##############ECHO OF PROBLEM################# ##############temp/add_c_linpostode.ode################# diff ( y , x , 1 ) = 0.3 + ( 0.1 * x + 0.2 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.1); x_end=c(1.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_display_interval=c(0.1); glob_look_poles=true; glob_min_h=c(0.1); glob_type_given_pole=3; // 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(0.05) * c(x) * c(x) + c(0.5) * c(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.0505 y[1] (numeric) = 0.0505 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] = 0.11 y[1] (closed_form) = 0.05560500000000001 y[1] (numeric) = 0.055605 absolute error = 6.938893903907228e-18 relative error = 1.247890280353786e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 0.06072000000000001 y[1] (numeric) = 0.06072 absolute error = 1.387778780781446e-17 relative error = 2.285538176517532e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 0.06584500000000001 y[1] (numeric) = 0.065845 absolute error = 1.387778780781446e-17 relative error = 2.107644894496842e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 0.07098000000000002 y[1] (numeric) = 0.07098 absolute error = 1.387778780781446e-17 relative error = 1.955168752861997e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 0.07612500000000003 y[1] (numeric) = 0.076125 absolute error = 2.775557561562891e-17 relative error = 3.646052626026785e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 0.08128000000000003 y[1] (numeric) = 0.08128000000000001 absolute error = 2.775557561562891e-17 relative error = 3.414809992080327e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 0.08644500000000004 y[1] (numeric) = 0.08644500000000001 absolute error = 2.775557561562891e-17 relative error = 3.21077860091722e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 0.09162000000000003 y[1] (numeric) = 0.09162000000000001 absolute error = 2.775557561562891e-17 relative error = 3.029423228075628e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 0.09680500000000004 y[1] (numeric) = 0.09680500000000002 absolute error = 2.775557561562891e-17 relative error = 2.8671634332554e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 0.102 y[1] (numeric) = 0.102 absolute error = 2.775557561562891e-17 relative error = 2.721134864277343e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (closed_form) = 0.1072050000000001 y[1] (numeric) = 0.107205 absolute error = 2.775557561562891e-17 relative error = 2.589018759911282e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (closed_form) = 0.1124200000000001 y[1] (numeric) = 0.11242 absolute error = 4.163336342344337e-17 relative error = 3.703376927899248e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (closed_form) = 0.1176450000000001 y[1] (numeric) = 0.117645 absolute error = 5.551115123125783e-17 relative error = 4.718530428939419e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = 0.1228800000000001 y[1] (numeric) = 0.12288 absolute error = 5.551115123125783e-17 relative error = 4.517509052022932e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = 0.128125 y[1] (numeric) = 0.128125 absolute error = 2.775557561562891e-17 relative error = 2.16628882853689e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 0.1333800000000001 y[1] (numeric) = 0.13338 absolute error = 2.775557561562891e-17 relative error = 2.080939842227388e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 0.1386450000000001 y[1] (numeric) = 0.138645 absolute error = 5.551115123125783e-17 relative error = 4.003833620488138e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 0.1439200000000001 y[1] (numeric) = 0.14392 absolute error = 5.551115123125783e-17 relative error = 3.857083882105183e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 0.1492050000000001 y[1] (numeric) = 0.149205 absolute error = 5.551115123125783e-17 relative error = 3.720461863292638e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 0.1545000000000001 y[1] (numeric) = 0.1545 absolute error = 5.551115123125783e-17 relative error = 3.592954772249696e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 0.1598050000000001 y[1] (numeric) = 0.159805 absolute error = 5.551115123125783e-17 relative error = 3.473680500063064e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 0.1651200000000001 y[1] (numeric) = 0.16512 absolute error = 5.551115123125783e-17 relative error = 3.361867201505438e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 0.1704450000000001 y[1] (numeric) = 0.170445 absolute error = 5.551115123125783e-17 relative error = 3.256836588416075e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 0.1757800000000001 y[1] (numeric) = 0.17578 absolute error = 5.551115123125783e-17 relative error = 3.157990171308328e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = 0.1811250000000001 y[1] (numeric) = 0.1811250000000001 absolute error = 5.551115123125783e-17 relative error = 3.064797859558746e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (closed_form) = 0.1864800000000001 y[1] (numeric) = 0.1864800000000001 absolute error = 5.551115123125783e-17 relative error = 2.976788461564661e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (closed_form) = 0.1918450000000001 y[1] (numeric) = 0.1918450000000001 absolute error = 5.551115123125783e-17 relative error = 2.893541725416758e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (closed_form) = 0.1972200000000001 y[1] (numeric) = 0.1972200000000001 absolute error = 5.551115123125783e-17 relative error = 2.814681636307565e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = 0.2026050000000001 y[1] (numeric) = 0.2026050000000001 absolute