##############ECHO OF PROBLEM################# ##############temp/arccos_sqrtpostode.ode################# diff ( y , x , 1 ) = arccos(sqrt(0.1 * x + 0.2)); ! /* BEGIN FIRST INPUT BLOCK */ Digits = 32; max_terms = 30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start = 0.1; x_end = 0.5 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.05; glob_look_poles = true; glob_max_iter = 1000000; /* 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(10.0 * (0.1 * x + 0.2) * arccos(sqrt ( 0.1 * x + 0.2)) - 5.0 * sqrt( 0.1 * x + 0.2) * sqrt( 0.8 - 0.1 * x) + 5.0 * arcsin(sqrt( 0.1 * x + 0.2))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 2.642629173205489 y[1] (numeric) = 2.642629173205489 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) = 2.642640120824439 y[1] (numeric) = 2.642640120824438 absolute error = 4.440892098500626e-16 relative error = 1.680475545461399e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10002 y[1] (analytic) = 2.642651068431112 y[1] (numeric) = 2.642651068431112 absolute error = 4.440892098500626e-16 relative error = 1.680468583821432e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10003 y[1] (analytic) = 2.64266201602551 y[1] (numeric) = 2.64266201602551 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10004 y[1] (analytic) = 2.642672963607633 y[1] (numeric) = 2.642672963607632 absolute error = 4.440892098500626e-16 relative error = 1.680454660737953e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10005 y[1] (analytic) = 2.64268391117748 y[1] (numeric) = 2.642683911177479 absolute error = 4.440892098500626e-16 relative error = 1.680447699294439e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10006 y[1] (analytic) = 2.64269485873505 y[1] (numeric) = 2.64269485873505 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10007 y[1] (analytic) = 2.642705806280346 y[1] (numeric) = 2.642705806280346 absolute error = 4.440892098500626e-16 relative error = 1.680433776603858e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10008 y[1] (analytic) = 2.642716753813366 y[1] (numeric) = 2.642716753813366 absolute error = 4.440892098500626e-16 relative error = 1.680426815356789e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10009 y[1] (analytic) = 2.642727701334112 y[1] (numeric) = 2.642727701334111 absolute error = 8.881784197001252e-16 relative error = 3.360839708350397e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001 y[1] (analytic) = 2.64273864884258 y[1] (numeric) = 2.64273864884258 absolute error = 4.440892098500626e-16 relative error = 1.680412893059088e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10011 y[1] (analytic) = 2.642749596338774 y[1] (numeric) = 2.642749596338773 absolute error = 4.440892098500626e-16 relative error = 1.680405932008455e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10012 y[1] (analytic) = 2.642760543822692 y[1] (numeric) = 2.642760543822691 absolute error = 4.440892098500626e-16 relative error = 1.680398971023299e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10013 y[1] (analytic) = 2.642771491294334 y[1] (numeric) = 2.642771491294334 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10014 y[1] (analytic) = 2.642782438753701 y[1] (numeric) = 2.642782438753701 absolute error = 4.440892098500626e-16 relative error = 1.680385049249415e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001499999999999 y[1] (analytic) = 2.642793386200793 y[1] (numeric) = 2.642793386200792 absolute error = 4.440892098500626e-16 relative error = 1.680378088460684e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001599999999999 y[1] (analytic) = 2.64280433363561 y[1] (numeric) = 2.642804333635609 absolute error = 8.881784197001252e-16 relative error = 3.360742255474852e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001699999999999 y[1] (analytic) = 2.64281528105815 y[1] (numeric) = 2.64281528105815 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001799999999999 y[1] (analytic) = 2.642826228468416 y[1] (numeric) = 2.642826228468415 absolute error = 8.881784197001252e-16 relative error = 3.360714412974654e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001899999999999 y[1] (analytic) = 2.642837175866406 y[1] (numeric) = 2.642837175866406 absolute error = 4.440892098500626e-16 relative error = 1.680350245960484e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001999999999999 y[1] (analytic) = 2.642848123252121 y[1] (numeric) = 2.64284812325212 absolute error = 8.881784197001252e-16 relative error = 3.36068657099822e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002099999999999 y[1] (analytic) = 2.642859070625561 y[1] (numeric) = 2.64285907062556 absolute error = 8.881784197001252e-16 relative error = 3.36067265020641e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002199999999999 y[1] (analytic) = 2.642870017986725 y[1] (numeric) = 2.642870017986724 absolute error = 4.440892098500626e-16 relative error = 1.680329364772768e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002299999999999 y[1] (analytic) = 2.642880965335614 y[1] (numeric) = 2.642880965335614 absolute error = 4.440892098500626e-16 relative error = 1.680322404507797e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002399999999999 y[1] (analytic) = 2.642891912672228 y[1] (numeric) = 2.642891912672228 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002499999999999 y[1] (analytic) = 2.642902859996567 y[1] (numeric) = 2.642902859996566 absolute error = 8.881784197001252e-16 relative error = 3.360616968348503e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002599999999999 y[1] (analytic) = 2.642913807308631 y[1] (numeric) = 2.64291380730863 absolute error = 8.881784197001252e-16 relative error = 3.360603048211351e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002699999999999 y[1] (analytic) = 2.64292475460842 y[1] (numeric) = 2.642924754608418 absolute error = 1.332267629550188e-15 relative error = 5.040883692307687e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002799999999999 y[1] (analytic) = 2.642935701895932 y[1] (numeric) = 2.642935701895932 absolute error = 4.440892098500626e-16 relative error = 1.680287604164912e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002899999999999 y[1] (analytic) = 2.64294664917117 y[1] (numeric) = 2.64294664917117 absolute error = 4.440892098500626e-16 relative error = 1.680280644292722e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002999999999999 y[1] (analytic) = 2.642957596434133 y[1] (numeric) = 2.642957596434133 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003099999999999 y[1] (analytic) = 2.642968543684821 y[1] (numeric) = 2.642968543684821 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003199999999999 y[1] (analytic) = 2.642979490923234 y[1] (numeric) = 2.642979490923234 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003299999999999 y[1] (analytic) = 2.642990438149372 y[1] (numeric) = 2.642990438149373 absolute error = 4.440892098500626e-16 relative error = 1.680252805458558e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003399999999999 y[1] (analytic) = 2.643001385363236 y[1] (numeric) = 2.643001385363235 absolute error = 4.440892098500626e-16 relative error = 1.68024584591366e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003499999999999 y[1] (analytic) = 2.643012332564823 y[1] (numeric) = 2.643012332564823 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003599999999999 y[1] (analytic) = 2.643023279754136 y[1] (numeric) = 2.643023279754136 absolute error = 4.440892098500626e-16 relative error = 1.680231927020232e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003699999999999 y[1] (analytic) = 2.643034226931174 y[1] (numeric) = 2.643034226931174 absolute error = 4.440892098500626e-16 relative error = 1.680224967671699e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003799999999999 y[1] (analytic) = 2.643045174095937 y[1] (numeric) = 2.643045174095938 absolute error = 4.440892098500626e-16 relative error = 1.680218008388619e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003899999999999 y[1] (analytic) = 2.643056121248426 y[1] (numeric) = 2.643056121248426 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003999999999999 y[1] (analytic) = 2.643067068388639 y[1] (numeric) = 2.643067068388639 absolute error = 4.440892098500626e-16 relative error = 1.680204090018814e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004099999999998 y[1] (analytic) = 2.643078015516577 y[1] (numeric) = 2.643078015516577 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004199999999998 y[1] (analytic) = 2.643088962632241 y[1] (numeric) = 2.643088962632241 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004299999999998 y[1] (analytic) = 2.643099909735629 y[1] (numeric) = 2.64309990973563 absolute error = 4.440892098500626e-16 relative error = 1.68018321295498e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004399999999998 y[1] (analytic) = 2.643110856826743 y[1] (numeric) = 2.643110856826744 absolute error = 4.440892098500626e-16 relative error = 1.680176254064597e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004499999999998 y[1] (analytic) = 2.643121803905583 y[1] (numeric) = 2.643121803905583 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004599999999998 y[1] (analytic) = 2.643132750972147 y[1] (numeric) = 2.643132750972148 absolute error = 4.440892098500626e-16 relative error = 1.680162336480171e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004699999999998 y[1] (analytic) = 2.643143698026437 y[1] (numeric) = 2.643143698026437 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004799999999998 y[1] (analytic) = 2.643154645068452 y[1] (numeric) = 2.643154645068452 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004899999999998 y[1] (analytic) = 2.643165592098192 y[1] (numeric) = 2.643165592098193 absolute error = 4.440892098500626e-16 relative error = 1.680141460594365e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004999999999998 y[1] (analytic) = 2.643176539115658 y[1] (numeric) = 2.643176539115659 absolute error = 4.440892098500626e-16 relative error = 1.680134502096647e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005099999999998 y[1] (analytic) = 2.643187486120849 y[1] (numeric) = 2.64318748612085 absolute error = 1.332267629550188e-15 relative error = 5.040382630993114e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005199999999998 y[1] (analytic) = 2.643198433113766 y[1] (numeric) = 2.643198433113767 absolute error = 4.440892098500626e-16 relative error = 1.680120585297534e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005299999999998 y[1] (analytic) = 2.643209380094408 y[1] (numeric) = 2.643209380094409 absolute error = 8.881784197001252e-16 relative error = 3.360227253992274e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005399999999998 y[1] (analytic) = 2.643220327062775 y[1] (numeric) = 2.643220327062776 absolute error = 1.332267629550188e-15 relative error = 5.040320006280534e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005499999999998 y[1] (analytic) = 2.643231274018868 y[1] (numeric) = 2.643231274018869 absolute error = 8.881784197001252e-16 relative error = 3.360199421179311e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005599999999998 y[1] (analytic) = 2.643242220962685 y[1] (numeric) = 2.643242220962687 absolute error = 1.332267629550188e-15 relative error = 5.04027825745371e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005699999999998 y[1] (analytic) = 2.643253167894229 y[1] (numeric) = 2.64325316789423 absolute error = 8.881784197001252e-16 relative error = 3.360171588889839e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005799999999998 y[1] (analytic) = 2.643264114813499 y[1] (numeric) = 2.643264114813499 absolute error = 8.881784197001252e-16 relative error = 3.360157672941407e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005899999999998 y[1] (analytic) = 2.643275061720493 y[1] (numeric) = 2.643275061720494 absolute error = 1.332267629550188e-15 relative error = 5.040215635685763e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005999999999998 y[1] (analytic) = 2.643286008615214 y[1] (numeric) = 2.643286008615214 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006099999999998 y[1] (analytic) = 2.64329695549766 y[1] (numeric) = 2.64329695549766 absolute error = 4.440892098500626e-16 relative error = 1.680057962940652e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006199999999998 y[1] (analytic) = 2.64330790236783 y[1] (numeric) = 2.643307902367831 absolute error = 8.881784197001252e-16 relative error = 3.360102010456331e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006299999999998 y[1] (analytic) = 2.643318849225727 y[1] (numeric) = 2.643318849225728 absolute error = 8.881784197001252e-16 relative error = 3.360088095162215e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006399999999998 y[1] (analytic) = 2.64332979607135 y[1] (numeric) = 2.643329796071351 absolute error = 8.881784197001252e-16 relative error = 3.360074179998957e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006499999999998 y[1] (analytic) = 2.643340742904698 y[1] (numeric) = 2.643340742904699 absolute error = 1.332267629550188e-15 relative error = 5.040090397449834e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006599999999997 y[1] (analytic) = 2.643351689725773 y[1] (numeric) = 2.643351689725773 absolute error = 8.881784197001252e-16 relative error = 3.360046350065008e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006699999999997 y[1] (analytic) = 2.643362636534572 y[1] (numeric) = 2.643362636534573 absolute error = 8.881784197001252e-16 relative error = 3.360032435294312e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006799999999997 y[1] (analytic) = 2.643373583331097 y[1] (numeric) = 2.643373583331099 absolute error = 1.332267629550188e-15 relative error = 5.040027780981701e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006899999999997 y[1] (analytic) = 2.643384530115349 y[1] (numeric) = 2.64338453011535 absolute error = 8.881784197001252e-16 relative error = 3.360004606145471e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006999999999997 y[1] (analytic) = 2.643395476887326 y[1] (numeric) = 2.643395476887326 absolute error = 4.440892098500626e-16 relative error = 1.67999534588366e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007099999999997 y[1] (analytic) = 2.643406423647028 y[1] (numeric) = 2.643406423647029 absolute error = 8.881784197001252e-16 relative error = 3.359976777520016e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007199999999997 y[1] (analytic) = 2.643417370394457 y[1] (numeric) = 2.643417370394458 absolute error = 4.440892098500626e-16 relative error = 1.679981431701777e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007299999999997 y[1] (analytic) = 2.643428317129612 y[1] (numeric) = 2.643428317129612 absolute error = 4.440892098500626e-16 relative error = 1.679974474708966e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007399999999997 y[1] (analytic) = 2.643439263852492 y[1] (numeric) = 2.643439263852492 absolute error = 4.440892098500626e-16 relative error = 1.679967517781576e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007499999999997 y[1] (analytic) = 2.643450210563097 y[1] (numeric) = 2.643450210563098 absolute error = 8.881784197001252e-16 relative error = 3.359921121839208e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007599999999997 y[1] (analytic) = 2.643461157261429 y[1] (numeric) = 2.64346115726143 absolute error = 4.440892098500626e-16 relative error = 1.67995360412305e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007699999999997 y[1] (analytic) = 2.643472103947488 y[1] (numeric) = 2.643472103947488 absolute error = 4.440892098500626e-16 relative error = 1.679946647391912e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007799999999997 y[1] (analytic) = 2.643483050621272 y[1] (numeric) = 2.643483050621272 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007899999999997 y[1] (analytic) = 2.643493997282782 y[1] (numeric) = 2.643493997282782 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007999999999997 y[1] (analytic) = 2.643504943932017 y[1] (numeric) = 2.643504943932018 absolute error = 8.881784197001252e-16 relative error = 3.359851555181985e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008099999999997 y[1] (analytic) = 2.643515890568978 y[1] (numeric) = 2.643515890568979 absolute error = 8.881784197001252e-16 relative error = 3.359837642243027e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008199999999997 y[1] (analytic) = 2.643526837193666 y[1] (numeric) = 2.643526837193667 absolute error = 4.440892098500626e-16 relative error = 1.679911864717447e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008299999999997 y[1] (analytic) = 2.64353778380608 y[1] (numeric) = 2.643537783806081 absolute error = 8.881784197001252e-16 relative error = 3.359809816757583e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008399999999997 y[1] (analytic) = 2.64354873040622 y[1] (numeric) = 2.64354873040622 absolute error = 4.440892098500626e-16 relative error = 1.679897952105546e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008499999999997 y[1] (analytic) = 2.643559676994086 y[1] (numeric) = 2.643559676994086 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008599999999997 y[1] (analytic) = 2.643570623569678 y[1] (numeric) = 2.643570623569679 absolute error = 4.440892098500626e-16 relative error = 1.679884039755284e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008699999999997 y[1] (analytic) = 2.643581570132996 y[1] (numeric) = 2.643581570132997 absolute error = 4.440892098500626e-16 relative error = 1.679877083678265e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008799999999997 y[1] (analytic) = 2.64359251668404 y[1] (numeric) = 2.643592516684041 absolute error = 4.440892098500626e-16 relative error = 1.679870127666653e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008899999999997 y[1] (analytic) = 2.643603463222811 y[1] (numeric) = 2.643603463222811 absolute error = 4.440892098500626e-16 relative error = 1.679863171720446e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008999999999997 y[1] (analytic) = 2.643614409749308 y[1] (numeric) = 2.643614409749308 absolute error = 4.440892098500626e-16 relative error = 1.679856215839644e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009099999999997 y[1] (analytic) = 2.643625356263531 y[1] (numeric) = 2.643625356263531 absolute error = 4.440892098500626e-16 relative error = 1.679849260024246e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009199999999996 y[1] (analytic) = 2.643636302765481 y[1] (numeric) = 2.643636302765481 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009299999999996 y[1] (analytic) = 2.643647249255156 y[1] (numeric) = 2.643647249255156 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009399999999996 y[1] (analytic) = 2.643658195732557 y[1] (numeric) = 2.643658195732558 absolute error = 1.332267629550188e-15 relative error = 5.039485178911403e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009499999999996 y[1] (analytic) = 2.643669142197685 y[1] (numeric) = 2.643669142197686 absolute error = 8.881784197001252e-16 relative error = 3.359642874833352e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009599999999996 y[1] (analytic) = 2.64368008865054 y[1] (numeric) = 2.64368008865054 absolute error = 8.881784197001252e-16 relative error = 3.359628963856568e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009699999999996 y[1] (analytic) = 2.64369103509112 y[1] (numeric) = 2.643691035091121 absolute error = 8.881784197001252e-16 relative error = 3.359615053010582e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009799999999996 y[1] (analytic) = 2.643701981519427 y[1] (numeric) = 2.643701981519428 absolute error = 8.881784197001252e-16 relative error = 3.35960114229539e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009899999999996 y[1] (analytic) = 2.64371292793546 y[1] (numeric) = 2.643712927935462 absolute error = 1.332267629550188e-15 relative error = 5.039380847566487e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009999999999996 y[1] (analytic) = 2.643723874339221 y[1] (numeric) = 2.643723874339222 absolute error = 8.881784197001252e-16 relative error = 3.359573321257383e-14 % Correct digits = 15 h = 1e-05 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = arccos(sqrt(0.1 * x + 0.2)); Iterations = 100 Total Elapsed Time = 18 Seconds Elapsed Time(since restart) = 17 Seconds Expected Time Remaining = 1 Hours 58 Minutes 30 Seconds Optimized Time Remaining = 1 Hours 51 Minutes 55 Seconds Time to Timeout = 42 Seconds Percent Done = 0.2525 %