##############ECHO OF PROBLEM################# ##############temp/sinh_sqrtpostode.ode################# diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; ! /* 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(0.01); glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-2.0); 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(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * cosh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * sinh( sqrt(c(0.1) * c(x) + c(0.2)))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 1.754980921980319 y[1] (numeric) = 1.754980921980319 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) = 1.761740396662258 y[1] (numeric) = 1.761739919816042 absolute error = 4.768462165127829e-07 relative error = 2.706676973612013e-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) = 1.768509403906236 y[1] (numeric) = 1.768508450597341 absolute error = 9.53308895823568e-07 relative error = 5.390465516993717e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999997 y[1] (closed_form) = 1.775287936060636 y[1] (numeric) = 1.775286506670873 absolute error = 1.429389762774846e-06 relative error = 8.051593962535804e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999996 y[1] (closed_form) = 1.782075985508248 y[1] (numeric) = 1.782074080417719 absolute error = 1.905090529552567e-06 relative error = 0.0001069028787237282 % 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) = 1.788873544666064 y[1] (numeric) = 1.788871164253159 absolute error = 2.380412904789964e-06 relative error = 0.00013306770128541 % 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) = 1.795680605985051 y[1] (numeric) = 1.795677750626464 absolute error = 2.85535858735031e-06 relative error = 0.0001590126093601124 % 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) = 1.802497161949926 y[1] (numeric) = 1.802493832020676 absolute error = 3.329929249673569e-06 relative error = 0.0001847397776799426 % 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) = 1.809323205078972 y[1] (numeric) = 1.8093194009524 absolute error = 3.804126571971267e-06 relative error = 0.0002102513559375495 % 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) = 1.816158727923806 y[1] (numeric) = 1.816154449971588 absolute error = 4.277952218245673e-06 relative error = 0.0002355494678119977 % 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) = 1.823003723069165 y[1] (numeric) = 1.822998971661338 absolute error = 4.751407827852105e-06 relative error = 0.0002606362108714046 % 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) = 1.829858183132746 y[1] (numeric) = 1.829852958637679 absolute error = 5.224495066791235e-06 relative error = 0.0002855136597442113 % 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) = 1.836722100764916 y[1] (numeric) = 1.836716403549375 absolute error = 5.697215541333733e-06 relative error = 0.0003101838617263377 % 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) = 1.843595468648594 y[1] (numeric) = 1.843589299077714 absolute error = 6.169570880176778e-06 relative error = 0.000334648841630059 % 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) = 1.850478279499015 y[1] (numeric) = 1.85047163793631 absolute error = 6.641562704912118e-06 relative error = 0.0003589106004913609 % 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) = 1.857370526063509 y[1] (numeric) = 1.857363412870903 absolute error = 7.113192605601171e-06 relative error = 0.0003829711145829796 % 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) = 1.864272201121342 y[1] (numeric) = 1.864264616659161 absolute error = 7.584462180076912e-06 relative error = 0.0004068323378697023 % 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) = 1.871183297483487 y[1] (numeric) = 1.871175242110485 absolute error = 8.055373002413546e-06 relative error = 0.0004304962006259376 % 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) = 1.878103807992462 y[1] (numeric) = 1.878095282065808 absolute error = 8.525926653568661e-06 relative error = 0.0004539646113961173 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.189999999999979 y[1] (closed_form) = 1.885033725522101 y[1] (numeric) = 1.885024729397412 absolute error = 8.996124689186757e-06 relative error = 0.0004772394555803019 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999978 y[1] (closed_form) = 1.891973042977392 y[1] (numeric) = 1.891963577008728 absolute error = 9.465968664912339e-06 relative error = 0.0005003225970923863 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999977 y[1] (closed_form) = 1.898921753294275 y[1] (numeric) = 1.89891181783415 absolute error = 9.935460124399498e-06 relative error = 0.0005232158780193723 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999976 y[1] (closed_form) = 1.905879849439454 y[1] (numeric) = 1.905869444838848 absolute error = 1.040460060641735e-05 relative error = 0.0005459211192918317 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999975 y[1] (closed_form) = 1.912847324410205 y[1] (numeric) = 1.912836451018578 absolute error = 1.087339162642031e-05 relative error = 0.0005684401200065953 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999974 y[1] (closed_form) = 1.919824171234202 y[1] (numeric) = 1.9198128293995 absolute error = 1.134183470252736e-05 relative error = 0.0005907746590791183 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999972 y[1] (closed_form) = 1.926810382969339 y[1] (numeric) = 1.926798573037991 absolute error = 1.180993134819452e-05 relative error = 0.0006129264951330943 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999971 y[1] (closed_form) = 1.933805952703517 y[1] (numeric) = 1.933793675020467 absolute error = 1.227768305001042e-05 relative error = 0.0006348973656248117 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.26999999999997 y[1] (closed_form) = 1.940810873554508 y[1] (numeric) = 1.940798128463201 absolute error = 1.27450913065541e-05 relative error = 0.000656688989134322 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.279999999999969 y[1] (closed_form) = 1.947825138669735 y[1] (numeric) = 1.947811926512142 absolute error = 1.321215759308991e-05 relative error = 0.0006783030638013605 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999968 y[1] (closed_form) = 1.954848741226117 y[1] (numeric) = 1.95483506234274 absolute error = 1.367888337666656e-05 relative error = 0.0006997412683749084 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999967 y[1] (closed_form) = 1.961881674429893 y[1] (numeric) = 1.961867529159771 absolute error = 1.414527012211231e-05 relative error = 0.0007210052627777772 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999966 y[1] (closed_form) = 1.968923931516439 y[1] (numeric) = 1.968909320197158 absolute error = 1.461131928137682e-05 relative error = 0.0007420966878148196 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999965 y[1] (closed_form) = 1.97597550575011 y[1] (numeric) = 1.975960428717801 absolute error = 1.507703230907431e-05 relative error = 0.0007630171662148637 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999964 y[1] (closed_form) = 1.983036390424029 y[1] (numeric) = 1.983020848013407 absolute error = 1.55424106220714e-05 relative error = 0.0007837683008302229 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999963 y[1] (closed_form) = 1.990106578859983 y[1] (numeric) = 1.990090571404316 absolute error = 1.600745566676665e-05 relative error = 0.0008043516782873202 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999961 y[1] (closed_form) = 1.997186064408181 y[1] (numeric) = 1.997169592239333 absolute error = 1.647216884781422e-05 relative error = 0.0008247688656237122 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.35999999999996 y[1] (closed_form) = 2.004274840447152 y[1] (numeric) = 2.004257903895563 absolute error = 1.693655158918617e-05 relative error = 0.0008450214136005236 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.369999999999959 y[1] (closed_form) = 2.011372900383519 y[1] (numeric) = 2.011355499778241 absolute error = 1.740060527799514e-05 relative error = 0.0008651108541174677 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999958 y[1] (closed_form) = 2.018480237651891 y[1] (numeric) = 2.01846237332057 absolute error = 1.786433132178189e-05 relative error = 0.0008850387033049955 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999957 y[1] (closed_form) = 2.025596845714654 y[1] (numeric) = 2.025578517983556 absolute error = 1.832773109811114e-05 relative error = 0.0009048064592362113 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999956 y[1] (closed_form) = 2.032722718061837 y[1] (numeric) = 2.032703927255848 absolute error = 1.879080598943261e-05 relative error = 0.000924415603882722 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999955 y[1] (closed_form) = 2.039857848210939 y[1] (numeric) = 2.039838594653574 absolute error = 1.925355736531742e-05 relative error = 0.0009438676024510132 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999954 y[1] (closed_form) = 2.047002229706774 y[1] (numeric) = 2.046982513720185 absolute error = 1.971598658867535e-05 relative error = 0.0009631639039054491 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999953 y[1] (closed_form) = 2.054155856121305 y[1] (numeric) = 2.054135678026292 absolute error = 2.01780950135344e-05 relative error = 0.000982305941070852 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999952 y[1] (closed_form) = 2.061318721053492 y[1] (numeric) = 2.061298081169512 absolute error = 2.063988398015582e-05 relative error = 0.0010012951306049 % 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) = 2.068490818129149 y[1] (numeric) = 2.068469716774315 absolute error = 2.11013548336858e-05 relative error = 0.001020132874110167 % 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) = 2.075672141000775 y[1] (numeric) = 2.075650578491864 absolute error = 2.156250891083289e-05 relative error = 0.001038820557683866 % 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) = 2.082862683347386 y[1] (numeric) = 2.082840659999864 absolute error = 2.202334752254842e-05 relative error = 0.001057359551286142 % 