##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrt_tonepostode.ode################# diff ( y , x , 1 ) = sqrt ( 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(0.5); x_end=c(1.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=c(0.001); 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(0.8) * (c(x) + c(2.0)) * sqrt(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] = 0.5 y[1] (closed_form) = 1.414213562373095 y[1] (numeric) = 1.414213562373095 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] = 0.51 y[1] (closed_form) = 1.421288162189506 y[1] (numeric) = 1.421288162189506 absolute error = 2.220446049250313e-16 relative error = 1.562277171034548e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (closed_form) = 1.42836981194674 y[1] (numeric) = 1.42836981194674 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (closed_form) = 1.435458490652309 y[1] (numeric) = 1.435458490652308 absolute error = 8.881784197001252e-16 relative error = 6.187419737205458e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (closed_form) = 1.442554177459 y[1] (numeric) = 1.442554177459 absolute error = 4.440892098500626e-16 relative error = 3.078492418442872e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (closed_form) = 1.44965685166331 y[1] (numeric) = 1.449656851663309 absolute error = 8.881784197001252e-16 relative error = 6.126818347949346e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000001 y[1] (closed_form) = 1.456766492703885 y[1] (numeric) = 1.456766492703885 absolute error = 6.661338147750939e-16 relative error = 4.572687648373155e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000001 y[1] (closed_form) = 1.46388308016 y[1] (numeric) = 1.463883080159998 absolute error = 1.110223024625157e-15 relative error = 7.584096296159195e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000001 y[1] (closed_form) = 1.471006593750045 y[1] (numeric) = 1.471006593750045 absolute error = 6.661338147750939e-16 relative error = 4.528421678089934e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000001 y[1] (closed_form) = 1.478137013330054 y[1] (numeric) = 1.478137013330054 absolute error = 8.881784197001252e-16 relative error = 6.008769225656372e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000001 y[1] (closed_form) = 1.485274318892232 y[1] (numeric) = 1.485274318892231 absolute error = 8.881784197001252e-16 relative error = 5.979894814060738e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000001 y[1] (closed_form) = 1.492418490563516 y[1] (numeric) = 1.492418490563515 absolute error = 1.110223024625157e-15 relative error = 7.439086500502629e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000001 y[1] (closed_form) = 1.499569508604159 y[1] (numeric) = 1.499569508604159 absolute error = 4.440892098500626e-16 relative error = 2.961444649961128e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000001 y[1] (closed_form) = 1.506727353406328 y[1] (numeric) = 1.506727353406327 absolute error = 4.440892098500626e-16 relative error = 2.947376038843987e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000001 y[1] (closed_form) = 1.513892005492721 y[1] (numeric) = 1.51389200549272 absolute error = 6.661338147750939e-16 relative error = 4.400140910700496e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000001 y[1] (closed_form) = 1.521063445515209 y[1] (numeric) = 1.521063445515208 absolute error = 1.110223024625157e-15 relative error = 7.298992214286667e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000001 y[1] (closed_form) = 1.528241654253497 y[1] (numeric) = 1.528241654253497 absolute error = 4.440892098500626e-16 relative error = 2.905883428933152e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000002 y[1] (closed_form) = 1.5354266126138 y[1] (numeric) = 1.535426612613799 absolute error = 4.440892098500626e-16 relative error = 2.892285480802479e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000002 y[1] (closed_form) = 1.542618301627535 y[1] (numeric) = 1.542618301627535 absolute error = 2.220446049250313e-16 relative error = 1.439400820609763e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000002 y[1] (closed_form) = 1.549816702450045 y[1] (numeric) = 1.549816702450044 absolute error = 4.440892098500626e-16 relative error = 2.865430532191448e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000002 y[1] (closed_form) = 1.557021796359321 y[1] (numeric) = 1.557021796359321 absolute error = 2.220446049250313e-16 relative error = 1.42608539870298e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000002 y[1] (closed_form) = 1.564233564754762 y[1] (numeric) = 1.564233564754762 absolute error = 2.220446049250313e-16 relative error = 1.41951055090576e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000002 y[1] (closed_form) = 1.571451989155936 y[1] (numeric) = 1.571451989155935 absolute error = 4.440892098500626e-16 relative error = 