) = 1.00500082763656 y[1] (numeric) = 1.005000826517619 absolute error = 1.118940495814513e-09 relative error = 1.11337271079259e-07 % Correct digits = 8 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10006 y[1] (analytic) = 1.005001826517977 y[1] (numeric) = 1.005001824906709 absolute error = 1.611268007906119e-09 relative error = 1.603248835366468e-07 % Correct digits = 8 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10007 y[1] (analytic) = 1.005002825498894 y[1] (numeric) = 1.005002823305788 absolute error = 2.193105919090499e-09 relative error = 2.182188809272071e-07 % Correct digits = 8 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10008 y[1] (analytic) = 1.005003824579311 y[1] (numeric) = 1.005003821714858 absolute error = 2.864452897100023e-09 relative error = 2.850191041112771e-07 % Correct digits = 8 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10009 y[1] (analytic) = 1.005004823759227 y[1] (numeric) = 1.005004820133919 absolute error = 3.625308719890086e-09 relative error = 3.607255044139584e-07 % Correct digits = 8 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001 y[1] (analytic) = 1.005005823038643 y[1] (numeric) = 1.005005818562972 absolute error = 4.475671389059244e-09 relative error = 4.453378564043555e-07 % Correct digits = 8 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10011 y[1] (analytic) = 1.005006822417558 y[1] (numeric) = 1.005006817002018 absolute error = 5.415540016429077e-09 relative error = 5.388560451163822e-07 % Correct digits = 8 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10012 y[1] (analytic) = 1.005007821895973 y[1] (numeric) = 1.005007815451059 absolute error = 6.44491393586577e-09 relative error = 6.412799776729374e-07 % Correct digits = 8 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10013 y[1] (analytic) = 1.005008821473887 y[1] (numeric) = 1.005008813910095 absolute error = 7.563791815101695e-09 relative error = 7.526094949106099e-07 % Correct digits = 8 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10014 y[1] (analytic) = 1.0050098211513 y[1] (numeric) = 1.005009812379128 absolute error = 8.77217232186922e-09 relative error = 8.728444376613319e-07 % Correct digits = 8 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001499999999999 y[1] (analytic) = 1.005010820928212 y[1] (numeric) = 1.005010810858157 absolute error = 1.007005501207914e-08 relative error = 1.001984735127388e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001599999999999 y[1] (analytic) = 1.005011820804623 y[1] (numeric) = 1.005011809347185 absolute error = 1.145743788733e-08 relative error = 1.140030161849943e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001699999999999 y[1] (analytic) = 1.005012820780533 y[1] (numeric) = 1.005012807846212 absolute error = 1.293432072557721e-08 relative error = 1.286980669115435e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001799999999999 y[1] (analytic) = 1.005013820855941 y[1] (numeric) = 1.005013806355239 absolute error = 1.450070197250852e-08 relative error = 1.442836075643089e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001899999999999 y[1] (analytic) = 1.005014821030848 y[1] (numeric) = 1.005014804874268 absolute error = 1.615658029585632e-08 relative error = 1.607596222241224e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001999999999999 y[1] (analytic) = 1.005015821305254 y[1] (numeric) = 1.005015803403299 absolute error = 1.790195525153138e-08 relative error = 1.781261038088077e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002099999999999 y[1] (analytic) = 1.005016821679158 y[1] (numeric) = 1.005016801942333 absolute error = 1.973682506317687e-08 relative error = 1.963830319795151e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002199999999999 y[1] (analytic) = 1.00501782215256 y[1] (numeric) = 1.005017800491371 absolute error = 2.166118906465897e-08 relative error = 2.155303974437464e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002299999999999 y[1] (analytic) = 1.005018822725461 y[1] (numeric) = 1.005018799050414 absolute error = 2.367504614575466e-08 relative error = 2.355681864897961e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002399999999999 y[1] (analytic) = 1.005019823397859 y[1] (numeric) = 1.005019797619464 absolute error = 2.577839497419632e-08 relative error = 2.564963831961289e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002499999999999 y[1] (analytic) = 1.005020824169756 y[1] (numeric) = 1.005020796198521 absolute error = 2.797123466180551e-08 relative error = 2.783149760594508e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002599999999999 y[1] (analytic) = 1.00502182504115 y[1] (numeric) = 1.005021794787587 absolute error = 3.025356387631462e-08 relative error = 3.010239491572821e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002699999999999 y[1] (analytic) = 1.005022826012043 y[1] (numeric) = 1.005022793386661 absolute error = 3.262538195158982e-08 relative error = 3.246232931947246e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002799999999999 y[1] (analytic) = 1.005023827082433 y[1] (numeric) = 1.005023791995746 absolute error = 3.508668755536348e-08 relative error = 3.491129922483483e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002899999999999 