##############ECHO OF PROBLEM################# ##############temp/exp_sqrtpostode.ode################# diff ( y , x , 1 ) = exp ( sqrt ( 0.1 * x + 0.2 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=16; 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) * exp(sqrt(c(0.1) * x + c(0.2))) * sqrt( c(0.1) * x + c(0.2)) - c(20.0) * exp(sqrt(c(0.1) * 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) = -13.83604079041925 y[1] (numeric) = -13.83604079041925 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) = -13.8172110836278 y[1] (numeric) = -13.81721182750928 absolute error = 7.43881479081665e-07 relative error = 5.3837310190846e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999998 y[1] (closed_form) = -13.79836650334326 y[1] (numeric) = -13.79836799076601 absolute error = 1.487422750301448e-06 relative error = 1.077970171281546e-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) = -13.77950705634999 y[1] (numeric) = -13.77950928697554 absolute error = 2.230625552712695e-06 relative error = 1.618799238311475e-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) = -13.76063274939782 y[1] (numeric) = -13.76063572288942 absolute error = 2.973491604052469e-06 relative error = 2.160868368631227e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999994 y[1] (closed_form) = -13.74174358920232 y[1] (numeric) = -13.74174730522493 absolute error = 3.716022609623337e-06 relative error = 2.704185670109017e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999993 y[1] (closed_form) = -13.722839582445 y[1] (numeric) = -13.72284404066528 absolute error = 4.458220274727864e-06 relative error = 3.248759302288326e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999992 y[1] (closed_form) = -13.70392073577352 y[1] (numeric) = -13.70392593585979 absolute error = 5.200086278023264e-06 relative error = 3.794597457389442e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999991 y[1] (closed_form) = -13.68498705580188 y[1] (numeric) = -13.68499299742418 absolute error = 5.941622303495819e-06 relative error = 4.341708383989164e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.08999999999999 y[1] (closed_form) = -13.66603854911068 y[1] (numeric) = -13.6660452319407 absolute error = 6.682830017368246e-06 relative error = 4.890100370603104e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.099999999999989 y[1] (closed_form) = -13.64707522224732 y[1] (numeric) = -13.64708264595839 absolute error = 7.423711071652406e-06 relative error = 5.439781748656556e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999988 y[1] (closed_form) = -13.62809708172614 y[1] (numeric) = -13.62810524599325 absolute error = 8.164267116583801e-06 relative error = 5.990760901998002e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999987 y[1] (closed_form) = -13.6091041340287 y[1] (numeric) = -13.60911303852849 absolute error = 8.904499784634368e-06 relative error = 6.543046255608573e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999986 y[1] (closed_form) = -13.59009638560397 y[1] (numeric) = -13.59010603001468 absolute error = 9.644410706499684e-06 relative error = 7.096646287745269e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999985 y[1] (closed_form) = -13.57107384286851 y[1] (numeric) = -13.57108422687 absolute error = 1.038400149511176e-05 relative error = 7.651569518626171e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999983 y[1] (closed_form) = -13.55203651220666 y[1] (numeric) = -13.55204763548041 absolute error = 1.112327375629718e-05 relative error = 8.207824518682612e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999982 y[1] (closed_form) = -13.53298439997077 y[1] (numeric) = -13.53299626219986 absolute error = 1.186222909055346e-05 relative error = 8.765419910318583e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999981 y[1] (closed_form) = -13.51391751248139 y[1] (numeric) = -13.51393011335047 absolute error = 1.26008690735091e-05 relative error = 9.324364353912179e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.17999999999998 y[1] (closed_form) = -13.49483585602745 y[1] (numeric) = -13.49484919522274 absolute error = 1.333919529145078e-05 relative error = 9.884666574505125e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.189999999999979 y[1] (closed_form) = -13.47573943686646 y[1] (numeric) = -13.47575351407576 absolute error = 1.407720930401979e-05 relative error = 0.0001044633533467399 % 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) = -13.4566282612247 y[1] (numeric) = -13.45664307613737 absolute error = 1.481491267085744e-05 relative error = 0.0001100937945469345 % 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) = -13.4375023352974 y[1] (numeric) = -13.43751788760435 absolute error = 1.555230694805232e-05 relative error = 0.0001157380781039925 % 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) = -13.41836166524898 y[1] (numeric) = -13.41837795464264 absolute error = 1.628939366149496e-05 relative error = 0.0001213962931382406 % 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) = -13.39920625721314 y[1] (numeric) = -13.39922328338749 absolute error = 1.702617434773401e-05 relative error = 0.0001270685294404538 % 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) = -13.38003611729314 y[1] (numeric) = -13.38005387994366 absolute error = 1.776265051844916e-05 relative error = 0.0001327548772121151 % 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) = -13.36085125156194 y[1] (numeric) = -13.36086975038563 absolute error = 1.84988236924255e-05 relative error = 0.0001384554273086673 % 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) = -13.34165166606237 y[1] (numeric) = -13.34167090075774 absolute error = 1.923469536713185e-05 relative error = 0.0001441702710321828 % 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) = -13.32243736680732 y[1] (numeric) = -13.32245733707437 absolute error = 1.99702670489188e-05 relative error = 0.0001498995003622569 % 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) = -13.30320835977997 y[1] (numeric) = -13.30322906532018 absolute error = 2.070554020683346e-05 relative error = 0.0001556432076147376 % 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) = -13.28396465093387 y[1] (numeric) = -13.28398609145018 absolute error = 2.144051631347565e-05 relative error = 0.000161401485752737 % 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) = -13.2647062461932 y[1] (numeric) = -13.26472842139005 absolute error = 2.217519684677427e-05 relative error = 0.0001671744284057422 % 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) = -13.2454331514529 y[1] (numeric) = -13.24545606103616 absolute error = 2.290958325801284e-05 relative error = 0.0001729621296340911 % 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) = -13.22614537257887 y[1] (numeric) = -13.22616901625586 absolute error = 2.36436769949222e-05 relative error = 0.0001787646841077484 % 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) = -13.2068429154081 y[1] (numeric) = -13.20686729288761 absolute error = 2.437747950345681e-05 relative error = 0.0001845821871252531 % 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) = -13.18752578574891 y[1] (numeric) = -13.18755089674112 absolute error = 2.511099220470214e-05 relative error = 0.0001904147344442603 % 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) = -13.16819398938103 y[1] (numeric) = -13.16821983359757 absolute error = 2.584421653573088e-05 relative error = 0.0001962624225962339 % 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) = -13.14884753205585 y[1] (numeric) = -13.14887410920976 absolute error = 2.6577153905194e-05 relative error = 0.0002021253485554608 % 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) = -13.12948641949654 y[1] (numeric) = -13.12951372930226 absolute error = 2.730980571818975e-05 relative error = 0.0002080036099328016 % 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) = -13.11011065739822 y[1] (numeric) = -13.11013869957159 absolute error = 2.804217337448733e-05 relative error = 0.0002138973049679237 % 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) = -13.09072025142812 y[1] (numeric) = -13.09074902568639 absolute error = 2.877425826675051e-05 relative error = 0.0002198065325214738 % 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) = -13.07131520722577 y[1] (numeric) = -13.07134471328755 absolute error = 2.950606178409032e-05 relative error = 0.0002257313921079609 % 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) = -13.05189553040314 y[1] (numeric) = -13.05192576798842 absolute error = 3.02375852836434e-05 relative error = 0.0002316719836839625 % 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) = -13.03246122654479 y[1] (numeric) = -13.03249219537493 absolute error = 3.096883014208629e-05 relative error = 0.0002376284080478086 % 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) = -13.01301230120804 y[1] (numeric) = -13.01304400100576 absolute error = 3.169979771833198e-05 relative error = 0.0002436007665603235 % 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) = -12.99354875992313 y[1] (numeric) = -12.9935811904125 absolute error = 3.243048936418802e-05 relative error = 0.0002495891612321919 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.44999999999995 y[1] (closed_form) = -12.97407060819338 y[1] (numeric) = -12.9741037690998 absolute error = 3.316090642080383e-05 relative error = 0.0002555936947025868 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.459999999999949 y[1] (closed_form) = -12.95457785149532 y[1] (numeric) = -12.95461174254554 absolute error = 3.389105022044703e-05 relative error = 0.0002616144702587515 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999948 y[1] (closed_form) = -12.93507049527886 y[1] (numeric) = -12.93510511620096 absolute error = 3.462092209716161e-05 relative error = 0.0002676515919244337 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999947 y[1] (closed_form) = -12.91554854496747 y[1] (numeric) = -12.91558389549084 absolute error = 3.535052336900435e-05 relative error = 0.0002737051643290725 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999946 y[1] (closed_form) = -12.89601200595826 y[1] (numeric) = -12.8960480858136 absolute error = 3.607985534159752e-05 relative error = 0.000279775292741103 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999945 y[1] (closed_form) = -12.8764608836222 y[1] (numeric) = -12.87649769254154 absolute error = 3.680891933122155e-05 relative error = 0.000285862083253322 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999944 y[1] (closed_form) = -12.85689518330424 y[1] (numeric) = -12.85693272102087 absolute error = 3.753771662928784e-05 