2.825980131207149e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000002 y[1] (closed_form) = 1.578677051201365 y[1] (numeric) = 1.578677051201364 absolute error = 2.220446049250313e-16 relative error = 1.406523295920826e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000002 y[1] (closed_form) = 1.585908732647328 y[1] (numeric) = 1.585908732647329 absolute error = 2.220446049250313e-16 relative error = 1.400109605010979e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000002 y[1] (closed_form) = 1.593147015366682 y[1] (numeric) = 1.593147015366682 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000002 y[1] (closed_form) = 1.600391881347687 y[1] (numeric) = 1.600391881347687 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000002 y[1] (closed_form) = 1.607643312692861 y[1] (numeric) = 1.607643312692861 absolute error = 4.440892098500626e-16 relative error = 2.762361565801539e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000002 y[1] (closed_form) = 1.614901291617847 y[1] (numeric) = 1.614901291617847 absolute error = 2.220446049250313e-16 relative error = 1.374973232590468e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000003 y[1] (closed_form) = 1.622165800450289 y[1] (numeric) = 1.622165800450289 absolute error = 2.220446049250313e-16 relative error = 1.368815720707433e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000003 y[1] (closed_form) = 1.62943682162873 y[1] (numeric) = 1.62943682162873 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000003 y[1] (closed_form) = 1.636714337701523 y[1] (numeric) = 1.636714337701523 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000003 y[1] (closed_form) = 1.643998331325752 y[1] (numeric) = 1.643998331325753 absolute error = 2.220446049250313e-16 relative error = 1.350637653907898e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000003 y[1] (closed_form) = 1.651288785266178 y[1] (numeric) = 1.651288785266178 absolute error = 2.220446049250313e-16 relative error = 1.344674577252937e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000003 y[1] (closed_form) = 1.658585682394183 y[1] (numeric) = 1.658585682394183 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000003 y[1] (closed_form) = 1.665889005686747 y[1] (numeric) = 1.665889005686747 absolute error = 2.220446049250313e-16 relative error = 1.332889551266925e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000003 y[1] (closed_form) = 1.673198738225421 y[1] (numeric) = 1.673198738225421 absolute error = 2.220446049250313e-16 relative error = 1.327066533414493e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000003 y[1] (closed_form) = 1.680514863195325 y[1] (numeric) = 1.680514863195325 absolute error = 4.440892098500626e-16 relative error = 2.642578292974292e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000003 y[1] (closed_form) = 1.687837363884153 y[1] (numeric) = 1.687837363884153 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000003 y[1] (closed_form) = 1.695166223681196 y[1] (numeric) = 1.695166223681196 absolute error = 2.220446049250313e-16 relative error = 1.309869214140208e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000004 y[1] (closed_form) = 1.702501426076371 y[1] (numeric) = 1.702501426076371 absolute error = 2.220446049250313e-16 relative error = 1.304225661864854e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000004 y[1] (closed_form) = 1.70984295465927 y[1] (numeric) = 1.70984295465927 absolute error = 2.220446049250313e-16 relative error = 1.298625726532174e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000004 y[1] (closed_form) = 1.717190793118215 y[1] (numeric) = 1.717190793118215 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000004 y[1] (closed_form) = 1.724544925239331 y[1] (numeric) = 1.72454492523933 absolute error = 6.661338147750939e-16 relative error = 3.862664318139747e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000004 y[1] (closed_form) = 1.73190533490562 y[1] (numeric) = 1.73190533490562 absolute error = 4.440892098500626e-16 relative error = 2.564165609399565e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000004 y[1] (closed_form) = 1.739272006096067 y[1] (numeric) = 1.739272006096066 absolute error = 6.661338147750939e-16 relative error = 3.829957662978108e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000004 y[1] (closed_form) = 1.746644922884733 y[1] (numeric) = 1.746644922884733 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000004 y[1] (closed_form) = 1.754024069439877 y[1] (numeric) = 1.754024069439877 absolute error = 2.220446049250313e-16 relative error = 1.265915381628361e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000004 y[1] (closed_form) = 1.761409430023084 y[1] (numeric) = 1.761409430023084 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000004 y[1] (closed_form) = 1.7688009889884 y[1] (numeric) = 1.7688009889884 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 1.776198730781485 y[1] (numeric) = 1.776198730781485 absolute error = 2.220446049250313e-16 relative error = 1.250111268953204e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.009999999999999 y[1] (closed_form) = 1.783602639938768 y[1] (numeric) = 1.783602639938768 absolute error = 4.440892098500626e-16 relative error = 2.489843869401923e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = 1.791012701086623 y[1] (numeric) = 1.791012701086624 absolute error = 1.110223024625157e-15 relative error = 6.198856233412384e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = 1.798428898940547 y[1] (numeric) = 1.798428898940549 absolute error = 1.998401444325282e-15 relative error = 1.111192911492102e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 1.80585121830435 y[1] (numeric) = 1.805851218304352 absolute error = 2.442490654175344e-15 relative error = 1.352542573506572e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = 1.813279644069356 y[1] (numeric) = 1.81327964406936 absolute error = 3.552713678800501e-15 relative error = 1.959275112595161e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = 1.820714161213615 y[1] (numeric) = 1.82071416121362 absolute error = 4.662936703425657e-15 relative error = 2.561048187990986e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = 1.828154754801123 y[1] (numeric) = 1.828154754801128 absolute error = 5.10702591327572e-15 relative error = 2.793541356312197e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = 1.835601409981048 y[1] (numeric) = 1.835601409981055 absolute error = 6.217248937900877e-15 relative error = 3.387036479757915e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = 1.843054111986978 y[1] (numeric) = 1.843054111986985 absolute error = 6.883382752675971e-15 relative error = 3.734769754131128e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.099999999999989 y[1] (closed_form) = 1.850512846136159 y[1] (numeric) = 1.850512846136166 absolute error = 7.549516567451064e-15 relative error = 4.07968881881276e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999988 y[1] (closed_form) = 1.857977597828759 y[1] (numeric) = 1.857977597828767 absolute error = 7.993605777301127e-15 relative error = 4.302315478207322e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 1.865448352547133 y[1] (numeric) = 1.865448352547142 absolute error = 8.881784197001252e-15 relative error = 4.761206165195529e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 1.872925095855098 y[1] (numeric) = 1.872925095855108 absolute error = 9.547918011776346e-15 relative error = 5.097864315506526e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 1.880407813397218 y[1] (numeric) = 1.880407813397229 absolute error = 1.043609643147647e-14 relative error = 5.549911225173125e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 1.887896490898095 y[1] (numeric) = 1.887896490898106 absolute error = 1.110223024625157e-14 relative error = 5.880740972705607e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 1.895391114161669 y[1] (numeric) = 1.895391114161681 absolute error = 1.199040866595169e-14 relative error = 6.326086777744045e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 1.902891669070533 y[1] (numeric) = 1.902891669070546 absolute error = 1.310063169057685e-14 relative error = 6.884591437081571e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = 1.910398141585242 y[1] (numeric) = 1.910398141585256 absolute error = 1.398881011027697e-14 relative error = 7.322457976570845e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = 1.917910517743645 y[1] (numeric) = 1.917910517743661 absolute error = 1.532107773982716e-14 relative error = 7.988421565074826e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999978 y[1] (closed_form) = 1.925428783660217 y[1] (numeric) = 1.925428783660233 absolute error = 1.576516694967722e-14 relative error = 8.18787331085174e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999977 y[1] (closed_form) = 1.932952925525398 y[1] (numeric) = 1.932952925525415 absolute error = 1.687538997430238e-14 relative error = 8.730367797092347e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 1.940482929604945 y[1] (numeric) = 1.940482929604963 absolute error = 1.77635683940025e-14 relative error = 9.154199773155911e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 1.948018782239284 y[1] (numeric) = 1.948018782239303 absolute error = 1.909583602355269e-14 relative error = 9.802696050805869e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 1.955560469842882 y[1] (numeric) = 1.955560469842901 absolute error = 1.976196983832779e-14 relative error = 1.010552736316845e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = 1.963107978903607 y[1] (numeric) = 1.963107978903628 absolute error = 2.087219286295294e-14 relative error = 1.063221844506487e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = 1.970661295982119 y[1] (numeric) = 1.970661295982141 absolute error = 2.153832667772804e-14 relative error = 1.092949190286602e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = 1.978220407711247 y[1] (numeric) = 1.978220407711269 absolute error = 2.19824158875781e-14 relative error = 1.111221772957606e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = 1.985785300795383 y[1] (numeric) = 1.985785300795406 absolute error = 2.309263891220326e-14 relative error = 1.162897061578297e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = 1.993355962009886 y[1] (numeric) = 1.993355962009909 absolute error = 2.375877272697835e-14 relative error = 1.191898144625537e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999967 y[1] (closed_form) = 2.000932378200484 y[1] (numeric) = 2.000932378200509 absolute error = 2.442490654175344e-14 relative error = 1.220676261119814e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999966 y[1] (closed_form) = 2.008514536282691 y[1] (numeric) = 2.008514536282717 absolute error = 2.531308496145357e-14 relative error = 1.260288860458157e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = 2.016102423241226 y[1] (numeric) = 2.016102423241251 absolute error = 2.575717417130363e-14 relative error = 1.277572700393595e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = 2.023696026129434 y[1] (numeric) = 2.023696026129461 absolute error = 2.664535259100376e-14 relative error = 1.316667733047154e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = 2.031295332068729 y[1] (numeric) = 2.031295332068757 absolute error = 2.797762022055394e-14 relative error = 1.377329026403105e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y[1] (closed_form) = 2.038900328248026 y[1] (numeric) = 2.038900328248055 absolute error = 2.97539770599542e-14 relative error = 1.459314937946036e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y[1] (closed_form) = 2.046511001923189 y[1] (numeric) = 2.046511001923219 absolute error = 2.97539770599542e-14 relative error = 1.453887960142564e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y[1] (closed_form) = 2.054127340416482 y[1] (numeric) = 2.054127340416513 absolute error = 3.064215547965432e-14 relative error = 1.491735924874137e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y[1] (closed_form) = 2.06174933111603 y[1] (numeric) = 2.061749331116061 absolute error = 3.108624468950438e-14 relative error = 1.507760629303918e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999957 y[1] (closed_form) = 2.069376961475278 y[1] (numeric) = 2.06937696147531 absolute error = 3.153033389935445e-14 relative error = 1.523663135636543e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999956 y[1] (closed_form) = 2.077010219012465 y[1] (numeric) = 2.077010219012498 absolute error = 3.286260152890463e-14 relative error = 1.582207021808948e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999955 y[1] (closed_form) = 2.084649091310099 y[1] (numeric) = 2.084649091310132 absolute error = 3.33066907387547e-14 relative error = 1.597712098290034e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = 2.092293566014435 y[1] (numeric) = 2.092293566014469 absolute error = 3.419486915845482e-14 relative error = 1.634324633688565e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = 2.099943630834967 y[1] (numeric) = 2.099943630835002 absolute error = 3.463895836830488e-14 relative error = 1.649518485147716e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = 2.107599273543919 y[1] (numeric) = 2.107599273543955 absolute error = 3.597122599785507e-14 relative error = 1.70673934316601e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y[1] (closed_form) = 2.115260481975743 y[1] (numeric) = 2.115260481975779 absolute error = 3.641531520770513e-14 relative error = 1.721552287200661e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y[1] (closed_form) = 2.122927244026622 y[1] (numeric) = 2.12292724402666 absolute error = 3.730349362740526e-14 relative error = 1.757172495306554e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y[1] (closed_form) = 2.130599547653981 y[1] (numeric) = 2.130599547654019 absolute error = 3.730349362740526e-14 relative error = 1.750844905063479e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y[1] (closed_form) = 2.138277380876 y[1] (numeric) = 2.138277380876039 absolute error = 3.819167204710538e-14 relative error = 1.786095311519368e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999946 y[1] (closed_form) = 2.145960731771136 y[1] (numeric) = 2.145960731771175 absolute error = 3.907985046680551e-14 relative error = 1.821088796650606e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999945 y[1] (closed_form) = 2.153649588477642 y[1] (numeric) = 2.153649588477682 absolute error = 3.996802888650564e-14 relative error = 1.855827851491754e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = sqrt ( 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 %