error = 5.551115123125783e-17 relative error = 2.73987074510786e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (closed_form) = 0.2080000000000001 y[1] (numeric) = 0.2080000000000001 absolute error = 5.551115123125783e-17 relative error = 2.668805347656625e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 0.2134050000000002 y[1] (numeric) = 0.2134050000000001 absolute error = 8.326672684688674e-17 relative error = 3.90181705428114e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 0.2188200000000002 y[1] (numeric) = 0.2188200000000001 absolute error = 8.326672684688674e-17 relative error = 3.805261257969412e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 0.2242450000000001 y[1] (numeric) = 0.2242450000000001 absolute error = 8.326672684688674e-17 relative error = 3.713203275296514e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 0.2296800000000002 y[1] (numeric) = 0.2296800000000001 absolute error = 1.110223024625157e-16 relative error = 4.833781890565812e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 0.2351250000000002 y[1] (numeric) = 0.2351250000000001 absolute error = 1.110223024625157e-16 relative error = 4.721841678363236e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (closed_form) = 0.2405800000000002 y[1] (numeric) = 0.24058 absolute error = 1.110223024625157e-16 relative error = 4.614776891783007e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = 0.2460450000000002 y[1] (numeric) = 0.246045 absolute error = 1.387778780781446e-16 relative error = 5.6403453871505e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (closed_form) = 0.2515200000000002 y[1] (numeric) = 0.2515200000000001 absolute error = 1.110223024625157e-16 relative error = 4.414054646251415e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = 0.2570050000000002 y[1] (numeric) = 0.257005 absolute error = 2.220446049250313e-16 relative error = 8.639699808370698e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (closed_form) = 0.2625000000000002 y[1] (numeric) = 0.2625000000000001 absolute error = 1.110223024625157e-16 relative error = 4.229421046191069e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (closed_form) = 0.2680050000000002 y[1] (numeric) = 0.268005 absolute error = 2.220446049250313e-16 relative error = 8.285091879816836e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (closed_form) = 0.2735200000000002 y[1] (numeric) = 0.2735200000000001 absolute error = 1.110223024625157e-16 relative error = 4.059019540162166e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (closed_form) = 0.2790450000000002 y[1] (numeric) = 0.279045 absolute error = 2.220446049250313e-16 relative error = 7.95730455392611e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (closed_form) = 0.2845800000000002 y[1] (numeric) = 0.2845800000000001 absolute error = 1.110223024625157e-16 relative error = 3.901268622619845e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (closed_form) = 0.2901250000000002 y[1] (numeric) = 0.290125 absolute error = 2.220446049250313e-16 relative error = 7.653411630332828e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (closed_form) = 0.2956800000000002 y[1] (numeric) = 0.2956800000000001 absolute error = 1.110223024625157e-16 relative error = 3.754812718564515e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = 0.3012450000000002 y[1] (numeric) = 0.301245 absolute error = 2.220446049250313e-16 relative error = 7.370897605770424e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = 0.3068200000000002 y[1] (numeric) = 0.3068200000000001 absolute error = 1.110223024625157e-16 relative error = 3.618483229988774e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = 0.3124050000000002 y[1] (numeric) = 0.312405 absolute error = 2.220446049250313e-16 relative error = 7.107588064372567e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = 0.3180000000000002 y[1] (numeric) = 0.3180000000000001 absolute error = 1.665334536937735e-16 relative error = 5.236901059552622e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 0.3236050000000003 y[1] (numeric) = 0.323605 absolute error = 2.775557561562891e-16 relative error = 8.576992202107165e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = 0.3292200000000002 y[1] (numeric) = 0.3292200000000001 absolute error = 1.665334536937735e-16 relative error = 5.058424570007088e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (closed_form) = 0.3348450000000002 y[1] (numeric) = 0.334845 absolute error = 2.220446049250313e-16 relative error = 6.631265359346299e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = 0.3404800000000003 y[1] (numeric) = 0.3404800000000001 absolute error = 2.220446049250313e-16 relative error = 6.521516826980473e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = 0.3461250000000002 y[1] (numeric) = 0.346125 absolute error = 2.220446049250313e-16 relative error = 6.415156516432825e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = 0.3517800000000003 y[1] (numeric) = 0.35178 absolute error = 2.220446049250313e-16 relative error = 6.312030386179747e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (closed_form) = 0.3574450000000003 y[1] (numeric) = 0.357445 absolute error = 2.775557561562891e-16 relative error = 7.764991989153265e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (closed_form) = 0.3631200000000003 y[1] (numeric) = 0.3631200000000001 absolute error = 2.220446049250313e-16 relative error = 6.114909807364814e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (closed_form) = 0.3688050000000003 y[1] (numeric) = 0.368805 absolute error = 2.220446049250313e-16 relative error = 6.020650612790802e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 