##############ECHO OF PROBLEM################# ##############temp/sin_sqrt_linpostode.ode################# diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(2.0); x_end=c(3.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.0001); glob_upper_ratio_limit=c(1.001); glob_lower_ratio_limit=c(0.999); glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-1.5); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.5); array_given_ord_poles[1][2]=c(0.0); // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(sin(sqrt(c(2.0)*c(x)+c(3.0)))-sqrt(c(2.0)*c(x)+c(3.0))*cos(sqrt(c(2.0)*c(x)+c(3.0)))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 2.80289196959102 y[1] (numeric) = 2.80289196959102 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.009999999999999 y[1] (closed_form) = 2.807633062296781 y[1] (numeric) = 2.807634725094881 absolute error = 1.662798100099394e-06 relative error = 5.922419572660054e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999998 y[1] (closed_form) = 2.812340890281375 y[1] (numeric) = 2.812344216873596 absolute error = 3.326592221242208e-06 relative error = 0.0001182855262225833 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999997 y[1] (closed_form) = 2.817015433909018 y[1] (numeric) = 2.81702042526352 absolute error = 4.991354502603684e-06 relative error = 0.0001771859125271975 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999996 y[1] (closed_form) = 2.821656674099206 y[1] (numeric) = 2.821663331156476 absolute error = 6.657057270320621e-06 relative error = 0.0002359272597345968 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999994 y[1] (closed_form) = 2.826264592323067 y[1] (numeric) = 2.826272915996097 absolute error = 8.323673030385947e-06 relative error = 0.000294511457030435 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999993 y[1] (closed_form) = 2.83083917059973 y[1] (numeric) = 2.830849161774197 absolute error = 9.991174467760544e-06 relative error = 0.0003529403779460864 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999992 y[1] (closed_form) = 2.835380391492725 y[1] (numeric) = 2.835392051027176 absolute error = 1.165953445081414e-05 relative error = 0.0004112158807967144 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999991 y[1] (closed_form) = 2.839888238106417 y[1] (numeric) = 2.839901566832439 absolute error = 1.332872602199942e-05 relative error = 0.0004693398086287633 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.08999999999999 y[1] (closed_form) = 2.844362694082461 y[1] (numeric) = 2.844377692804863 absolute error = 1.499872240140476e-05 relative error = 0.0005273139896191429 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.099999999999989 y[1] (closed_form) = 2.848803743596285 y[1] (numeric) = 2.84882041309327 absolute error = 1.666949698497788e-05 relative error = 0.0005851402372820028 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999988 y[1] (closed_form) = 2.8532113713536 y[1] (numeric) = 2.853229712376943 absolute error = 1.834102334363763e-05 relative error = 0.0006428203507031592 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999987 y[1] (closed_form) = 2.857585562586939 y[1] (numeric) = 2.857605575862157 absolute error = 2.001327521750085e-05 relative error = 0.0007003561145998744 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999986 y[1] (closed_form) = 2.861926303052219 y[1] (numeric) = 2.861947989278741 absolute error = 2.168622652209962e-05 relative error = 0.0007577492997975332 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999985 y[1] (closed_form) = 2.866233579025332 y[1] (numeric) = 2.86625693887667 absolute error = 2.335985133772311e-05 relative error = 0.000815001663111723 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999983 y[1] (closed_form) = 2.870507377298757 y[1] (numeric) = 2.870532411422675 absolute error = 2.503412391874349e-05 relative error = 0.0008721149479260854 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999982 y[1] (closed_form) = 2.874747685178202 y[1] (numeric) = 2.874774394196885 absolute error = 2.670901868340181e-05 relative error = 0.0009290908840838374 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999981 y[1] (closed_form) = 2.878954490479271 y[1] (numeric) = 2.878982874989487 absolute error = 2.83845102160285e-05 relative error = 0.0009859311882107322 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.17999999999998 y[1] (closed_form) = 