y[1] (analytic) = 1.005024828252321 y[1] (numeric) = 1.005024790614842 absolute error = 3.763747935536799e-08 relative error = 3.744930303942576e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002999999999999 y[1] (analytic) = 1.005025829521706 y[1] (numeric) = 1.00502578924395 absolute error = 4.027775646342491e-08 relative error = 4.007633961267759e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003099999999999 y[1] (analytic) = 1.005026830890589 y[1] (numeric) = 1.005026787883071 absolute error = 4.300751799135583e-08 relative error = 4.279240779397441e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003199999999999 y[1] (analytic) = 1.005027832358969 y[1] (numeric) = 1.005027786532206 absolute error = 4.582676260689311e-08 relative error = 4.559750599078438e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003299999999999 y[1] (analytic) = 1.005028833926846 y[1] (numeric) = 1.005028785191357 absolute error = 4.873548942185835e-08 relative error = 4.849163305239628e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003399999999999 y[1] (analytic) = 1.00502983559422 y[1] (numeric) = 1.005029783860523 absolute error = 5.17336971039839e-08 relative error = 5.147478738618394e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003499999999999 y[1] (analytic) = 1.005030837361092 y[1] (numeric) = 1.005030782539707 absolute error = 5.482138432100214e-08 relative error = 5.454696739947462e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003599999999999 y[1] (analytic) = 1.00503183922746 y[1] (numeric) = 1.005031781228909 absolute error = 5.799855062882386e-08 relative error = 5.770817238328065e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003699999999999 y[1] (analytic) = 1.005032841193325 y[1] (numeric) = 1.005032779928131 absolute error = 6.126519447313683e-08 relative error = 6.095840052390093e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003799999999999 y[1] (analytic) = 1.005033843258687 y[1] (numeric) = 1.005033778637372 absolute error = 6.462131474371802e-08 relative error = 6.429765044945362e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003899999999999 y[1] (analytic) = 1.005034845423545 y[1] (numeric) = 1.005034777356635 absolute error = 6.8066910552389e-08 relative error = 6.772592100894174e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003999999999999 y[1] (analytic) = 1.0050358476879 y[1] (numeric) = 1.00503577608592 absolute error = 7.160198056688216e-08 relative error = 7.124321060945595e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004099999999998 y[1] (analytic) = 1.005036850051751 y[1] (numeric) = 1.005036774825228 absolute error = 7.522652389901907e-08 relative error = 7.4849518099904e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004199999999998 y[1] (analytic) = 1.005037852515099 y[1] (numeric) = 1.005037773574559 absolute error = 7.894053966062131e-08 relative error = 7.854484232914537e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004299999999998 y[1] (analytic) = 1.005038855077943 y[1] (numeric) = 1.005038772333917 absolute error = 8.274402651942125e-08 relative error = 8.232918170412849e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004399999999998 y[1] (analytic) = 1.005039857740283 y[1] (numeric) = 1.0050397711033 absolute error = 8.663698314315127e-08 relative error = 8.62025346317554e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004499999999998 y[1] (analytic) = 1.005040860502119 y[1] (numeric) = 1.00504076988271 absolute error = 9.061940886567754e-08 relative error = 9.016490018167424e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004599999999998 y[1] (analytic) = 1.005041863363451 y[1] (numeric) = 1.005041768672149 absolute error = 9.469130235473244e-08 relative error = 9.421627676069195e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004699999999998 y[1] (analytic) = 1.005042866324279 y[1] (numeric) = 1.005042767471616 absolute error = 9.885266250009295e-08 relative error = 9.835666299649947e-06 % Correct digits = 7 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004799999999998 y[1] (analytic) = 1.005043869384602 y[1] (numeric) = 1.005043766281114 absolute error = 1.03103488191536e-07 relative error = 1.025860575167403e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004899999999998 y[1] (analytic) = 1.005044872544421 y[1] (numeric) = 1.005044765100643 absolute error = 1.074437783188387e-07 relative error = 1.069044589490106e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004999999999998 y[1] (analytic) = 1.005045875803736 y[1] (numeric) = 1.005045763930204 absolute error = 1.11873532215867e-07 relative error = 1.113118663627187e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005099999999998 y[1] (analytic) = 1.005046879162546 y[1] (numeric) = 1.005046762769798 absolute error = 1.163927481062643e-07 relative error = 1.158082777225759e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005199999999998 y[1] (analytic) = 1.005047882620851 y[1] (numeric) = 1.005047761619426 absolute error = 1.210014253238967e-07 relative error = 1.203936920978956e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005299999999998 y[1] (analytic) = 1.005048886178652 y[1] (numeric) = 1.005048760479089 