relative error = 0.0002919656425140163 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999943 y[1] (closed_form) = -12.83731491032345 y[1] (numeric) = -12.83735317657197 absolute error = 3.826624852365512e-05 relative error = 0.0002980860778984424 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999942 y[1] (closed_form) = -12.81772006997317 y[1] (numeric) = -12.81775906448947 absolute error = 3.899451630218209e-05 relative error = 0.0003042234975433016 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999941 y[1] (closed_form) = -12.79811066752116 y[1] (numeric) = -12.7981503900424 absolute error = 3.972252124029296e-05 relative error = 0.0003103780102566244 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.549999999999939 y[1] (closed_form) = -12.77848670820975 y[1] (numeric) = -12.77852715847436 absolute error = 4.045026460453016e-05 relative error = 0.0003165497255519482 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999938 y[1] (closed_form) = -12.75884819725598 y[1] (numeric) = -12.75888937500364 absolute error = 4.117774766143611e-05 relative error = 0.0003227387537245887 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999937 y[1] (closed_form) = -12.73919513985172 y[1] (numeric) = -12.73923704482339 absolute error = 4.190497166156604e-05 relative error = 0.0003289452057334117 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999936 y[1] (closed_form) = -12.71952754116384 y[1] (numeric) = -12.71957017310169 absolute error = 4.263193785192243e-05 relative error = 0.0003351691933049707 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999935 y[1] (closed_form) = -12.69984540633434 y[1] (numeric) = -12.69988876498181 absolute error = 4.335864747062601e-05 relative error = 0.000341410828898751 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999934 y[1] (closed_form) = -12.68014874048046 y[1] (numeric) = -12.68019282558222 absolute error = 4.408510176112657e-05 relative error = 0.0003476702258262008 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999933 y[1] (closed_form) = -12.66043754869487 y[1] (numeric) = -12.66048235999682 absolute error = 4.481130194378125e-05 relative error = 0.0003539474980341474 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999932 y[1] (closed_form) = -12.64071183604578 y[1] (numeric) = -12.64075737329502 absolute error = 4.553724923539448e-05 relative error = 0.0003602427602656218 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999931 y[1] (closed_form) = -12.62097160757705 y[1] (numeric) = -12.62101787052191 absolute error = 4.626294485987614e-05 relative error = 0.0003665561281518295 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999993 y[1] (closed_form) = -12.60121686830837 y[1] (numeric) = -12.60126385669838 absolute error = 4.698839001093802e-05 relative error = 0.0003728877179243872 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999928 y[1] (closed_form) = -12.58144762323536 y[1] (numeric) = -12.58149533682126 absolute error = 4.771358589650276e-05 relative error = 0.0003792376467743309 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999927 y[1] (closed_form) = -12.56166387732971 y[1] (numeric) = -12.56171231586342 absolute error = 4.843853370850582e-05 relative error = 0.0003856060326205974 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999926 y[1] (closed_form) = -12.54186563553934 y[1] (numeric) = -12.54191479877397 absolute error = 4.916323463177719e-05 relative error = 0.0003919929941879257 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999925 y[1] (closed_form) = -12.52205290278847 y[1] (numeric) = -12.52210279047832 absolute error = 4.988768985292324e-05 relative error = 0.0003983986510855103 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999924 y[1] (closed_form) = -12.5022256839778 y[1] (numeric) = -12.50227629587834 absolute error = 5.061190054256315e-05 relative error = 0.0004048231236732889 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999923 y[1] (closed_form) = -12.48238398398463 y[1] (numeric) = -12.4824353198525 absolute error = 5.13358678695397e-05 relative error = 0.0004112665331831289 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999922 y[1] (closed_form) = -12.46252780766295 y[1] (numeric) = -12.46257986725595 absolute error = 5.205959299203755e-05 relative error = 0.0004177290016558853 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999921 y[1] (closed_form) = -12.44265715984364 y[1] (numeric) = -12.44270994292071 absolute error = 5.278307706468865e-05 relative error = 0.0004242106520063592 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999992 y[1] (closed_form) = -12.42277204533452 y[1] (numeric) = -12.42282555165576 absolute error = 5.350632123857224e-05 relative error = 0.0004307116080316954 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999919 y[1] (closed_form) = -12.4028724689205 y[1] (numeric) = -12.40292669824715 absolute error = 5.42293266541094e-05 relative error = 0.0004372319943625877 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999917 y[1] (closed_form) = -12.38295843536372 y[1] (numeric) = -12.38301338745817 absolute error = 5.495209444816851e-05 relative error = 0.0004437719365287881 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999916 y[1] (closed_form) = -12.36302994940366 y[1] (numeric) = -12.36308562402942 absolute error = 5.56746257593943e-05 