##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrtpostode.ode################# diff ( y , x , 1 ) = sqrt(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(0.8 * (x + 2.0) * sqrt(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) = 1.137271367855683 y[1] (numeric) = 1.137271367855683 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10001 y[1] (analytic) = 1.13727813733214 y[1] (numeric) = 1.13727813733214 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10002 y[1] (analytic) = 1.137284906816656 y[1] (numeric) = 1.137284906816656 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10003 y[1] (analytic) = 1.137291676309231 y[1] (numeric) = 1.137291676309231 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) = 1.137298445809865 y[1] (numeric) = 1.137298445809865 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10005 y[1] (analytic) = 1.137305215318557 y[1] (numeric) = 1.137305215318557 absolute error = 2.220446049250313e-16 relative error = 1.952374806114267e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10006 y[1] (analytic) = 1.137311984835308 y[1] (numeric) = 1.137311984835309 absolute error = 2.220446049250313e-16 relative error = 1.952363185174604e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10007 y[1] (analytic) = 1.137318754360118 y[1] (numeric) = 1.137318754360118 absolute error = 2.220446049250313e-16 relative error = 1.952351564359446e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10008 y[1] (analytic) = 1.137325523892987 y[1] (numeric) = 1.137325523892987 absolute error = 2.220446049250313e-16 relative error = 1.952339943668792e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10009 y[1] (analytic) = 1.137332293433914 y[1] (numeric) = 1.137332293433915 absolute error = 2.220446049250313e-16 relative error = 1.95232832310264e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001 y[1] (analytic) = 1.1373390629829 y[1] (numeric) = 1.1373390629829 absolute error = 2.220446049250313e-16 relative error = 1.952316702660988e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10011 y[1] (analytic) = 1.137345832539945 y[1] (numeric) = 1.137345832539945 absolute error = 2.220446049250313e-16 relative error = 1.952305082343834e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10012 y[1] (analytic) = 1.137352602105048 y[1] (numeric) = 1.137352602105048 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.10013 y[1] (analytic) = 1.13735937167821 y[1] (numeric) = 1.13735937167821 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) = 1.13736614125943 y[1] (numeric) = 1.13736614125943 absolute error = 2.220446049250313e-16 relative error = 1.952270222139342e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001499999999999 y[1] (analytic) = 1.137372910848708 y[1] (numeric) = 1.137372910848709 absolute error = 2.220446049250313e-16 relative error = 1.952258602320162e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001599999999999 y[1] (analytic) = 1.137379680446045 y[1] (numeric) = 1.137379680446046 absolute error = 2.220446049250313e-16 relative error = 1.95224698262547e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001699999999999 y[1] (analytic) = 1.137386450051441 y[1] (numeric) = 1.137386450051441 absolute error = 2.220446049250313e-16 relative error = 1.952235363055264e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001799999999999 y[1] (analytic) = 1.137393219664895 y[1] (numeric) = 1.137393219664895 absolute error = 2.220446049250313e-16 relative error = 1.952223743609543e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001899999999999 y[1] (analytic) = 1.137399989286408 y[1] (numeric) = 1.137399989286408 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001999999999999 y[1] (analytic) = 1.137406758915978 y[1] (numeric) = 1.137406758915978 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002099999999999 y[1] (analytic) = 1.137413528553607 y[1] (numeric) = 1.137413528553607 absolute error = 2.220446049250313e-16 relative error = 1.95218888601927e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002199999999999 y[1] (analytic) = 1.137420298199294 y[1] (numeric) = 1.137420298199295 absolute error = 2.220446049250313e-16 relative error = 1.952177267071468e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002299999999999 y[1] (analytic) = 1.13742706785304 y[1] (numeric) = 1.13742706785304 absolute error = 2.220446049250313e-16 relative error = 1.952165648248142e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002399999999999 y[1] (analytic) = 1.137433837514844 y[1] (numeric) = 1.137433837514844 absolute error = 2.220446049250313e-16 relative error = 1.952154029549289e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002499999999999 y[1] (analytic) = 1.137440607184706 y[1] (numeric) = 1.137440607184706 absolute error = 2.220446049250313e-16 relative error = 1.952142410974906e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002599999999999 y[1] (analytic) = 1.137447376862626 y[1] (numeric) = 1.137447376862626 absolute error = 4.440892098500626e-16 relative error = 3.904261585049988e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002699999999999 y[1] (analytic) = 1.137454146548604 y[1] (numeric) = 1.137454146548605 absolute