##############ECHO OF PROBLEM################# ##############temp/lin_arctanpostode.ode################# diff ( y , x , 1 ) = arctan ( 0.1 * x + 0.2 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.0; x_end=-0.6; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(10.0 * (0.1 * x + 0.2) * arctan(0.1 * x + 0.2) - 5.0 * ln(1.0 + expt((0.1 * x + 0.2) , 2))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 400000.0000000001 step_error = 5.270462766947299e-15 est_needed_step_err = 5.270462766947299e-15 opt_iter = 1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 400000.0000000001 step_error = 5.270462766947299e-15 est_needed_step_err = 5.270462766947299e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.471162334935134e-185 estimated_step_error = 2.471162334935134e-185 Double H and LOOP opt_iter = 2 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 200000 step_error = 7.453559924999299e-15 est_needed_step_err = 7.453559924999299e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.658368769248977e-177 estimated_step_error = 1.658368769248977e-177 Double H and LOOP opt_iter = 3 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 100000 step_error = 1.05409255338946e-14 est_needed_step_err = 1.05409255338946e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.112912171764129e-169 estimated_step_error = 1.112912171764129e-169 Double H and LOOP opt_iter = 4 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 50000.00000000001 step_error = 1.49071198499986e-14 est_needed_step_err = 1.49071198499986e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.468623531193766e-162 estimated_step_error = 7.468623531193766e-162 Double H and LOOP opt_iter = 5 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 25000 step_error = 2.10818510677892e-14 est_needed_step_err = 2.10818510677892e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.012103540555958e-154 estimated_step_error = 5.012103540555958e-154 Double H and LOOP opt_iter = 6 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 12500 step_error = 2.98142396999972e-14 est_needed_step_err = 2.98142396999972e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.363559215300437e-146 estimated_step_error = 3.363559215300437e-146 Double H and LOOP opt_iter = 7 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 6250.000000000001 step_error = 4.216370213557839e-14 est_needed_step_err = 4.216370213557839e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.257237610544898e-138 estimated_step_error = 2.257237610544898e-138 Double H and LOOP opt_iter = 8 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 3125 step_error = 5.962847939999439e-14 est_needed_step_err = 5.962847939999439e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.514794748910067e-130 estimated_step_error = 1.514794748910067e-130 Double H and LOOP opt_iter = 9 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 1562.5 step_error = 8.432740427115678e-14 est_needed_step_err = 8.432740427115678e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.016545751403892e-122 estimated_step_error = 1.016545751403892e-122 Double H and LOOP opt_iter = 10 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 781.2500000000001 step_error = 1.192569587999888e-13 est_needed_step_err = 1.192569587999888e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.821711040100051e-115 estimated_step_error = 6.821711040100051e-115 Double H and LOOP opt_iter = 11 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 390.6250000000001 step_error = 1.686548085423136e-13 est_needed_step_err = 1.686548085423136e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.577688216910538e-107 estimated_step_error = 4.577688216910538e-107 Double H and LOOP opt_iter = 12 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 195.3125 step_error = 2.385139175999776e-13 est_needed_step_err = 2.385139175999776e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.071652615137071e-99 estimated_step_error = 3.071652615137071e-99 Double H and LOOP opt_iter = 13 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 97.65625000000001 step_error = 3.373096170846271e-13 est_needed_step_err = 3.373096170846271e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.060838525925138e-91 estimated_step_error = 2.060838525925138e-91 Double H and LOOP opt_iter = 14 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 48.82812500000001 step_error = 4.770278351999551e-13 est_needed_step_err = 4.770278351999551e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.38231722244458e-83 estimated_step_error = 1.38231722244458e-83 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = 0.04991699822532158 y[1] (numeric) = 0.04991699822532158 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (analytic) = 0.0509186349177335 y[1] (numeric) = 0.05091863557199164 absolute error = 6.542581337809494e-10 relative error = 1.284909021693137e-06 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 8 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (analytic) = 0.05193017062867282 y[1] (numeric) = 0.05193017194346111 absolute error = 1.314788285189383e-09 relative error = 2.531838946940478e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (analytic) = 0.0529516033693342 y[1] (numeric) = 0.05295160535091471 absolute error = 1.981580510790337e-09 relative error = 3.742248363980472e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (analytic) = 0.05398293113212667 y[1] (numeric) = 0.05398293378675376 absolute error = 2.65462709453379e-09 relative error = 4.91753048391615e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (analytic) = 0.05502415189069715 y[1] (numeric) = 0.05502415522461953 absolute error = 3.33392238122121e-09 relative error = 6.059016389464554e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9399999999999999 y[1] (analytic) = 0.05607526359996047 y[1] (numeric) = 0.05607526761941675 absolute error = 4.019456281700862e-09 relative error = 7.167966806853664e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9299999999999999 y[1] (analytic) = 0.0571362641961155 y[1] (numeric) = 0.05713626890733741 absolute error = 4.711221905651097e-09 relative error = 8.245589682727974e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9199999999999999 y[1] (analytic) = 0.05820715159667454 y[1] (numeric) = 0.05820715700588468 absolute error = 5.409210142304222e-09 relative error = 9.293033577360721e-06 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 8 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9099999999999999 y[1] (analytic) = 0.05928792370048203 y[1] (numeric) = 0.05928792981389709 absolute error = 6.113415065844841e-09 relative error = 1.031140017101853e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8999999999999999 y[1] (analytic) = 0.06037857838774653 y[1] (numeric) = 0.06037858521157286 absolute error = 6.823826330382143e-09 relative error = 1.130173401327878e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8899999999999999 y[1] (analytic) = 0.06147911352005771 y[1] (numeric) = 0.06147912106049448 absolute error = 7.540436774977621e-09 relative error = 1.226503822719815e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8799999999999999 y[1] (analytic) = 0.06258952694041534 y[1] (numeric) = 0.06258953520365346 absolute error = 8.263238121530847e-09 relative error = 1.320226965351148e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8699999999999999 y[1] (analytic) = 0.06370981647325438 y[1] (numeric) = 0.06370982546547527 absolute error = 8.992220884573854e-09 relative error = 1.411434121513883e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8599999999999999 y[1] (analytic) = 0.06483997992446676 y[1] (numeric) = 0.0648399896518445 absolute error = 9.727377736634679e-09 relative error = 1.500212947006812e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8499999999999999 y[1] (analytic) = 0.06598001508143005 y[1] (numeric) = 0.06598002555013024 absolute error = 1.046870019838497e-08 relative error = 1.586647136328311e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8399999999999999 y[1] (analytic) = 0.06712991971303305 y[1] (numeric) = 0.0671299309292116 absolute error = 1.121617855537327e-08 relative error = 1.670816619969186e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8299999999999998 y[1] (analytic) = 0.068289691569697 y[1] (numeric) = 0.06828970353950342 absolute error = 1.196980642381718e-08 relative error = 1.752798431019519e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8199999999999998 y[1] (analytic) = 0.06945932838340939 y[1] (numeric) = 0.06945934111298228 absolute error = 1.272957289577548e-08 relative error = 1.832665704095115e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8099999999999998 y[1] (analytic) = 0.0706388278677423 y[1] (numeric) = 0.07063884136321259 absolute error = 1.349547029683151e-08 relative error = 1.910488990856304e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7999999999999998 y[1] (analytic) = 0.07182818771788424 y[1] (numeric) = 0.07182820198537292 absolute error = 1.426748867661143e-08 relative error = 1.986335605827769e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7899999999999998 y[1] (analytic) = 0.07302740561066216 y[1] (numeric) = 0.07302742065628251 absolute error = 1.504562034682078e-08 relative error = 2.06027041779834e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7799999999999998 y[1] (analytic) = 0.07423647920457176 y[1] (numeric) = 0.07423649503442802 absolute error = 1.582985625914191e-08 relative error = 2.132355471158584e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7699999999999998 y[1] (analytic) = 0.07545540613980296 y[1] (numeric) = 0.07545542275999037 absolute error = 1.662018740689053e-08 relative error = 2.202650314557558e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7599999999999998 y[1] (analytic) = 0.07668418403826716 y[1] (numeric) = 0.07668420145487191 absolute error = 1.741660475562679e-08 relative error = 2.271212111605113e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7499999999999998 y[1] (analytic) = 0.07792281050362559 y[1] (numeric) = 0.07792282872272364 absolute error = 1.821909804966548e-08 relative error = 2.338095601520659e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7399999999999998 y[1] (analytic) = 0.07917128312131357 y[1] (numeric) = 0.07917130214897274 absolute error = 1.902765917050075e-08 relative error = 2.403353642929446e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7299999999999998 y[1] (analytic) = 0.08042959945857128 y[1] (numeric) = 0.08042961930085014 absolute error = 1.984227886164813e-08 relative error = 2.46703688632302e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7199999999999998 y[1] (analytic) = 0.08169775706447183 y[1] (numeric) = 0.08169777772741851 absolute error = 2.066294668701119e-08 relative error = 2.529193876241304e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7099999999999997 y[1] (analytic) = 0.08297575346994582 y[1] (numeric) = 0.08297577495960015 absolute error = 2.148965433379502e-08 relative error = 2.589871551040348e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6999999999999997 y[1] (analytic) = 0.08426358618781293 y[1] (numeric) = 0.08426360851020531 absolute error = 2.23223923789817e-08 relative error = 2.649114924829795e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6899999999999997 y[1] (analytic) = 0.08556125271280927 y[1] (numeric) = 0.08556127587396055 absolute error = 2.316115127465324e-08 relative error = 2.70696729422544e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6799999999999997 y[1] (analytic) = 0.08686875052161584 y[1] (numeric) = 0.08686877452753736 absolute error = 2.400592151452496e-08 relative error = 2.763470335463325e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6699999999999997 y[1] (analytic) = 0.08818607707288864 y[1] (numeric) = 0.08818610192958092 absolute error = 2.48566922739224e-08 relative error = 2.818664022595941e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6599999999999997 y[1] (analytic) = 0.08951322980728404 y[1] (numeric) = 0.08951325552073905 absolute error = 2.571345500412825e-08 relative error = 2.872587109133207e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6499999999999997 y[1] (analytic) = 0.09085020614749255 y[1] (numeric) = 0.09085023272369139 absolute error = 2.657619883883466e-08 relative error = 2.925276668683505e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6399999999999997 y[1] (analytic) = 0.09219700349826254 y[1] (numeric) = 0.09219703094317867 absolute error = 2.744491613138056e-08 relative error = 2.976768776644434e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6299999999999997 y[1] (analytic) = 0.09355361924643742 y[1] (numeric) = 0.09355364756603225 absolute error = 2.831959483584612e-08 relative error = 3.027097728976909e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6199999999999997 y[1] (analytic) = 0.09492005076097768 y[1] (numeric) = 0.0949200799612038 absolute error = 2.92002261259583e-08 relative error = 3.07629693535338e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6099999999999997 y[1] (analytic) = 0.09629629539299625 y[1] (numeric) = 0.09629632547979512 absolute error = 3.008679887173127e-08 relative error = 3.124398373680273e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arctan ( 0.1 * x + 0.2 ) ; Iterations = 40 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 102.5 %