relative error = 0.0004503315610108976 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999915 y[1] (closed_form) = -12.34308701575727 y[1] (numeric) = -12.34314341267897 absolute error = 5.639692170156252e-05 relative error = 0.0004569109950336233 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999914 y[1] (closed_form) = -12.32312963911907 y[1] (numeric) = -12.32318675810247 absolute error = 5.711898339733068e-05 relative error = 0.0004635103668471499 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999913 y[1] (closed_form) = -12.30315782416129 y[1] (numeric) = -12.30321566497325 absolute error = 5.78408119533691e-05 relative error = 0.0004701298055348007 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999912 y[1] (closed_form) = -12.28317157553397 y[1] (numeric) = -12.28323013794246 absolute error = 5.856240848522987e-05 relative error = 0.0004767694412237667 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999911 y[1] (closed_form) = -12.26317089786511 y[1] (numeric) = -12.26323018163919 absolute error = 5.92837740871488e-05 relative error = 0.0004834294048488675 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.81999999999991 y[1] (closed_form) = -12.24315579576074 y[1] (numeric) = -12.24321580067059 absolute error = 6.0004909849809e-05 relative error = 0.0004901098283057546 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999909 y[1] (closed_form) = -12.22312627380508 y[1] (numeric) = -12.22318699962196 absolute error = 6.072581687632805e-05 relative error = 0.0004968108445911031 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999907 y[1] (closed_form) = -12.20308233656065 y[1] (numeric) = -12.20314378305689 absolute error = 6.14464962396255e-05 relative error = 0.0005035325874638304 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999906 y[1] (closed_form) = -12.18302398856835 y[1] (numeric) = -12.18308615551737 absolute error = 6.216694901794995e-05 relative error = 0.000510275191744536 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999905 y[1] (closed_form) = -12.1629512343476 y[1] (numeric) = -12.16301412152388 absolute error = 6.288717627889184e-05 relative error = 0.0005170387931943804 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999904 y[1] (closed_form) = -12.14286407839646 y[1] (numeric) = -12.14292768557557 absolute error = 6.360717910247615e-05 relative error = 0.0005238235287146182 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999903 y[1] (closed_form) = -12.12276252519174 y[1] (numeric) = -12.12282685215027 absolute error = 6.432695853497705e-05 relative error = 0.0005306295359766577 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999902 y[1] (closed_form) = -12.10264657918906 y[1] (numeric) = -12.1027116257047 absolute error = 6.504651563865593e-05 relative error = 0.0005374569538410366 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999901 y[1] (closed_form) = -12.08251624482306 y[1] (numeric) = -12.08258201067451 absolute error = 6.57658514544579e-05 relative error = 0.0005443059220602025 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.9099999999999 y[1] (closed_form) = -12.06237152650741 y[1] (numeric) = -12.06243801147444 absolute error = 6.648496703576257e-05 relative error = 0.0005511765815673969 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999899 y[1] (closed_form) = -12.04221242863498 y[1] (numeric) = -12.0422796324984 absolute error = 6.720386341463325e-05 relative error = 0.000558069074207911 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999898 y[1] (closed_form) = -12.02203895557794 y[1] (numeric) = -12.02210687811957 absolute error = 6.792254162846234e-05 relative error = 0.0005649835429700377 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999896 y[1] (closed_form) = -12.00185111168782 y[1] (numeric) = -12.00191975269053 absolute error = 6.864100271108953e-05 relative error = 0.0005719201319223543 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999895 y[1] (closed_form) = -11.9816489012957 y[1] (numeric) = -11.98171826054337 absolute error = 6.93592476750382e-05 relative error = 0.0005788789860762628 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999894 y[1] (closed_form) = -11.96143232871223 y[1] (numeric) = -11.96150240598977 absolute error = 7.007727753638449e-05 relative error = 0.0005858602516035719 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999893 y[1] (closed_form) = -11.94120139822781 y[1] (numeric) = -11.94127219332112 absolute error = 7.079509331298084e-05 relative error = 0.0005928640758331696 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999892 y[1] (closed_form) = -11.92095611411263 y[1] (numeric) = -11.92102762680864 absolute error = 7.151269601024524e-05 relative error = 0.0005998906071433724 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999891 y[1] (closed_form) = -11.90069648061681 y[1] (numeric) = -11.90076871070344 absolute error = 7.223008663004293e-05 relative error = 0.0006069399950472416 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99999999999989 y[1] (closed_form) = -11.88042250197051 y[1] (numeric) = -11.88049544923667 absolute error = 7.294726616713376e-05 relative error = 0.0006140123901741256 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 Finished! diff ( y , x , 1 ) = exp ( 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 %