error = 2.220446049250313e-16 relative error = 1.952119174199548e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002799999999999 y[1] (analytic) = 1.137460916242641 y[1] (numeric) = 1.137460916242641 absolute error = 2.220446049250313e-16 relative error = 1.952107555998568e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002899999999999 y[1] (analytic) = 1.137467685944735 y[1] (numeric) = 1.137467685944735 absolute error = 2.220446049250313e-16 relative error = 1.952095937922051e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002999999999999 y[1] (analytic) = 1.137474455654888 y[1] (numeric) = 1.137474455654888 absolute error = 2.220446049250313e-16 relative error = 1.952084319969996e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003099999999999 y[1] (analytic) = 1.137481225373099 y[1] (numeric) = 1.137481225373099 absolute error = 2.220446049250313e-16 relative error = 1.9520727021424e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003199999999999 y[1] (analytic) = 1.137487995099367 y[1] (numeric) = 1.137487995099367 absolute error = 2.220446049250313e-16 relative error = 1.952061084439262e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003299999999999 y[1] (analytic) = 1.137494764833694 y[1] (numeric) = 1.137494764833694 absolute error = 4.440892098500626e-16 relative error = 3.904098933721161e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003399999999999 y[1] (analytic) = 1.137501534576078 y[1] (numeric) = 1.137501534576079 absolute error = 4.440892098500626e-16 relative error = 3.904075698812704e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003499999999999 y[1] (analytic) = 1.137508304326521 y[1] (numeric) = 1.137508304326521 absolute error = 2.220446049250313e-16 relative error = 1.952026232076575e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003599999999999 y[1] (analytic) = 1.137515074085022 y[1] (numeric) = 1.137515074085022 absolute error = 2.220446049250313e-16 relative error = 1.952014614871249e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003699999999999 y[1] (analytic) = 1.13752184385158 y[1] (numeric) = 1.13752184385158 absolute error = 4.440892098500626e-16 relative error = 3.904005995580741e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003799999999999 y[1] (analytic) = 1.137528613626196 y[1] (numeric) = 1.137528613626196 absolute error = 2.220446049250313e-16 relative error = 1.951991380833938e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003899999999999 y[1] (analytic) = 1.13753538340887 y[1] (numeric) = 1.13753538340887 absolute error = 2.220446049250313e-16 relative error = 1.95197976400195e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003999999999999 y[1] (analytic) = 1.137542153199601 y[1] (numeric) = 1.137542153199601 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004099999999998 y[1] (analytic) = 1.137548922998391 y[1] (numeric) = 1.137548922998391 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) = 1.137555692805238 y[1] (numeric) = 1.137555692805238 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) = 1.137562462620143 y[1] (numeric) = 1.137562462620143 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004399999999998 y[1] (analytic) = 1.137569232443105 y[1] (numeric) = 1.137569232443105 absolute error = 2.220446049250313e-16 relative error = 1.951921681708606e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004499999999998 y[1] (analytic) = 1.137576002274125 y[1] (numeric) = 1.137576002274125 absolute error = 2.220446049250313e-16 relative error = 1.951910065623243e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004599999999998 y[1] (analytic) = 1.137582772113203 y[1] (numeric) = 1.137582772113203 absolute error = 2.220446049250313e-16 relative error = 1.95189844966231e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004699999999998 y[1] (analytic) = 1.137589541960338 y[1] (numeric) = 1.137589541960338 absolute error = 2.220446049250313e-16 relative error = 1.951886833825806e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004799999999998 y[1] (analytic) = 1.137596311815531 y[1] (numeric) = 1.137596311815531 absolute error = 4.440892098500626e-16 relative error = 3.903750436227459e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004899999999998 y[1] (analytic) = 1.137603081678781 y[1] (numeric) = 1.137603081678781 absolute error = 4.440892098500626e-16 relative error = 3.903727205052156e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004999999999998 y[1] (analytic) = 1.137609851550089 y[1] (numeric) = 1.137609851550089 absolute error = 2.220446049250313e-16 relative error = 1.951851987062849e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005099999999998 y[1] (analytic) = 1.137616621429454 y[1] (numeric) = 1.137616621429454 absolute error = 2.220446049250313e-16 relative error = 1.951840371724041e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005199999999998 y[1] (analytic) = 1.137623391316877 y[1] (numeric) = 1.137623391316877 absolute error = 2.220446049250313e-16 relative error = 1.951828756509652e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005299999999998 y[1] (analytic) = 1.137630161212357 y[1] (numeric) = 1.137630161212357 absolute error = 2.220446049250313e-16 relative error = 1.951817141419681e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005399999999998 y[1] (analytic) = 1.137636931115894 y[1] (numeric) = 1.137636931115894 absolute error = 2.220446049250313e-16 relative error = 1.951805526454125e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005499999999998 y[1] (analytic) = 1.137643701027489 y[1] (numeric) = 1.137643701027489 absolute error = 4.440892098500626e-16 relative error = 3.903587823225965e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005599999999998 y[1] (analytic) = 1.137650470947141 y[1] (numeric) = 1.137650470947142 absolute error = 4.440892098500626e-16 relative error = 3.903564593792503e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005699999999998 y[1] (analytic) = 1.13765724087485 y[1] (numeric) = 1.137657240874851 absolute error = 4.440892098500626e-16 relative error = 3.90354136460786e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005799999999998 y[1] (analytic) = 1.137664010810617 y[1] (numeric) = 1.137664010810618 absolute error = 4.440892098500626e-16 relative error = 3.903518135672032e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005899999999998 y[1] (analytic) = 1.137670780754441 y[1] (numeric) = 1.137670780754442 absolute error = 6.661338147750939e-16 relative error = 5.855242360477524e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005999999999998 y[1] (analytic) = 1.137677550706322 y[1] (numeric) = 1.137677550706323 absolute error = 4.440892098500626e-16 relative error = 3.903471678546806e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006099999999998 y[1] (analytic) = 1.13768432066626 y[1] (numeric) = 1.137684320666261 absolute error = 4.440892098500626e-16 relative error = 3.903448450357401e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006199999999998 y[1] (analytic) = 1.137691090634256 y[1] (numeric) = 1.137691090634256 absolute error = 4.440892098500626e-16 relative error = 3.903425222416796e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006299999999998 y[1] (analytic) = 1.137697860610308 y[1] (numeric) = 1.137697860610309 absolute error = 4.440892098500626e-16 relative error = 3.903401994724986e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006399999999998 y[1] (analytic) = 1.137704630594418 y[1] (numeric) = 1.137704630594418 absolute error = 2.220446049250313e-16 relative error = 1.951689383640984e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006499999999998 y[1] (analytic) = 1.137711400586584 y[1] (numeric) = 1.137711400586585 absolute error = 4.440892098500626e-16 relative error = 3.903355540087741e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006599999999997 y[1] (analytic) = 1.137718170586808 y[1] (numeric) = 1.137718170586808 absolute error = 6.661338147750939e-16 relative error = 5.854998469713445e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006699999999997 y[1] (analytic) = 1.137724940595089 y[1] (numeric) = 1.137724940595089 absolute error = 4.440892098500626e-16 relative error = 3.903309086445632e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006799999999997 y[1] (analytic) = 1.137731710611426 y[1] (numeric) = 1.137731710611427 absolute error = 4.440892098500626e-16 relative error = 3.903285859997745e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006899999999997 y[1] (analytic) = 1.137738480635821 y[1] (numeric) = 1.137738480635821 absolute error = 6.661338147750939e-16 relative error = 5.854893950697947e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006999999999997 y[1] (analytic) = 1.137745250668272 y[1] (numeric) = 1.137745250668273 absolute error = 6.661338147750939e-16 relative error = 5.854859111772428e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007099999999997 y[1] (analytic) = 1.137752020708781 y[1] (numeric) = 1.137752020708781 absolute error = 6.661338147750939e-16 relative error = 5.854824273220059e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007199999999997 y[1] (analytic) = 1.137758790757346 y[1] (numeric) = 1.137758790757347 absolute error = 6.661338147750939e-16 relative error = 5.85478943504083e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007299999999997 y[1] (analytic) = 1.137765560813968 y[1] (numeric) = 1.137765560813969 absolute error = 8.881784197001252e-16 relative error = 7.806339462979654e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007399999999997 y[1] (analytic) = 1.137772330878647 y[1] (numeric) = 1.137772330878647 absolute error = 6.661338147750939e-16 relative error = 5.854719759801778e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007499999999997 y[1] (analytic) = 1.137779100951382 y[1] (numeric) = 1.137779100951383 absolute error = 6.661338147750939e-16 relative error = 5.854684922741942e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007599999999997 y[1] (analytic) = 1.137785871032174 y[1] (numeric) = 1.137785871032175 absolute error = 8.881784197001252e-16 relative error = 7.8062001147403e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007699999999997 y[1] (analytic) = 1.137792641121024 y[1] (numeric) = 1.137792641121024 absolute error = 8.881784197001252e-16 relative error = 7.80615366632216e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007799999999997 