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) = 2.090062438874401 y[1] (numeric) = 2.09003995500241 absolute error = 2.248387199133006e-05 relative error = 0.001075751210736015 % 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) = 2.09727140131346 y[1] (numeric) = 2.097248457229838 absolute error = 2.2944083622356e-05 relative error = 0.001093996876512348 % 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) = 2.104489564422288 y[1] (numeric) = 2.104466160438572 absolute error = 2.340398371591945e-05 relative error = 0.001112097874542998 % 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) = 2.111716921984545 y[1] (numeric) = 2.111693058410976 absolute error = 2.386357356920499e-05 relative error = 0.001130055516474174 % 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) = 2.118953467809677 y[1] (numeric) = 2.118929144955208 absolute error = 2.432285446829496e-05 relative error = 0.001147871099474263 % 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) = 2.12619919573277 y[1] (numeric) = 2.126174413905076 absolute error = 2.478182769394266e-05 relative error = 0.001165545906690172 % 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) = 2.133454099614392 y[1] (numeric) = 2.133428859119888 absolute error = 2.524049450380872e-05 relative error = 0.001183081206592201 % 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) = 2.14071817334049 y[1] (numeric) = 2.14069247448431 absolute error = 2.569885617997869e-05 relative error = 0.001200478255382717 % 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) = 2.147991410822195 y[1] (numeric) = 2.147965253908225 absolute error = 2.615691396989916e-05 relative error = 0.001217738294395087 % 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) = 2.155273805995716 y[1] (numeric) = 2.15524719132659 absolute error = 2.661466912590171e-05 relative error = 0.001234862552120425 % 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) = 2.162565352822183 y[1] (numeric) = 2.162538280699294 absolute error = 2.707212288877159e-05 relative error = 0.001251852243606975 % 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) = 2.169866045287527 y[1] (numeric) = 2.169838516011023 absolute error = 2.752927650462311e-05 relative error = 0.001268708571407468 % 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) = 2.177175877402306 y[1] (numeric) = 2.177147891271114 absolute error = 2.798613119159299e-05 relative error = 0.001285432724203458 % 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) = 2.184494843201596 y[1] (numeric) = 2.184466400513426 absolute error = 2.844268817092654e-05 relative error = 0.001302025878405871 % 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) = 2.191822936744867 y[1] (numeric) = 2.191794037796197 absolute error = 2.889894867008636e-05 relative error = 0.001318489198447979 % 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) = 2.199160152115804 y[1] (numeric) = 2.199130797201915 absolute error = 2.935491388900147e-05 relative error = 0.001334823835397309 % 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) = 2.206506483422208 y[1] (numeric) = 2.206476672837177 absolute error = 2.981058503115364e-05 relative error = 0.001351030928534529 % 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) = 2.213861924795859 y[1] (numeric) = 2.213831658832563 absolute error = 3.026596329602782e-05 relative error = 0.001367111605156616 % 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) = 2.221226470392365 y[1] (numeric) = 2.221195749342497 absolute error = 3.072104986756585e-05 relative error = 0.001383066980204823 % 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) = 2.22860011439105 y[1] (numeric) = 2.228568938545119 absolute error = 3.117584593059775e-05 relative error = 0.001398898157156217 % 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) = 2.235982850994821 y[1] (numeric) = 2.235951220642157 absolute error = 3.163035266462444e-05 relative error = 0.001414606227885497 % 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) = 2.243374674430026 y[1] (numeric) = 2.243342589858793 absolute error = 3.208457123271558e-05 relative error = 0.001430192272312573 % 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) = 2.250775578946346 y[1] (numeric) = 2.25074304044354 absolute error = 3.253850280637849e-05 relative error = 0.001445657359656031 % 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) = 2.258185558816646 y[1] (numeric) = 2.25815256666811 absolute error = 3.299214853536014e-05 relative error = 0.001461002547224196 % 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) = 2.265604608336863 y[1] (numeric) = 2.265571162827293 absolute error = 3.344550957073977e-05 relative error = 0.001476228881582805 % 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) = 2.273032721825883 y[1] (numeric) = 2.272998823238824 absolute error = 3.389858705915572e-05 relative error = 0.001491337398430659 % 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) = 2.280469893625405 y[1] (numeric) = 2.280435542243267 absolute error = 3.435138213836453e-05 relative error = 0.001506329122536847 % 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) = 2.287916118099833 y[1] (numeric) = 2.287881314203887 absolute error = 3.480389594656685e-05 relative error = 0.001521205068281624 % 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) = 2.295371389636124 y[1] (numeric) = 2.295336133506526 absolute error = 3.525612959753843e-05 relative error = 0.001535966238697758 % 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) = 2.302835702643701 y[1] (numeric) = 2.302799994559487 absolute error = 3.570808421393679e-05 relative error = 0.001550613627057423 % 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) = 2.310309051554327 y[1] (numeric) = 2.310272891793409 absolute error = 3.615976091841944e-05 relative error = 0.001565148216602965 % 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) = 2.317791430821954 y[1] (numeric) = 2.317754819661145 absolute error = 3.6611160809219e-05 relative error = 0.001579570979612935 % 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) = 2.325282834922643 y[1] (numeric) = 2.325245772637649 absolute error = 3.706228499389397e-05 relative error = 0.001593882878988652 % 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) = 2.332783258354425 y[1] (numeric) = 2.332745745219856 absolute error = 3.75131345689006e-05 relative error = 0.001608084867488411 % 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) = 2.340292695637187 y[1] (numeric) = 2.340254731926563 absolute error = 3.796371062403381e-05 relative error = 0.001622177888039663 % 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) = 2.347811141312549 y[1] (numeric) = 2.347772727298312 absolute error = 3.84140142375422e-05 relative error = 0.001636162873648634 % 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) = 2.355338589943777 y[1] (numeric) = 2.355299725897278 absolute error = 3.886404649922071e-05 relative error = 0.00165004074850013 % 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) = 2.362875036115629 y[1] (numeric) = 2.362835722307153 absolute error = 3.931380847577159e-05 relative error = 0.001663812426593674 % 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) = 2.370420474434255 y[1] (numeric) = 2.37038071113303 absolute error = 3.976330122457128e-05 relative error = 0.001677478812448308 % 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) = 2.377974899527121 y[1] (numeric) = 2.377934687001293 absolute error = 4.021252582786516e-05 relative error = 0.001691040802653625 % 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) = 2.385538306042829 y[1] (numeric) = 2.385497644559504 absolute error = 4.0661483324822e-05 relative error = 0.001704499283110316 % 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) = 2.393110688651063 y[1] (numeric) = 2.39306957847629 absolute error = 4.111017477326229e-05 relative error = 0.001717855131742154 % 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) = 2.400692042042458 y[1] (numeric) = 2.400650483441236 absolute error = 4.155860122212474e-05 relative error = 0.001731109217439133 % 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) = 2.408282360928474 y[1] (numeric) = 2.408240354164771 absolute error = 4.200676370302858e-05 relative error = 0.001744262399814013 % 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) = 2.415881640041317 y[1] (numeric) = 2.415839185378064 absolute error = 4.245466325292213e-05 relative error = 0.001757315530250732 % 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) = 2.423489874133814 y[1] (numeric) = 2.423446971832911 absolute error = 4.290230090342462e-05 relative error = 0.001770269451559332 % 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) = 2.431107057979302 y[1] (numeric) = 2.43106370830163 absolute error = 4.334967767238851e-05 relative error = 0.001783124997729227 % 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) = 2.43873318637154 y[1] (numeric) = 2.438689389576955 absolute error = 4.379679458432761e-05 relative error = 0.001795882994871223 % 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) = 2.446368254124581 y[1] (numeric) = 2.446324010471931 absolute error = 4.42436526491008e-05 relative error = 0.001808544260436095 % 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) = 2.454012256072676 y[1] (numeric) = 2.453967565819805 absolute error = 4.469025287123785e-05 relative error = 0.001821109603696874 % 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) = 2.461665187070185 y[1] (numeric) = 2.461620050473926 absolute error = 4.513659625926536e-05 relative error = 0.001833579826222666 % 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) = 2.469327041991441 y[1] (numeric) = 2.469281459307638 absolute error = 4.558268380350228e-05 relative error = 0.001845955721067273 % 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) = 2.476997815730684 y[1] (numeric) = 2.47695178721418 absolute error = 4.60285165040375e-05 relative error = 0.001858238073999256 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 Finished! diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; 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 %