2.883127781524151 y[1] (numeric) = 2.883157842097417 absolute error = 3.006057326659928e-05 relative error = 0.001042637563941336 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.189999999999979 y[1] (closed_form) = 2.887267547138328 y[1] (numeric) = 2.88729928432108 absolute error = 3.173718275162329e-05 relative error = 0.001099211702188082 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999978 y[1] (closed_form) = 2.891373776647332 y[1] (numeric) = 2.891407190961077 absolute error = 3.341431374526138e-05 relative error = 0.001155655281068734 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999977 y[1] (closed_form) = 2.89544645987349 y[1] (numeric) = 2.895481551814975 absolute error = 3.50919414850992e-05 relative error = 0.001211969966339231 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999976 y[1] (closed_form) = 2.89948558713272 y[1] (numeric) = 2.899522357174089 absolute error = 3.677004136903861e-05 relative error = 0.0012681574115152 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999975 y[1] (closed_form) = 2.903491149231342 y[1] (numeric) = 2.903529597820296 absolute error = 3.844858895396541e-05 relative error = 0.001324219258052298 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999974 y[1] (closed_form) = 2.907463137462911 y[1] (numeric) = 2.907503265022865 absolute error = 4.012755995397299e-05 relative error = 0.001380157135508477 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999972 y[1] (closed_form) = 2.91140154360507 y[1] (numeric) = 2.911443350535312 absolute error = 4.180693024169457e-05 relative error = 0.001435972661810392 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999971 y[1] (closed_form) = 2.915306359916441 y[1] (numeric) = 2.915349846592282 absolute error = 4.348667584030963e-05 relative error = 0.001491667443196469 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.26999999999997 y[1] (closed_form) = 2.919177579133517 y[1] (numeric) = 2.919222745906449 absolute error = 4.516677293286975e-05 relative error = 0.001547243074752457 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.279999999999969 y[1] (closed_form) = 2.923015194467592 y[1] (numeric) = 2.923062041665444 absolute error = 4.684719785208458e-05 relative error = 0.001602701140272981 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999968 y[1] (closed_form) = 2.926819199601709 y[1] (numeric) = 2.926867727528793 absolute error = 4.852792708343046e-05 relative error = 0.001658043212578156 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999967 y[1] (closed_form) = 2.93058958868763 y[1] (numeric) = 2.930639797624894 absolute error = 5.020893726470632e-05 relative error = 0.00171327085370527 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999966 y[1] (closed_form) = 2.934326356342824 y[1] (numeric) = 2.934378246548006 absolute error = 5.189020518159282e-05 relative error = 0.001768385614961582 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999965 y[1] (closed_form) = 2.938029497647483 y[1] (numeric) = 2.938083069355255 absolute error = 5.35717077716491e-05 relative error = 0.001823389037262717 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999964 y[1] (closed_form) = 2.941699008141555 y[1] (numeric) = 2.941754261563673 absolute error = 5.52534221176515e-05 relative error = 0.001878282651105027 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999963 y[1] (closed_form) = 2.945334883821801 y[1] (numeric) = 2.945391819147249 absolute error = 5.693532544892577e-05 relative error = 0.001933067976808388 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999961 y[1] (closed_form) = 2.948937121138864 y[1] (numeric) = 2.948995738534008 absolute error = 5.861739514401165e-05 relative error = 0.001987746524801245 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.35999999999996 y[1] (closed_form) = 2.952505716994378 y[1] (numeric) = 2.952566016603098 absolute error = 6.029960872000473e-05 relative error = 0.002042319795451205 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.369999999999959 y[1] (closed_form) = 2.956040668738076 y[1] (numeric) = 2.956102650681919 absolute error = 6.198194384321454e-05 relative error = 0.00209678927961686 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999958 y[1] (closed_form) = 2.95954197416493 y[1] (numeric) = 2.95960563854325 absolute error = 6.366437831983873e-05 relative error = 0.002151156458519308 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999957 y[1] (closed_form) = 2.96300963151231 y[1] (numeric) = 2.963074978402409 absolute error = 6.534689009907169e-05 relative error = 0.00220542280403317 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999956 y[1] (closed_form) = 2.966443639457161 y[1] (numeric) = 2.966510668914429 absolute error = 6.702945726777543e-05 relative error = 0.00225958977869006 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999955 y[1] (closed_form) = 2.9698439971132 y[1] (numeric) = 2.969912709171258 absolute error = 6.871205805758507e-05 relative error = 0.002313658836099666 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999954 y[1] (closed_form) = 2.973210704028132 y[1] (numeric) = 2.973281098698968 absolute error = 7.039467083558293e-05 relative error = 0.00236763142081426 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999953 y[1] (closed_form) = 2.97654376018089 y[1] (numeric) = 2.976615837454996 absolute error = 7.207727410563081e-05 relative error = 0.002421508968551181 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999952 y[1] (closed_form) = 2.979843165978886 y[1] (numeric) = 2.979916925825396 absolute error = 7.375984651059042e-05 relative error = 0.002475292906442616 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.44999999999995 y[1] (closed_form) = 2.983108922255287 y[1] (numeric) = 2.983184364622114 absolute error = 7.544236682743843e-05 relative error = 0.002528984653044535 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.459999999999949 y[1] (closed_form) = 2.986341030266308 y[1] (numeric) = 2.986418155080279 absolute error = 7.712481397037507e-05 relative error = 0.002582585618612267 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999948 y[1] (closed_form) = 2.989539491688526 y[1] (numeric) = 2.989618298855512 absolute error = 7.880716698593915e-05 relative error = 0.002636097205105927 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999947 y[1] (closed_form) = 2.992704308616204 y[1] (numeric) = 2.992784798021257 absolute error = 8.048940505345215e-05 relative error = 0.002689520806372937 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999946 y[1] (closed_form) = 2.995835483558646 y[1] (numeric) = 2.99591765506613 absolute error = 8.217150748457414e-05 relative error = 0.00274285780829879 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999945 y[1] (closed_form) = 2.99893301943756 y[1] (numeric) = 2.999016872891283 absolute error = 8.385345372285968e-05 relative error = 0.002796109588955945 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999944 y[1] (closed_form) = 3.001996919584443 y[1] (numeric) = 3.002082454807785 absolute error = 8.553522334198149e-05 relative error = 0.00284927751870651 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999943 y[1] (closed_form) = 3.005027187737983 y[1] (numeric) = 3.005114404534027 absolute error = 8.721679604395405e-05 relative error = 0.002902362960303397 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999942 y[1] (closed_form) = 3.008023828041478 y[1] (numeric) = 3.00811272619314 absolute error = 8.889815166179815e-05 relative error = 0.002955367269137614 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999941 y[1] (closed_form) = 3.010986845040275 y[1] (numeric) = 3.011077424310429 absolute error = 9.057927015421186e-05 relative error = 0.003008291793217724 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.549999999999939 y[1] (closed_form) = 3.013916243679221 y[1] (numeric) = 3.014008503810829 absolute error = 9.22601316077909e-05 relative error = 0.003061137873399059 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999938 y[1] (closed_form) = 3.016812029300137 y[1] (numeric) = 3.016905970016371 absolute error = 9.394071623392009e-05 relative error = 0.003113906843434099 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999937 y[1] (closed_form) = 3.019674207639305 y[1] (numeric) = 3.019769828643676 absolute error = 9.562100437143783e-05 relative error = 0.003166600030212915 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999936 y[1] (closed_form) = 3.022502784824975 y[1] (numeric) = 3.022600085801456 absolute error = 9.7300976480863e-05 relative error = 0.003219218753722255 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999935 y[1] (closed_form) = 3.025297767374884 y[1] (numeric) = 3.025396747988031 absolute error = 9.898061314705942e-05 relative error = 0.003271764327282964 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999934 y[1] (closed_form) = 3.028059162193794 y[1] (numeric) = 3.028159822088874 absolute error = 0.0001006598950801241 relative error = 0.003324238057726624 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999933 y[1] (closed_form) = 3.030786976571049 y[1] (numeric) = 3.030889315374158 absolute error = 0.0001023388031087258 relative error = 0.003376641245321344 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999932 y[1] (closed_form) = 3.033481218178144 y[1] (numeric) = 3.033585235496327 absolute error = 0.0001040173181832138 relative error = 0.003428975184019264 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999931 y[1] (closed_form) = 3.036141895066309 y[1] (numeric) = 3.036247590487686 absolute error = 0.0001056954213769501 relative error = 0.003481241161643459 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999993 y[1] (closed_form) = 3.038769015664119 y[1] (numeric) = 3.038876388757997 absolute error = 0.0001073730938778716 relative error = 0.003533440459751608 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999928 y[1] (closed_form) = 3.041362588775103 y[1] (numeric) = 3.041471639092101 absolute error = 0.0001090503169978163 relative error = 0.003585574354083704 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999927 y[1] (closed_form) = 3.043922623575383 y[1] (numeric) = 3.044033350647546 absolute error = 0.0001107270721636411 relative error = 0.003637644114408578 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999926 y[1] (closed_form) = 3.046449129611322 y[1] (numeric) = 3.046561532952242 absolute error = 0.0001124033409203307 relative error = 0.003689651004764079 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999925 y[1] (closed_form) = 3.048942116797189 y[1] (numeric) = 3.049056195902117 absolute error = 0.0001140791049274448 relative error = 0.003741596283476875 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999924 y[1] (closed_form) = 3.051401595412838 y[1] (numeric) = 3.051517349758802 absolute error = 0.0001157543459640031 relative error = 0.003793481203457987 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999923 y[1] (closed_form) = 3.053827576101401 y[1] (numeric) = 3.053945005147322 absolute error = 0.0001174290459209359 relative error = 0.00384530701208904 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999922 y[1] (closed_form) = 3.056220069867003 y[1] (numeric) = 3.056339173053805 absolute error = 0.0001191031868019721 relative error = 0.003897074951384474 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999921 y[1] (closed_form) = 3.05857908807248 y[1] (numeric) = 3.058699864823209 absolute error = 0.0001207767507289681 relative error = 0.003948786258297534 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999992 y[1] (closed_form) = 3.06090464243712 y[1] (numeric) = 3.061027092157052 absolute error = 0.0001224497199325825 relative error = 0.00400044216454541 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999919 y[1] (closed_form) = 3.063196745034417 y[1] (numeric) = 3.063320867111174 absolute error = 0.0001241220767571605 relative error = 0.004052043896898496 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999917 y[1] (closed_form) = 3.065455408289843 y[1] (numeric) = 3.0655812020935 absolute error = 0.0001257938036576256 relative error = 0.004103592677206924 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999916 y[1] (closed_form) = 3.06768064497862 y[1] (numeric) = 3.06780810986182 absolute error = 0.0001274648831999237 relative error = 0.004155089722542225 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999915 y[1] (closed_form) = 3.069872468223526 y[1] (numeric) = 3.070001603521584 absolute error = 0.0001291352980583582 relative error = 0.004206536245236476 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999914 y[1] (closed_form) = 3.0720308914927 y[1] (numeric) = 3.07216169652372 absolute error = 0.0001308050310195874 relative error = 0.004257933453137551 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999913 y[1] (closed_form) = 3.074155928597467 y[1] (numeric) = 3.074288402662443 absolute error = 0.0001324740649759626 relative error = 0.004309282549516014 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999912 y[1] (closed_form) = 3.076247593690177 y[1] (numeric) = 3.076381736073106 absolute error = 0.0001341423829295252 relative error = 0.004360584733318293 