y[1] (analytic) = 1.137799411217929 y[1] (numeric) = 1.13779941121793 absolute error = 8.881784197001252e-16 relative error = 7.806107218401498e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007899999999997 y[1] (analytic) = 1.137806181322892 y[1] (numeric) = 1.137806181322893 absolute error = 8.881784197001252e-16 relative error = 7.806060770978305e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007999999999997 y[1] (analytic) = 1.137812951435911 y[1] (numeric) = 1.137812951435912 absolute error = 1.110223024625157e-15 relative error = 9.757517905065717e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008099999999997 y[1] (analytic) = 1.137819721556986 y[1] (numeric) = 1.137819721556987 absolute error = 8.881784197001252e-16 relative error = 7.805967877624293e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008199999999997 y[1] (analytic) = 1.137826491686118 y[1] (numeric) = 1.137826491686119 absolute error = 8.881784197001252e-16 relative error = 7.80592143169346e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008299999999997 y[1] (analytic) = 1.137833261823307 y[1] (numeric) = 1.137833261823308 absolute error = 8.881784197001252e-16 relative error = 7.805874986260065e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008399999999997 y[1] (analytic) = 1.137840031968552 y[1] (numeric) = 1.137840031968553 absolute error = 6.661338147750939e-16 relative error = 5.854371405993074e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008499999999997 y[1] (analytic) = 1.137846802121854 y[1] (numeric) = 1.137846802121855 absolute error = 8.881784197001252e-16 relative error = 7.805782096885559e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008599999999997 y[1] (analytic) = 1.137853572283212 y[1] (numeric) = 1.137853572283213 absolute error = 1.110223024625157e-15 relative error = 9.75716956618054e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008699999999997 y[1] (analytic) = 1.137860342452627 y[1] (numeric) = 1.137860342452628 absolute error = 1.110223024625157e-15 relative error = 9.75711151187589e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008799999999997 y[1] (analytic) = 1.137867112630097 y[1] (numeric) = 1.137867112630099 absolute error = 1.110223024625157e-15 relative error = 9.75705345819299e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008899999999997 y[1] (analytic) = 1.137873882815625 y[1] (numeric) = 1.137873882815626 absolute error = 1.110223024625157e-15 relative error = 9.756995405131831e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008999999999997 y[1] (analytic) = 1.137880653009208 y[1] (numeric) = 1.137880653009209 absolute error = 8.881784197001252e-16 relative error = 7.80554988215392e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009099999999997 y[1] (analytic) = 1.137887423210848 y[1] (numeric) = 1.137887423210849 absolute error = 1.110223024625157e-15 relative error = 9.756879300874692e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009199999999996 y[1] (analytic) = 1.137894193420545 y[1] (numeric) = 1.137894193420546 absolute error = 8.881784197001252e-16 relative error = 7.805456999742953e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009299999999996 y[1] (analytic) = 1.137900963638297 y[1] (numeric) = 1.137900963638298 absolute error = 8.881784197001252e-16 relative error = 7.805410559283516e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009399999999996 y[1] (analytic) = 1.137907733864106 y[1] (numeric) = 1.137907733864107 absolute error = 8.881784197001252e-16 relative error = 7.805364119321433e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009499999999996 y[1] (analytic) = 1.137914504097971 y[1] (numeric) = 1.137914504097971 absolute error = 8.881784197001252e-16 relative error = 7.805317679856694e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009599999999996 y[1] (analytic) = 1.137921274339892 y[1] (numeric) = 1.137921274339893 absolute error = 8.881784197001252e-16 relative error = 7.805271240889293e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009699999999996 y[1] (analytic) = 1.137928044589869 y[1] (numeric) = 1.13792804458987 absolute error = 6.661338147750939e-16 relative error = 5.853918601814417e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009799999999996 y[1] (analytic) = 1.137934814847902 y[1] (numeric) = 1.137934814847903 absolute error = 8.881784197001252e-16 relative error = 7.805178364446477e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009899999999996 y[1] (analytic) = 1.137941585113992 y[1] (numeric) = 1.137941585113992 absolute error = 6.661338147750939e-16 relative error = 5.853848945228282e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009999999999996 y[1] (analytic) = 1.137948355388137 y[1] (numeric) = 1.137948355388138 absolute error = 6.661338147750939e-16 relative error = 5.853814117494689e-14 % Correct digits = 15 h = 1e-05 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2)); Iterations = 100 Total Elapsed Time = 17 Seconds Elapsed Time(since restart) = 16 Seconds Expected Time Remaining = 1 Hours 51 Minutes 55 Seconds Optimized Time Remaining = 1 Hours 45 Minutes 20 Seconds Time to Timeout = 43 Seconds Percent Done = 0.2525 %