absolute error = 1.256995627585411e-07 relative error = 1.250681081160837e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005399999999998 y[1] (analytic) = 1.005049889835947 y[1] (numeric) = 1.005049759348788 absolute error = 1.3048715907793e-07 relative error = 1.298315241835698e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005499999999998 y[1] (analytic) = 1.005050893592738 y[1] (numeric) = 1.005050758228524 absolute error = 1.353642133938848e-07 relative error = 1.346839391485945e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005599999999998 y[1] (analytic) = 1.005051897449023 y[1] (numeric) = 1.005051757118299 absolute error = 1.403307245961827e-07 relative error = 1.396253516384215e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005699999999998 y[1] (analytic) = 1.005052901404804 y[1] (numeric) = 1.005052756018112 absolute error = 1.453866913525559e-07 relative error = 1.446557600593391e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005799999999998 y[1] (analytic) = 1.005053905460079 y[1] (numeric) = 1.005053754927966 absolute error = 1.505321129968706e-07 relative error = 1.49775163480373e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005899999999998 y[1] (analytic) = 1.005054909614848 y[1] (numeric) = 1.00505475384786 absolute error = 1.557669879748147e-07 relative error = 1.549835600867886e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005999999999998 y[1] (analytic) = 1.005055913869113 y[1] (numeric) = 1.005055752777797 absolute error = 1.610913156202542e-07 relative error = 1.60280948947516e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006099999999998 y[1] (analytic) = 1.005056918222871 y[1] (numeric) = 1.005056751717777 absolute error = 1.665050946009217e-07 relative error = 1.656673284686541e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006199999999998 y[1] (analytic) = 1.005057922676124 y[1] (numeric) = 1.0050577506678 absolute error = 1.720083240286385e-07 relative error = 1.711426974981097e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006299999999998 y[1] (analytic) = 1.005058927228871 y[1] (numeric) = 1.005058749627869 absolute error = 1.776010023490926e-07 relative error = 1.767070542209605e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006399999999998 y[1] (analytic) = 1.005059931881112 y[1] (numeric) = 1.005059748597984 absolute error = 1.832831288961501e-07 relative error = 1.823603977059454e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006499999999998 y[1] (analytic) = 1.005060936632848 y[1] (numeric) = 1.005060747578145 absolute error = 1.890547025595879e-07 relative error = 1.881027265799011e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006599999999997 y[1] (analytic) = 1.005061941484077 y[1] (numeric) = 1.005061746568355 absolute error = 1.949157220071385e-07 relative error = 1.939340392486909e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006699999999997 y[1] (analytic) = 1.0050629464348 y[1] (numeric) = 1.005062745568614 absolute error = 2.008661861285788e-07 relative error = 1.998543343390575e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006799999999997 y[1] (analytic) = 1.005063951485016 y[1] (numeric) = 1.005063744578922 absolute error = 2.069060940357303e-07 relative error = 2.058636106986222e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006899999999997 y[1] (analytic) = 1.005064956634727 y[1] (numeric) = 1.005064743599282 absolute error = 2.130354446183702e-07 relative error = 2.119618669540323e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006999999999997 y[1] (analytic) = 1.00506596188393 y[1] (numeric) = 1.005065742629694 absolute error = 2.192542365442307e-07 relative error = 2.181491015109625e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007099999999997 y[1] (analytic) = 1.005066967232628 y[1] (numeric) = 1.005066741670159 absolute error = 2.255624689251334e-07 relative error = 2.244253132168913e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007199999999997 y[1] (analytic) = 1.005067972680818 y[1] (numeric) = 1.005067740720677 absolute error = 2.319601406508554e-07 relative error = 2.307905006983239e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007299999999997 y[1] (analytic) = 1.005068978228502 y[1] (numeric) = 1.005068739781251 absolute error = 2.384472506111734e-07 relative error = 2.372446625817185e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007399999999997 y[1] (analytic) = 1.005069983875678 y[1] (numeric) = 1.005069738851881 absolute error = 2.450237976958647e-07 relative error = 2.437877974934855e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007499999999997 y[1] (analytic) = 1.005070989622348 y[1] (numeric) = 1.005070737932567 absolute error = 2.516897807947061e-07 relative error = 2.504199040599884e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007599999999997 y[1] (analytic) = 1.005071995468511 y[1] (numeric) = 1.005071737023312 absolute error = 2.584451987974745e-07 relative error = 2.57140980907543e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007699999999997 y[1] (analytic) = 1.005073001414166 y[1] (numeric) = 1.005072736124116 absolute error = 2.652900505939471e-07 relative error = 2.63951026662418e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007799999999997 y[1] (analytic) = 1.005074007459315 y[1] (numeric) = 1.005073735234979 absolute error = 2.722243352959453e-07 relative error = 2.708500401717581e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007899999999997 y[1] (analytic) = 1.005075013603955 y[1] (numeric) = 1.005074734355904 absolute error = 2.792480515712015e-07 relative error = 2.778380198408134e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007999999999997 y[1] (analytic) = 1.005076019848088 y[1] (numeric) = 1.00507573348689 absolute error = 2.863611983094927e-07 relative error = 2.849149642957103e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008099999999997 y[1] (analytic) = 1.005077026191714 y[1] (numeric) = 1.00507673262794 absolute error = 2.935637746226405e-07 relative error = 2.92080872383451e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008199999999997 y[1] (analytic) = 1.005078032634832 y[1] (numeric) = 1.005077731779053 absolute error = 3.008557791783772e-07 relative error = 2.993357425091441e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008299999999997 y[1] (analytic) = 1.005079039177442 y[1] (numeric) = 1.005078730940231 absolute error = 3.082372110885245e-07 relative error = 3.066795735196967e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008399999999997 y[1] (analytic) = 1.005080045819544 y[1] (numeric) = 1.005079730111475 absolute error = 3.157080690208147e-07 relative error = 3.141123638201231e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008499999999997 y[1] (analytic) = 1.005081052561139 y[1] (numeric) = 1.005080729292786 absolute error = 3.23268352309114e-07 relative error = 3.216341124781573e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008599999999997 y[1] (analytic) = 1.005082059402225 y[1] (numeric) = 1.005081728484165 absolute error = 3.309180596211547e-07 relative error = 3.292448178987187e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008699999999997 y[1] (analytic) = 1.005083066342803 y[1] (numeric) = 1.005082727685613 absolute error = 3.386571896246693e-07 relative error = 3.369444784866804e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008799999999997 y[1] (analytic) = 1.005084073382872 y[1] (numeric) = 1.005083726897131 absolute error = 3.464857414314793e-07 relative error = 3.447330930887117e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008899999999997 y[1] (analytic) = 1.005085080522434 y[1] (numeric) = 1.005084726118719 absolute error = 3.544037141534062e-07 relative error = 3.526106605514336e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008999999999997 y[1] (analytic) = 1.005086087761486 y[1] (numeric) = 1.00508572535038 absolute error = 3.624111062361379e-07 relative error = 3.605771790586565e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009099999999997 y[1] (analytic) = 1.00508709510003 y[1] (numeric) = 1.005086724592114 absolute error = 3.70507916791496e-07 relative error = 3.686326474569067e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009199999999996 y[1] (analytic) = 1.005088102538066 y[1] (numeric) = 1.005087723843921 absolute error = 3.786941449313019e-07 relative error = 3.76777064592663e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009299999999996 y[1] (analytic) = 1.005089110075592 y[1] (numeric) = 1.005088723105803 absolute error = 3.869697893232882e-07 relative error = 3.850104288705151e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009399999999996 y[1] (analytic) = 1.00509011771261 y[1] (numeric) = 1.005089722377761 absolute error = 3.953348490792763e-07 relative error = 3.933327391368464e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009499999999996 y[1] (analytic) = 1.005091125449119 y[1] (numeric) = 1.005090721659796 absolute error = 4.037893228669986e-07 relative error = 4.017439937961524e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009599999999996 y[1] (analytic) = 1.005092133285118 y[1] (numeric) = 1.005091720951909 absolute error = 4.123332095762322e-07 relative error = 4.10244191473802e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009699999999996 y[1] (analytic) = 1.005093141220609 y[1] (numeric) = 1.0050927202541 absolute error = 4.20966508096754e-07 relative error = 4.188333307951166e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009799999999996 y[1] (analytic) = 1.00509414925559 y[1] (numeric) = 1.005093719566372 absolute error = 4.296892175403855e-07 relative error = 4.275114106062894e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009899999999996 y[1] (analytic) = 1.005095157390061 y[1] (numeric) = 1.005094718888724 absolute error = 4.385013367969037e-07 relative error = 4.362784295325466e-05 % Correct digits = 6 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009999999999996 y[1] (analytic) = 1.005096165624023 y[1] (numeric) = 1.005095718221159 absolute error = 4.474028647560857e-07 relative error = 4.451343861990672e-05 % Correct digits = 6 h = 1e-05 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 2 ) = sin(x); Iterations = 100 Total Elapsed Time = 14 Seconds Elapsed Time(since restart) = 13 Seconds Expected Time Remaining = 18 Hours 51 Minutes 46 Seconds Optimized Time Remaining = 17 Hours 30 Minutes 56 Seconds Time to Timeout = 46 Seconds Percent Done = 0.02061 %