0.3745000000000003 y[1] (numeric) = 0.3745000000000001 absolute error = 2.220446049250313e-16 relative error = 5.92909492456692e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = 0.3802050000000003 y[1] (numeric) = 0.3802050000000001 absolute error = 2.220446049250313e-16 relative error = 5.840128481346409e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (closed_form) = 0.3859200000000003 y[1] (numeric) = 0.38592 absolute error = 2.775557561562891e-16 relative error = 7.192054212175811e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (closed_form) = 0.3916450000000003 y[1] (numeric) = 0.3916450000000001 absolute error = 2.220446049250313e-16 relative error = 5.669537589527024e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (closed_form) = 0.3973800000000003 y[1] (numeric) = 0.39738 absolute error = 2.775557561562891e-16 relative error = 6.98464331763775e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (closed_form) = 0.4031250000000003 y[1] (numeric) = 0.4031250000000001 absolute error = 2.775557561562891e-16 relative error = 6.885104028683136e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 0.4088800000000004 y[1] (numeric) = 0.40888 absolute error = 3.33066907387547e-16 relative error = 8.145835144481184e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = 0.4146450000000003 y[1] (numeric) = 0.4146450000000001 absolute error = 2.220446049250313e-16 relative error = 5.355053236504266e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (closed_form) = 0.4204200000000003 y[1] (numeric) = 0.42042 absolute error = 3.33066907387547e-16 relative error = 7.922242219388865e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = 0.4262050000000003 y[1] (numeric) = 0.4262050000000001 absolute error = 2.220446049250313e-16 relative error = 5.209807602562878e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (closed_form) = 0.4320000000000003 y[1] (numeric) = 0.432 absolute error = 3.33066907387547e-16 relative error = 7.70988211545247e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (closed_form) = 0.4378050000000003 y[1] (numeric) = 0.4378050000000001 absolute error = 2.220446049250313e-16 relative error = 5.071769507544024e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (closed_form) = 0.4436200000000003 y[1] (numeric) = 0.44362 absolute error = 3.33066907387547e-16 relative error = 7.50793263125077e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = 0.4494450000000004 y[1] (numeric) = 0.4494450000000001 absolute error = 2.220446049250313e-16 relative error = 4.940417735763689e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (closed_form) = 0.4552800000000004 y[1] (numeric) = 0.45528 absolute error = 3.33066907387547e-16 relative error = 7.315649872332339e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = 0.4611250000000004 y[1] (numeric) = 0.4611250000000001 absolute error = 2.775557561562891e-16 relative error = 6.019100160613475e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (closed_form) = 0.4669800000000004 y[1] (numeric) = 0.46698 absolute error = 3.885780586188048e-16 relative error = 8.321085670024508e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (closed_form) = 0.4728450000000004 y[1] (numeric) = 0.4728450000000001 absolute error = 2.775557561562891e-16 relative error = 5.869909931505861e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (closed_form) = 0.4787200000000004 y[1] (numeric) = 0.47872 absolute error = 3.885780586188048e-16 relative error = 8.117021612190935e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (closed_form) = 0.4846050000000004 y[1] (numeric) = 0.4846050000000001 absolute error = 2.775557561562891e-16 relative error = 5.72746373141608e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = 0.4905000000000004 y[1] (numeric) = 0.4905 absolute error = 3.33066907387547e-16 relative error = 6.790354890673735e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = 0.4964050000000004 y[1] (numeric) = 0.4964050000000001 absolute error = 3.33066907387547e-16 relative error = 6.709580028153356e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (closed_form) = 0.5023200000000004 y[1] (numeric) = 0.50232 absolute error = 4.440892098500626e-16 relative error = 8.840763056419458e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = 0.5082450000000004 y[1] (numeric) = 0.5082449999999999 absolute error = 4.440892098500626e-16 relative error = 8.737699531723131e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = 0.5141800000000004 y[1] (numeric) = 0.51418 absolute error = 4.440892098500626e-16 relative error = 8.636843320433744e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = 0.5201250000000004 y[1] (numeric) = 0.5201249999999999 absolute error = 4.440892098500626e-16 relative error = 8.538124678684207e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = 0.5260800000000004 y[1] (numeric) = 0.52608 absolute error = 4.440892098500626e-16 relative error = 8.441476768743579e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = 0.5320450000000004 y[1] (numeric) = 0.532045 absolute error = 4.440892098500626e-16 relative error = 8.346835509215617e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 0.5380200000000005 y[1] (numeric) = 0.5380199999999999 absolute error = 5.551115123125783e-16 relative error = 1.0317674293011e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = 0.5440050000000005 y[1] (numeric) = 0.544005 absolute error = 5.551115123125783e-16 relative error = 1.020416195278679e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 Finished! diff ( y , x , 1 ) = 0.3 + ( 0.1 * x + 0.2 ) ; Iterations = 900 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %