##############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; /* # */ /* # Trouble further */ /* # */ array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=100; glob_max_h=0.00001; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; glob_max_minutes=30.0; 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 = 2.5e-16 est_needed_step_err = 2.5e-16 opt_iter = 1 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 best_h = 2e-06 opt_iter = 2 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 best_h = 4e-06 opt_iter = 3 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 best_h = 8e-06 opt_iter = 4 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 best_h = 1.6e-05 opt_iter = 5 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 best_h = 1e-05 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 % Correct digits = 16 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.17 Order of pole (six term test) = -0.4945 TOP MAIN SOLVE Loop x[1] = -0.9899900000000456 y[1] (analytic) = 0.05091964150920913 y[1] (numeric) = 0.05091964150921465 absolute error = 5.516420653606247e-15 relative error = 1.083358108993868e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.17 Order of pole (six term test) = -0.4946 TOP MAIN SOLVE Loop x[1] = -0.9799900000000911 y[1] (analytic) = 0.05193118711817116 y[1] (numeric) = 0.05193118711818169 absolute error = 1.052630205222727e-14 relative error = 2.026971197148702e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.17 Order of pole (six term test) = -0.4946 TOP MAIN SOLVE Loop x[1] = -0.9699900000001366 y[1] (analytic) = 0.05295262975485577 y[1] (numeric) = 0.05295262975487172 absolute error = 1.595251708508272e-14 relative error = 3.012601481538293e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.18 Order of pole (six term test) = -0.4947 TOP MAIN SOLVE Loop x[1] = -0.9599900000001821 y[1] (analytic) = 0.05398396741165431 y[1] (numeric) = 0.05398396741167503 absolute error = 2.071953719706698e-14 relative error = 3.838090861138515e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.18 Order of pole (six term test) = -0.4948 TOP MAIN SOLVE Loop x[1] = -0.9499900000002276 y[1] (analytic) = 0.05502519806219495 y[1] (numeric) = 0.05502519806222207 absolute error = 2.711719737646945e-14 relative error = 4.928141711697048e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.18 Order of pole (six term test) = -0.4949 TOP MAIN SOLVE Loop x[1] = -0.9399900000002731 y[1] (analytic) = 0.05607631966137489 y[1] (numeric) = 0.05607631966140655 absolute error = 3.166217288352868e-14 relative error = 5.646264425826333e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.19 Order of pole (six term test) = -0.4951 TOP MAIN SOLVE Loop x[1] = -0.9299900000003186 y[1] (analytic) = 0.05713733014537212 y[1] (numeric) = 0.05713733014540977 absolute error = 3.765737721650453e-14 relative error = 6.590678479497457e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.19 Order of pole (six term test) = -0.4952 TOP MAIN SOLVE Loop x[1] = -0.9199900000003641 y[1] (analytic) = 0.05820822743168132 y[1] (numeric) = 0.0582082274317244 absolute error = 4.307665335545607e-14 relative error = 7.400440668978437e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.19 Order of pole (six term test) = -0.4954 TOP MAIN SOLVE Loop x[1] = -0.9099900000004096 y[1] (analytic) = 0.05928900941912939 y[1] (numeric) = 0.05928900941917831 absolute error = 4.892614091644987e-14 relative error = 8.252143423510129e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.2 Order of pole (six term test) = -0.4956 TOP MAIN SOLVE Loop x[1] = -0.8999900000004551 y[1] (analytic) = 0.06037967398790411 y[1] (numeric) = 0.06037967398795923 absolute error = 5.511563427873512e-14 relative error = 9.128176857956612e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.2 Order of pole (six term test) = -0.4958 TOP MAIN SOLVE Loop x[1] = -0.8899900000005007 y[1] (analytic) = 0.06148021899957869 y[1] (numeric) = 0.06148021899963937 absolute error = 6.068756608357262e-14 relative error = 9.871071878255427e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.2 Order of pole (six term test) = -0.4961 TOP MAIN SOLVE Loop x[1] = -0.8799900000005462 y[1] (analytic) = 0.06259064229713324 y[1] (numeric) = 0.06259064229719993 absolute error = 6.669664820435628e-14 relative error = 1.065600954975519e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.21 Order of pole (six term test) = -0.4963 TOP MAIN SOLVE Loop x[1] = -0.8699900000005917 y[1] (analytic) = 0.06371094170498418 y[1] (numeric) = 0.06371094170505612 absolute error = 7.194245199571014e-14 relative error = 1.129200888739681e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.21 Order of pole (six term test) = -0.4966 TOP MAIN SOLVE Loop x[1] = -0.8599900000006372 y[1] (analytic) = 0.0648411150290049 y[1] (numeric) = 0.06484111502908245 absolute error = 7.754907827006718e-14 relative error = 1.195986192331482e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.21 Order of pole (six term test) = -0.4969 TOP MAIN SOLVE Loop x[1] = -0.8499900000006827 y[1] (analytic) = 0.06598116005655447 y[1] (numeric) = 0.06598116005663823 absolute error = 8.376632720796806e-14 relative error = 1.269549173372662e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.22 Order of pole (six term test) = -0.4973 TOP MAIN SOLVE Loop x[1] = -0.8399900000007282 y[1] (analytic) = 0.0671310745565032 y[1] (numeric) = 0.06713107455659233 absolute error = 8.912315330178444e-14 relative error = 1.327599087167461e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.22 Order of pole (six term test) = -0.4976 TOP MAIN SOLVE Loop x[1] = -0.8299900000007737 y[1] (analytic) = 0.06829085627925394 y[1] (numeric) = 0.06829085627935001 absolute error = 9.607592499349948e-14 relative error = 1.406863674407995e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.22 Order of pole (six term test) = -0.498 TOP MAIN SOLVE Loop x[1] = -0.8199900000008192 y[1] (analytic) = 0.06946050295677675 y[1] (numeric) = 0.0694605029568781 absolute error = 1.01349484360469e-13 relative error = 1.459095169862732e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.23 Order of pole (six term test) = -0.4984 TOP MAIN SOLVE Loop x[1] = -0.8099900000008647 y[1] (analytic) = 0.07064001230262319 y[1] (numeric) = 0.07064001230273124 absolute error = 1.080524558716434e-13 relative error = 1.52962113608849e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.23 Order of pole (six term test) = -0.4989 TOP MAIN SOLVE Loop x[1] = -0.7999900000009103 y[1] (analytic) = 0.07182938201196445 y[1] (numeric) = 0.07182938201207834 absolute error = 1.138811267509254e-13 relative error = 1.585439322476094e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.23 Order of pole (six term test) = -0.4993 TOP MAIN SOLVE Loop x[1] = -0.7899900000009558 y[1] (analytic) = 0.07302860976160921 y[1] (numeric) = 0.07302860976172942 absolute error = 1.202093979912888e-13 relative error = 1.646058967625073e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.24 Order of pole (six term test) = -0.4998 TOP MAIN SOLVE Loop x[1] = -0.7799900000010013 y[1] (analytic) = 0.07423769321003587 y[1] (numeric) = 0.07423769321016178 absolute error = 1.259131687803006e-13 relative error = 1.696081375051116e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.24 Order of pole (six term test) = -0.5004 TOP MAIN SOLVE Loop x[1] = -0.7699900000010468 y[1] (analytic) = 0.07545662999741495 y[1] (numeric) = 0.07545662999754703 absolute error = 1.320749065669702e-13 relative error = 1.750341972222917e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.25 Order of pole (six term test) = -0.501 TOP MAIN SOLVE Loop x[1] = -0.7599900000010923 y[1] (analytic) = 0.07668541774563967 y[1] (numeric) = 0.07668541774577838 absolute error = 1.387084891391055e-13 relative error = 1.808798767963841e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.25 Order of pole (six term test) = -0.5016 TOP MAIN SOLVE Loop x[1] = -0.7499900000011378 y[1] (analytic) = 0.07792405405835298 y[1] (numeric) = 0.07792405405849784 absolute error = 1.448563491379673e-13 relative error = 1.85894267037868e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.25 Order of pole (six term test) = -0.5022 TOP MAIN SOLVE Loop x[1] = -0.7399900000011833 y[1] (analytic) = 0.07917253652097198 y[1] (numeric) = 0.07917253652112338 absolute error = 1.514066649832557e-13 relative error = 1.912363448695997e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.26 Order of pole (six term test) = -0.5029 TOP MAIN SOLVE Loop x[1] = -0.7299900000012288 y[1] (analytic) = 0.08043086270071868 y[1] (numeric) = 0.08043086270087713 absolute error = 1.584427034018177e-13 relative error = 1.96992420672372e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.26 Order of pole (six term test) = -0.5036 TOP MAIN SOLVE Loop x[1] = -0.7199900000012743 y[1] (analytic) = 0.08169903014664687 y[1] (numeric) = 0.08169903014681276 absolute error = 1.65895075454614e-13 relative error = 2.030563583886348e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.26 Order of pole (six term test) = -0.5044 TOP MAIN SOLVE Loop x[1] = -0.7099900000013198 y[1] (analytic) = 0.0829770363896713 y[1] (numeric) = 0.08297703638984374 absolute error = 1.724453912999024e-13 relative error = 2.078230300851862e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.27 Order of pole (six term test) = -0.5052 TOP MAIN SOLVE Loop x[1] = -0.6999900000013654 y[1] (analytic) = 0.08426487894259359 y[1] (numeric) = 0.08426487894277186 absolute error = 1.782740621791845e-13 relative error = 2.115638975766354e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.27 Order of pole (six term test) = -0.506 TOP MAIN SOLVE Loop x[1] = -0.6899900000014109 y[1] (analytic) = 0.08556255530012949 y[1] (numeric) = 0.08556255530031515 absolute error = 1.856570452929418e-13 relative error = 2.169839886638599e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.27 Order of pole (six term test) = -0.5069 TOP MAIN SOLVE Loop x[1] = -0.6799900000014564 y[1] (analytic) = 0.08687006293894421 y[1] (numeric) = 0.08687006293913645 absolute error = 1.922351167138459e-13 relative error = 2.212904080073667e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.28 Order of pole (six term test) = -0.5078 TOP MAIN SOLVE Loop x[1] = -0.6699900000015019 y[1] (analytic) = 0.08818739931767458 y[1] (numeric) = 0.08818739931787298 absolute error = 1.983968545005155e-13 relative error = 2.249718849127606e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.28 Order of pole (six term test) = -0.5087 TOP MAIN SOLVE Loop x[1] = -0.6599900000015474 y[1] (analytic) = 0.08951456187695797 y[1] (numeric) = 0.08951456187716386 absolute error = 2.058908599167353e-13 relative error = 2.300082306158657e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.28 Order of pole (six term test) = -0.5098 TOP MAIN SOLVE Loop x[1] = -0.6499900000015929 y[1] (analytic) = 0.09085154803946803 y[1] (numeric) = 0.09085154803968085 absolute error = 2.128158760328347e-13 relative error = 2.342457345254948e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.29 Order of pole (six term test) = -0.5108 TOP MAIN SOLVE Loop x[1] = -0.6399900000016384 y[1] (analytic) = 0.09219835520993729 y[1] (numeric) = 0.0921983552101566 absolute error = 2.193106807268919e-13 relative error = 2.378683223008887e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.29 Order of pole (six term test) = -0.5119 TOP MAIN SOLVE Loop x[1] = -0.6299900000016839 y[1] (analytic) = 0.09355498077518698 y[1] (numeric) = 0.09355498077541399 absolute error = 2.270128529602289e-13 relative error = 2.426518086789433e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.3 Order of pole (six term test) = -0.5131 TOP MAIN SOLVE Loop x[1] = -0.6199900000017294 y[1] (analytic) = 0.094921422104163 y[1] (numeric) = 0.09492142210439701 absolute error = 2.340072580153674e-13 relative error = 2.465273410659367e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.3 Order of pole (six term test) = -0.5143 TOP MAIN SOLVE Loop x[1] = -0.6099900000017749 y[1] (analytic) = 0.09629767654795937 y[1] (numeric) = 0.0962976765481998 absolute error = 2.404326737703855e-13 relative error = 2.496765055911211e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.3 Order of pole (six term test) = -0.5155 Finished! diff ( y , x , 1 ) = arctan ( 0.1 * x + 0.2 ) ; Iterations = 40001 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Time to Timeout = 29 Minutes 59.0 Seconds Percent Done = 100 %