##############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=0.001; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; 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 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 = 9.686664026714653e-185 estimated_step_error = 9.686664026714653e-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 = 6.500610408548441e-177 estimated_step_error = 6.500610408548441e-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 = 4.362486094492729e-169 estimated_step_error = 4.362486094492729e-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 = 2.927615257792035e-161 estimated_step_error = 2.927615257792035e-161 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 = 1.964689875470974e-153 estimated_step_error = 1.964689875470974e-153 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.318481772838247e-145 estimated_step_error = 1.318481772838247e-145 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.848191011791846e-138 estimated_step_error = 8.848191011791846e-138 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.937933375903838e-130 estimated_step_error = 5.937933375903838e-130 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.984896951977728e-122 estimated_step_error = 3.984896951977728e-122 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.674242319674756e-114 estimated_step_error = 2.674242319674756e-114 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.794684836698649e-106 estimated_step_error = 1.794684836698649e-106 best_h = 0.001 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 = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2202 Order of pole (three term test) = -14.93 Radius of convergence (six term test) for eq 1 = 10.08 Order of pole (six term test) = -0.9445 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (analytic) = 0.0509186349177335 y[1] (numeric) = 0.0509186349210475 absolute error = 3.314001850718284e-12 relative error = 6.508426347392343e-09 % Correct digits = 11 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2198 Order of pole (three term test) = -15.51 Radius of convergence (six term test) for eq 1 = 10.08 Order of pole (six term test) = -0.9449 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (analytic) = 0.05193017062867283 y[1] (numeric) = 0.05193017063533453 absolute error = 6.661705909127846e-12 relative error = 1.282819953888162e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.219 Order of pole (three term test) = -16.08 Radius of convergence (six term test) for eq 1 = 10.08 Order of pole (six term test) = -0.9452 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (analytic) = 0.05295160336933419 y[1] (numeric) = 0.05295160337937507 absolute error = 1.004088479028553e-11 relative error = 1.896238102603046e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2177 Order of pole (three term test) = -16.65 Radius of convergence (six term test) for eq 1 = 10.08 Order of pole (six term test) = -0.9455 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (analytic) = 0.05398293113212667 y[1] (numeric) = 0.05398293114557818 absolute error = 1.345151073861572e-11 relative error = 2.49180814315034e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2159 Order of pole (three term test) = -17.21 Radius of convergence (six term test) for eq 1 = 10.08 Order of pole (six term test) = -0.9459 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (analytic) = 0.05502415189069714 y[1] (numeric) = 0.05502415190759293 absolute error = 1.689579032237987e-11 relative error = 3.070613492769966e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2138 Order of pole (three term test) = -17.76 Radius of convergence (six term test) for eq 1 = 10.08 Order of pole (six term test) = -0.9462 TOP MAIN SOLVE Loop x[1] = -0.9399999999999999 y[1] (analytic) = 0.05607526359996048 y[1] (numeric) = 0.05607526362033195 absolute error = 2.037146840105919e-11 relative error = 3.632879650176722e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2112 Order of pole (three term test) = -18.3 Radius of convergence (six term test) for eq 1 = 10.08 Order of pole (six term test) = -0.9466 TOP MAIN SOLVE Loop x[1] = -0.9299999999999999 y[1] (analytic) = 0.0571362641961155 y[1] (numeric) = 0.05713626421999518 absolute error = 2.387967601436003e-11 relative error = 4.179425510284504e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2082 Order of pole (three term test) = -18.83 Radius of convergence (six term test) for eq 1 = 10.08 Order of pole (six term test) = -0.9469 TOP MAIN SOLVE Loop x[1] = -0.9199999999999999 y[1] (analytic) = 0.05820715159667454 y[1] (numeric) = 0.05820715162409379 absolute error = 2.741924742810653e-11 relative error = 4.710632057397056e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2048 Order of pole (three term test) = -19.34 Radius of convergence (six term test) for eq 1 = 10.09 Order of pole (six term test) = -0.9473 TOP MAIN SOLVE Loop x[1] = -0.9099999999999999 y[1] (analytic) = 0.05928792370048203 y[1] (numeric) = 0.05928792373147439 absolute error = 3.099235451609061e-11 relative error = 5.227431251035468e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.201 Order of pole (three term test) = -19.85 Radius of convergence (six term test) for eq 1 = 10.09 Order of pole (six term test) = -0.9476 TOP MAIN SOLVE Loop x[1] = -0.8999999999999999 y[1] (analytic) = 0.06037857838774654 y[1] (numeric) = 0.06037857842234334 absolute error = 3.459680458783865e-11 relative error = 5.729979988210497e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1967 Order of pole (three term test) = -20.33 Radius of convergence (six term test) for eq 1 = 10.09 Order of pole (six term test) = -0.948 TOP MAIN SOLVE Loop x[1] = -0.8899999999999999 y[1] (analytic) = 0.06147911352005769 y[1] (numeric) = 0.06147911355829136 absolute error = 3.823366623301183e-11 relative error = 6.218968368914105e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1921 Order of pole (three term test) = -20.8 Radius of convergence (six term test) for eq 1 = 10.09 Order of pole (six term test) = -0.9483 TOP MAIN SOLVE Loop x[1] = -0.8799999999999999 y[1] (analytic) = 0.06258952694041532 y[1] (numeric) = 0.06258952698231822 absolute error = 4.190289781824674e-11 relative error = 6.69487370596968e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1871 Order of pole (three term test) = -21.26 Radius of convergence (six term test) for eq 1 = 10.09 Order of pole (six term test) = -0.9487 TOP MAIN SOLVE Loop x[1] = -0.8699999999999999 y[1] (analytic) = 0.06370981647325435 y[1] (numeric) = 0.06370981651885776 absolute error = 4.560340993720047e-11 relative error = 7.157987961924983e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1818 Order of pole (three term test) = -21.69 Radius of convergence (six term test) for eq 1 = 10.09 Order of pole (six term test) = -0.9491 TOP MAIN SOLVE Loop x[1] = -0.8599999999999999 y[1] (analytic) = 0.06483997992446676 y[1] (numeric) = 0.064839979973803 absolute error = 4.933624342395859e-11 relative error = 7.608923303404976e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1761 Order of pole (three term test) = -22.1 Radius of convergence (six term test) for eq 1 = 10.09 Order of pole (six term test) = -0.9495 TOP MAIN SOLVE Loop x[1] = -0.8499999999999999 y[1] (analytic) = 0.06598001508143005 y[1] (numeric) = 0.06598001513453149 absolute error = 5.310143991188454e-11 relative error = 8.048109695996393e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.17 Order of pole (three term test) = -22.5 Radius of convergence (six term test) for eq 1 = 10.09 Order of pole (six term test) = -0.9498 TOP MAIN SOLVE Loop x[1] = -0.8399999999999999 y[1] (analytic) = 0.06712991971303305 y[1] (numeric) = 0.06712991976993085 absolute error = 5.689780591122684e-11 relative error = 8.475774461589341e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1636 Order of pole (three term test) = -22.87 Radius of convergence (six term test) for eq 1 = 10.1 Order of pole (six term test) = -0.9502 TOP MAIN SOLVE Loop x[1] = -0.8299999999999998 y[1] (analytic) = 0.068289691569697 y[1] (numeric) = 0.06828969163042455 absolute error = 6.072754799024693e-11 relative error = 8.892637614019375e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1569 Order of pole (three term test) = -23.22 Radius of convergence (six term test) for eq 1 = 10.1 Order of pole (six term test) = -0.9506 TOP MAIN SOLVE Loop x[1] = -0.8199999999999998 y[1] (analytic) = 0.06945932838340939 y[1] (numeric) = 0.06945932844799785 absolute error = 6.458845958068338e-11 relative error = 9.298745191453732e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1499 Order of pole (three term test) = -23.55 Radius of convergence (six term test) for eq 1 = 10.1 Order of pole (six term test) = -0.951 TOP MAIN SOLVE Loop x[1] = -0.8099999999999998 y[1] (analytic) = 0.0706388278677423 y[1] (numeric) = 0.07063882793622389 absolute error = 6.848159539440957e-11 relative error = 9.694610947201483e-08 % Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1426 Order of pole (three term test) = -23.85 Radius of convergence (six term test) for eq 1 = 10.1 Order of pole (six term test) = -0.9514 TOP MAIN SOLVE Loop x[1] = -0.7999999999999998 y[1] (analytic) = 0.07182818771788423 y[1] (numeric) = 0.07182818779029003 absolute error = 7.240580357503745e-11 relative error = 1.008041632059852e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1351 Order of pole (three term test) = -24.13 Radius of convergence (six term test) for eq 1 = 10.1 Order of pole (six term test) = -0.9518 TOP MAIN SOLVE Loop x[1] = -0.7899999999999998 y[1] (analytic) = 0.07302740561066216 y[1] (numeric) = 0.07302740568702437 absolute error = 7.636220822337947e-11 relative error = 1.045665084016492e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1273 Order of pole (three term test) = -24.38 Radius of convergence (six term test) for eq 1 = 10.1 Order of pole (six term test) = -0.9522 TOP MAIN SOLVE Loop x[1] = -0.7799999999999998 y[1] (analytic) = 0.07423647920457176 y[1] (numeric) = 0.07423647928492252 absolute error = 8.035076770607219e-11 relative error = 1.082362317919893e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1193 Order of pole (three term test) = -24.61 Radius of convergence (six term test) for eq 1 = 10.1 Order of pole (six term test) = -0.9526 TOP MAIN SOLVE Loop x[1] = -0.7699999999999998 y[1] (analytic) = 0.07545540613980294 y[1] (numeric) = 0.07545540622417439 absolute error = 8.437145426754e-11 relative error = 1.118163145410913e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1111 Order of pole (three term test) = -24.81 Radius of convergence (six term test) for eq 1 = 10.11 Order of pole (six term test) = -0.953 TOP MAIN SOLVE Loop x[1] = -0.7599999999999998 y[1] (analytic) = 0.07668418403826713 y[1] (numeric) = 0.07668418412669138 absolute error = 8.84242540299951e-11 relative error = 1.153096367118797e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1026 Order of pole (three term test) = -24.99 Radius of convergence (six term test) for eq 1 = 10.11 Order of pole (six term test) = -0.9535 TOP MAIN SOLVE Loop x[1] = -0.7499999999999998 y[1] (analytic) = 0.07792281050362559 y[1] (numeric) = 0.07792281059613362 absolute error = 9.250802901483723e-11 relative error = 1.187175211173024e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09403 Order of pole (three term test) = -25.14 Radius of convergence (six term test) for eq 1 = 10.11 Order of pole (six term test) = -0.9539 TOP MAIN SOLVE Loop x[1] = -0.7399999999999998 y[1] (analytic) = 0.07917128312131357 y[1] (numeric) = 0.07917128321793744 absolute error = 9.662387556730323e-11 relative error = 1.220440944720413e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08528 Order of pole (three term test) = -25.26 Radius of convergence (six term test) for eq 1 = 10.11 Order of pole (six term test) = -0.9543 TOP MAIN SOLVE Loop x[1] = -0.7299999999999998 y[1] (analytic) = 0.08042959945857131 y[1] (numeric) = 0.08042959955934303 absolute error = 1.00771724298454e-10 relative error = 1.252918390453515e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0764 Order of pole (three term test) = -25.35 Radius of convergence (six term test) for eq 1 = 10.11 Order of pole (six term test) = -0.9548 TOP MAIN SOLVE Loop x[1] = -0.7199999999999998 y[1] (analytic) = 0.08169775706447184 y[1] (numeric) = 0.08169775716942236 absolute error = 1.049505204964163e-10 relative error = 1.284619361258529e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06741 Order of pole (three term test) = -25.41 Radius of convergence (six term test) for eq 1 = 10.11 Order of pole (six term test) = -0.9552 TOP MAIN SOLVE Loop x[1] = -0.7099999999999997 y[1] (analytic) = 0.08297575346994582 y[1] (numeric) = 0.08297575357910711 absolute error = 1.091612911174877e-10 relative error = 1.315580594962918e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05832 Order of pole (three term test) = -25.45 Radius of convergence (six term test) for eq 1 = 10.12 Order of pole (six term test) = -0.9557 TOP MAIN SOLVE Loop x[1] = -0.6999999999999997 y[1] (analytic) = 0.08426358618781295 y[1] (numeric) = 0.08426358630121693 absolute error = 1.134039806505172e-10 relative error = 1.345824285210861e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04917 Order of pole (three term test) = -25.46 Radius of convergence (six term test) for eq 1 = 10.12 Order of pole (six term test) = -0.9561 TOP MAIN SOLVE Loop x[1] = -0.6899999999999997 y[1] (analytic) = 0.08556125271280926 y[1] (numeric) = 0.0855612528304879 absolute error = 1.176786446066558e-10 relative error = 1.375373090920609e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03996 Order of pole (three term test) = -25.44 Radius of convergence (six term test) for eq 1 = 10.12 Order of pole (six term test) = -0.9566 TOP MAIN SOLVE Loop x[1] = -0.6799999999999997 y[1] (analytic) = 0.08686875052161586 y[1] (numeric) = 0.08686875064360107 absolute error = 1.219852135969646e-10 relative error = 1.404247360120721e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03073 Order of pole (three term test) = -25.39 Radius of convergence (six term test) for eq 1 = 10.12 Order of pole (six term test) = -0.9571 TOP MAIN SOLVE Loop x[1] = -0.6699999999999997 y[1] (analytic) = 0.08818607707288864 y[1] (numeric) = 0.0881860771992112 absolute error = 1.263225635206311e-10 relative error = 1.432454733372723e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02149 Order of pole (three term test) = -25.32 Radius of convergence (six term test) for eq 1 = 10.12 Order of pole (six term test) = -0.9575 TOP MAIN SOLVE Loop x[1] = -0.6599999999999997 y[1] (analytic) = 0.08951322980728406 y[1] (numeric) = 0.08951322993797579 absolute error = 1.306917352117409e-10 relative error = 1.460027031681366e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01226 Order of pole (three term test) = -25.22 Radius of convergence (six term test) for eq 1 = 10.12 Order of pole (six term test) = -0.958 TOP MAIN SOLVE Loop x[1] = -0.6499999999999997 y[1] (analytic) = 0.09085020614749258 y[1] (numeric) = 0.09085020628258424 absolute error = 1.350916600806329e-10 relative error = 1.486971420420507e-07 % Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.003069 Order of pole (three term test) = -25.09 Radius of convergence (six term test) for eq 1 = 10.12 Order of pole (six term test) = -0.9585 TOP MAIN SOLVE Loop x[1] = -0.6399999999999997 y[1] (analytic) = 0.09219700349826254 y[1] (numeric) = 0.09219700363778702 absolute error = 1.395244753066294e-10 relative error = 1.513329826486809e-07 % Correct digits = 9 h = 0.001 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 = 10.13 Order of pole (six term test) = -0.959 TOP MAIN SOLVE Loop x[1] = -0.6299999999999997 y[1] (analytic) = 0.09355361924643742 y[1] (numeric) = 0.09355361939042539 absolute error = 1.439879743214689e-10 relative error = 1.539095713038938e-07 % Correct digits = 9 h = 0.001 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 = 10.13 Order of pole (six term test) = -0.9595 TOP MAIN SOLVE Loop x[1] = -0.6199999999999997 y[1] (analytic) = 0.09492005076097768 y[1] (numeric) = 0.09492005090946089 absolute error = 1.48483211837025e-10 relative error = 1.564297644666531e-07 % Correct digits = 9 h = 0.001 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 = 10.13 Order of pole (six term test) = -0.96 TOP MAIN SOLVE Loop x[1] = -0.6099999999999997 y[1] (analytic) = 0.09629629539299625 y[1] (numeric) = 0.09629629554600529 absolute error = 1.530090359969094e-10 relative error = 1.588940004103605e-07 % Correct digits = 9 h = 0.001 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 = 10.13 Order of pole (six term test) = -0.9605 Finished! diff ( y , x , 1 ) = arctan (0.1 * x + 0.2 ) ; Iterations = 400 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 100.3 %