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999911 y[1] (closed_form) = 3.078305901262056 y[1] (numeric) = 3.078441711230042 absolute error = 0.0001358099679857894 relative error = 0.004411841199086467 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.81999999999991 y[1] (closed_form) = 3.080330866141069 y[1] (numeric) = 3.080468342944431 absolute error = 0.0001374768033621798 relative error = 0.004463053137353584 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999909 y[1] (closed_form) = 3.082322503489803 y[1] (numeric) = 3.082461646362181 absolute error = 0.0001391428723773735 relative error = 0.004514221734417346 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999907 y[1] (closed_form) = 3.084280828803354 y[1] (numeric) = 3.084421636961811 absolute error = 0.0001408081584575172 relative error = 0.004565348172661314 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999906 y[1] (closed_form) = 3.086205857907232 y[1] (numeric) = 3.086348330552363 absolute error = 0.0001424726451304537 relative error = 0.004616433630485845 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999905 y[1] (closed_form) = 3.088097606955285 y[1] (numeric) = 3.088241743271317 absolute error = 0.0001441363160323839 relative error = 0.004667479282641435 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999904 y[1] (closed_form) = 3.089956092427622 y[1] (numeric) = 3.090101891582521 absolute error = 0.0001457991548994286 relative error = 0.004718486300071715 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999903 y[1] (closed_form) = 3.091781331128562 y[1] (numeric) = 3.091928792274132 absolute error = 0.0001474611455702934 relative error = 0.004769455850115609 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999902 y[1] (closed_form) = 3.093573340184588 y[1] (numeric) = 3.093722462456574 absolute error = 0.0001491222719862684 relative error = 0.004820389096622177 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999901 y[1] (closed_form) = 3.095332137042318 y[1] (numeric) = 3.095482919560508 absolute error = 0.0001507825181894518 relative error = 0.004871287200007199 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.9099999999999 y[1] (closed_form) = 3.097057739466485 y[1] (numeric) = 3.097210181334809 absolute error = 0.0001524418683236384 relative error = 0.00492215131739516 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999899 y[1] (closed_form) = 3.098750165537933 y[1] (numeric) = 3.098904265844563 absolute error = 0.0001541003066298785 relative error = 0.004972982602588331 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999898 y[1] (closed_form) = 3.100409433651619 y[1] (numeric) = 3.100565191469073 absolute error = 0.0001557578174544716 relative error = 0.005023782206436594 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999896 y[1] (closed_form) = 3.102035562514637 y[1] (numeric) = 3.102192976899872 absolute error = 0.0001574143852347554 relative error = 0.005074551276489842 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999895 y[1] (closed_form) = 3.103628571144247 y[1] (numeric) = 3.103787641138758 absolute error = 0.0001590699945106522 relative error = 0.005125290957480978 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999894 y[1] (closed_form) = 3.105188478865915 y[1] (numeric) = 3.105349203495836 absolute error = 0.0001607246299211162 relative error = 0.005176002391320752 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999893 y[1] (closed_form) = 3.106715305311372 y[1] (numeric) = 3.106877683587571 absolute error = 0.0001623782761992487 relative error = 0.005226686717049353 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999892 y[1] (closed_form) = 3.108209070416675 y[1] (numeric) = 3.108373101334851 absolute error = 0.0001640309181754063 relative error = 0.005277345071044943 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999891 y[1] (closed_form) = 3.109669794420293 y[1] (numeric) = 3.109835476961067 absolute error = 0.0001656825407740925 relative error = 0.005327978587031269 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99999999999989 y[1] (closed_form) = 3.111097497861188 y[1] (numeric) = 3.111264830990206 absolute error = 0.0001673331290179547 relative error = 0.005378588396313282 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 Finished! diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 1001 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %