##############ECHO OF PROBLEM################# ##############temp/addpostode.ode################# diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ max_terms=40; Digits=32; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-5.0; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(2.0 - cos(x) - cos(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 10000000 step_error = 7.905694150420948e-22 est_needed_step_err = 7.905694150420948e-22 opt_iter = 1 NO POLE (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 = 1.432675629073548 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1.432675629073548 desired_abs_gbl_error = 1.432675629073548e-16 range = 10 estimated_steps = 10000000 step_error = 1.13262953402174e-21 est_needed_step_err = 1.13262953402174e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.525092801812542e-258 estimated_step_error = 1.525092801812542e-258 Double H and LOOP opt_iter = 2 NO POLE (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 = 1.432675629073548 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1.432675629073548 desired_abs_gbl_error = 1.432675629073548e-16 range = 10 estimated_steps = 5000000 step_error = 1.601780048157863e-21 est_needed_step_err = 1.601780048157863e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.048035745266941e-247 estimated_step_error = 1.048035745266941e-247 Double H and LOOP opt_iter = 3 NO POLE (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 = 1.432675629073548 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1.432675629073548 desired_abs_gbl_error = 1.432675629073548e-16 range = 10 estimated_steps = 2500000 step_error = 2.265259068043479e-21 est_needed_step_err = 2.265259068043479e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.202046143519769e-237 estimated_step_error = 7.202046143519769e-237 Double H and LOOP opt_iter = 4 NO POLE (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 = 1.432675629073548 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1.432675629073548 desired_abs_gbl_error = 1.432675629073548e-16 range = 10 estimated_steps = 1250000 step_error = 3.203560096315726e-21 est_needed_step_err = 3.203560096315726e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.949207519740312e-226 estimated_step_error = 4.949207519740312e-226 Double H and LOOP opt_iter = 5 NO POLE (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 = 1.432675629073548 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1.432675629073548 desired_abs_gbl_error = 1.432675629073548e-16 range = 10 estimated_steps = 625000 step_error = 4.530518136086959e-21 est_needed_step_err = 4.530518136086959e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.401068267185195e-215 estimated_step_error = 3.401068267185195e-215 Double H and LOOP opt_iter = 6 NO POLE (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 = 1.432675629073548 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1.432675629073548 desired_abs_gbl_error = 1.432675629073548e-16 range = 10 estimated_steps = 312500 step_error = 6.407120192631453e-21 est_needed_step_err = 6.407120192631453e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.337194608333651e-204 estimated_step_error = 2.337194608333651e-204 Double H and LOOP opt_iter = 7 NO POLE (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 = 1.432675629073548 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1.432675629073548 desired_abs_gbl_error = 1.432675629073548e-16 range = 10 estimated_steps = 156250 step_error = 9.061036272173918e-21 est_needed_step_err = 9.061036272173918e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.606105557264851e-193 estimated_step_error = 1.606105557264851e-193 Double H and LOOP opt_iter = 8 NO POLE (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 = 1.432675629073548 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1.432675629073548 desired_abs_gbl_error = 1.432675629073548e-16 range = 10 estimated_steps = 78125 step_error = 1.281424038526291e-20 est_needed_step_err = 1.281424038526291e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.103704107871764e-182 estimated_step_error = 1.103704107871764e-182 Double H and LOOP opt_iter = 9 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.272 Order of pole (three term test) = 32.92 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (closed_form) = 1.432675629073548 y[1] (numeric) = 1.432675629073548 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.000128 NO POLE (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] = -4.8999039999999 y[1] (closed_form) = 1.627163893775278 y[1] (numeric) = 1.627163893775085 absolute error = 1.929567616798522e-13 relative error = 1.185847119752405e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -4.7999359999998 y[1] (closed_form) = 1.825129542549745 y[1] (numeric) = 1.825129542549354 absolute error = 3.907985046680551e-13 relative error = 2.141209681599374e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -4.6999679999997 y[1] (closed_form) = 2.024841322002168 y[1] (numeric) = 2.02484132200158 absolute error = 5.88862292261183e-13 relative error = 2.90818982140741e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -4.5999999999996 y[1] (closed_form) = 2.224305053870904 y[1] (numeric) = 2.224305053870117 absolute error = 7.87370169064161e-13 relative error = 3.539847952482596e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -4.4999039999995 y[1] (closed_form) = 2.421779282702147 y[1] (numeric) = 2.421779282701161 absolute error = 9.85878045867139e-13 relative error = 4.070883143269467e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -4.3999359999994 y[1] (closed_form) = 2.614787543764521 y[1] (numeric) = 2.614787543763339 absolute error = 1.181721387411017e-12 relative error = 4.519378219576827e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -4.2999679999993 y[1] (closed_form) = 2.801656978370757 y[1] (numeric) = 2.801656978369384 absolute error = 1.373567926066244e-12 relative error = 4.90269842693238e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -4.1999999999992 y[1] (closed_form) = 2.980521642682794 y[1] (numeric) = 2.980521642681246 absolute error = 1.547206807117618e-12 relative error = 5.19106046727097e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -4.0999039999991 y[1] (closed_form) = 3.149804996975517 y[1] (numeric) = 3.149804996973802 absolute error = 1.715072528440942e-12 relative error = 5.445011770848597e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -3.999935999999 y[1] (closed_form) = 3.307384109770746 y[1] (numeric) = 3.307384109768867 absolute error = 1.878941446875615e-12 relative error = 5.681049991516876e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -3.8999679999989 y[1] (closed_form) = 3.451908624692619 y[1] (numeric) = 3.451908624690592 absolute error = 2.027267242965536e-12 relative error = 5.872887910368883e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -3.7999999999988 y[1] (closed_form) = 3.581935423830302 y[1] (numeric) = 3.581935423828144 absolute error = 2.158273559871304e-12 relative error = 6.025439614328331e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -3.6999039999987 y[1] (closed_form) = 3.696301784145002 y[1] (numeric) = 3.696301784142725 absolute error = 2.277289468111121e-12 relative error = 6.160994423884371e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -3.5999359999986 y[1] (closed_form) = 3.793573471613113 y[1] (numeric) = 3.793573471610741 absolute error = 2.372768648228885e-12 relative error = 6.254705928286476e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -3.4999679999985 y[1] (closed_form) = 3.872935823750282 y[1] (numeric) = 3.872935823747838 absolute error = 2.443822921804895e-12 relative error = 6.310001076750262e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -3.3999999999984 y[1] (closed_form) = 3.93359638515974 y[1] (numeric) = 3.933596385157231 absolute error = 2.509104035652854e-12 relative error = 6.378651467951664e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (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] = -3.2999039999983 y[1] (closed_form) = 3.974989817890881 y[1] (numeric) = 3.97498981788833 absolute error = 2.55129251058861e-12 relative error = 6.418362379459675e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -3.1999359999982 y[1] (closed_form) = 3.996597019391054 y[1] (numeric) = 3.996597019388483 absolute error = 2.571276525031863e-12 relative error = 6.433664721652717e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -3.0999679999981 y[1] (closed_form) = 3.998267638360891 y[1] (numeric) = 3.998267638358319 absolute error = 2.572608792661413e-12 relative error = 6.434308619009972e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -2.999999999998 y[1] (closed_form) = 3.979984993200326 y[1] (numeric) = 3.979984993197772 absolute error = 2.55440113505756e-12 relative error = 6.418117504014891e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -2.8999039999979 y[1] (closed_form) = 3.941870385478687 y[1] (numeric) = 3.941870385476169 absolute error = 2.518429909059705e-12 relative error = 6.388921153615953e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -2.7999359999978 y[1] (closed_form) = 3.884401798993308 y[1] (numeric) = 3.884401798990849 absolute error = 2.459366044149647e-12 relative error = 6.331389416993429e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -2.6999679999977 y[1] (closed_form) = 3.808116930794056 y[1] (numeric) = 3.808116930791668 absolute error = 2.388311770573637e-12 relative error = 6.271634547932943e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -2.5999999999976 y[1] (closed_form) = 3.71377750673542 y[1] (numeric) = 3.713777506733127 absolute error = 2.292832590455873e-12 relative error = 6.173855558922209e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -2.4999039999975 y[1] (closed_form) = 3.602172317056043 y[1] (numeric) = 3.602172317053856 absolute error = 2.186695269301708e-12 relative error = 6.070490461957784e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -2.3999359999974 y[1] (closed_form) = 3.474700968771562 y[1] (numeric) = 3.474700968769503 absolute error = 2.05924166607474e-12 relative error = 5.926385276263816e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -2.2999679999973 y[1] (closed_form) = 3.332504316739783 y[1] (numeric) = 3.33250431673787 absolute error = 1.91313631603407e-12 relative error = 5.740836722773422e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -2.1999999999972 y[1] (closed_form) = 3.177002234506164 y[1] (numeric) = 3.177002234504396 absolute error = 1.767919144413099e-12 relative error = 5.564740009343765e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -2.0999039999971 y[1] (closed_form) = 3.009526468343903 y[1] (numeric) = 3.009526468342302 absolute error = 1.601829779929176e-12 relative error = 5.322530958867554e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -1.999935999997 y[1] (closed_form) = 2.832177281313736 y[1] (numeric) = 2.832177281312312 absolute error = 1.424194095989151e-12 relative error = 5.028619166553453e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -1.899967999997073 y[1] (closed_form) = 2.646518570184818 y[1] (numeric) = 2.646518570183253 absolute error = 1.564970375511621e-12 relative error = 5.913317190146645e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -1.799999999997147 y[1] (closed_form) = 2.454404189380617 y[1] (numeric) = 2.45440418937891 absolute error = 1.707523011873491e-12 relative error = 6.956975624721346e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -1.69990399999722 y[1] (closed_form) = 2.257498587754791 y[1] (numeric) = 2.257498587752936 absolute error = 1.854960629543712e-12 relative error = 8.216885005401374e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -1.599935999997294 y[1] (closed_form) = 2.058271099056464 y[1] (numeric) = 2.058271099054463 absolute error = 2.000621890374532e-12 relative error = 9.719914404334983e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = -1.499967999997367 y[1] (closed_form) = 1.858461757052645 y[1] (numeric) = 1.858461757050496 absolute error = 2.148725641859528e-12 relative error = 1.156185018984311e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = -1.399999999997441 y[1] (closed_form) = 1.660065714194474 y[1] (numeric) = 1.660065714192175 absolute error = 2.298383705578999e-12 relative error = 1.384513688781447e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = -1.299903999997514 y[1] (closed_form) = 1.464817342039988 y[1] (numeric) = 1.464817342037544 absolute error = 2.444267011014745e-12 relative error = 1.668649694992496e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = -1.199935999997588 y[1] (closed_form) = 1.275165191523451 y[1] (numeric) = 1.275165191520869 absolute error = 2.582600799883039e-12 relative error = 2.025306852046034e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = -1.099967999997661 y[1] (closed_form) = 1.092750720338124 y[1] (numeric) = 1.09275072033541 absolute error = 2.714273250603583e-12 relative error = 2.483890607515426e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = -0.9999999999977344 y[1] (closed_form) = 0.9193953882599076 y[1] (numeric) = 0.9193953882570649 absolute error = 2.842726054552713e-12 relative error = 3.091951613911176e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = -0.8999039999977211 y[1] (closed_form) = 0.756629670417441 y[1] (numeric) = 0.7566296704146209 absolute error = 2.82007750485036e-12 relative error = 3.727156910585455e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = -0.7999359999977078 y[1] (closed_form) = 0.6064947625765189 y[1] (numeric) = 0.6064947625737198 absolute error = 2.799094289684945e-12 relative error = 4.615199441778847e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (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] = -0.6999679999976945 y[1] (closed_form) = 0.470274396279275 y[1] (numeric) = 0.4702743962764935 absolute error = 2.781552765895867e-12 relative error = 5.914744217212342e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (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] = -0.5999999999976813 y[1] (closed_form) = 0.3493287701780251 y[1] (numeric) = 0.3493287701752597 absolute error = 2.765454532038802e-12 relative error = 7.916480885984485e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (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] = -0.499903999997668 y[1] (closed_form) = 0.2447428346015492 y[1] (numeric) = 0.2447428345987985 absolute error = 2.750744076962519e-12 relative error = 1.123932425413327e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (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] = -0.3999359999976547 y[1] (closed_form) = 0.1578281702172878 y[1] (numeric) = 0.1578281702145488 absolute error = 2.738947957325877e-12 relative error = 1.735398663974288e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (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] = -0.2999679999976415 y[1] (closed_form) = 0.0893081094324355 y[1] (numeric) = 0.08930810942970549 absolute error = 2.730010661977644e-12 relative error = 3.056845206249704e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (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] = -0.199999999997639 y[1] (closed_form) = 0.0398668443165785 y[1] (numeric) = 0.03986684431385019 absolute error = 2.728303694077283e-12 relative error = 6.843540643478338e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 h = 0.000128 NO POLE (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] = -0.09990399999764472 y[1] (closed_form) = 0.009972510597470285 y[1] (numeric) = 0.009972510594739897 absolute error = 2.730388831695407e-12 relative error = 2.737915196989634e-08 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 10 h = 0.000128 NO POLE (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] = 6.400000235686883e-05 y[1] (closed_form) = 4.096000094655494e-09 y[1] (numeric) = 4.093270127789706e-09 absolute error = 2.729966865788382e-12 relative error = 0.06664958014406476 % Desired digits = 16 Estimated correct digits = 3 Correct digits = 4 h = 0.000128 NO POLE (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] = 0.1000320000023585 y[1] (closed_form) = 0.009998059801968107 y[1] (numeric) = 0.009998059799237704 absolute error = 2.730402709483215e-12 relative error = 2.730932564481899e-08 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 10 h = 0.000128 NO POLE (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] = 0.2000000000023528 y[1] (closed_form) = 0.03986684431845156 y[1] (numeric) = 0.03986684431572316 absolute error = 2.728393899698034e-12 relative error = 6.843766910428003e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 h = 0.000128 NO POLE (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] = 0.3000960000023552 y[1] (closed_form) = 0.08938377043415346 y[1] (numeric) = 0.08938377043142308 absolute error = 2.730385362248455e-12 relative error = 3.054676871412416e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (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] = 0.4000640000023685 y[1] (closed_form) = 0.157927861316522 y[1] (numeric) = 0.1579278613137828 absolute error = 2.739225513082033e-12 relative error = 1.734478951495471e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (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] = 0.5000320000023817 y[1] (closed_form) = 0.2448655603546483 y[1] (numeric) = 0.2448655603518977 absolute error = 2.750688565811288e-12 relative error = 1.123346444402944e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (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] = 0.600000000002395 y[1] (closed_form) = 0.3493287701833481 y[1] (numeric) = 0.3493287701805827 absolute error = 2.765399020887571e-12 relative error = 7.916321977820862e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (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] = 0.7000960000024082 y[1] (closed_form) = 0.4704393222786716 y[1] (numeric) = 0.4704393222758909 absolute error = 2.780720098627398e-12 relative error = 5.910900655919657e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (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] = 0.8000640000024215 y[1] (closed_form) = 0.6066784057424267 y[1] (numeric) = 0.6066784057396282 absolute error = 2.798539178172632e-12 relative error = 4.612887407370139e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (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] = 0.9000320000024348 y[1] (closed_form) = 0.7568301970212219 y[1] (numeric) = 0.7568301970184037 absolute error = 2.818190125708497e-12 relative error = 3.723675583770971e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 1.000000000002448 y[1] (closed_form) = 0.9193953882678406 y[1] (numeric) = 0.9193953882650006 absolute error = 2.840061519293613e-12 relative error = 3.089053475289174e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 1.100096000002375 y[1] (closed_form) = 1.092978873146289 y[1] (numeric) = 1.092978873143574 absolute error = 2.714495295208508e-12 relative error = 2.483575265635705e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 1.200064000002301 y[1] (closed_form) = 1.275403793538082 y[1] (numeric) = 1.275403793535502 absolute error = 2.580158309228864e-12 relative error = 2.023012886037667e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 1.300032000002228 y[1] (closed_form) = 1.465064010752893 y[1] (numeric) = 1.465064010750452 absolute error = 2.440714297335944e-12 relative error = 1.665943794552476e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 1.400000000002154 y[1] (closed_form) = 1.660065714203764 y[1] (numeric) = 1.660065714201468 absolute error = 2.296163259529749e-12 relative error = 1.383176123621759e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 1.500096000002081 y[1] (closed_form) = 1.858717116357793 y[1] (numeric) = 1.85871711635564 absolute error = 2.153166533958029e-12 relative error = 1.158415401143568e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (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] = 1.600064000002007 y[1] (closed_form) = 2.058526989908091 y[1] (numeric) = 2.058526989906088 absolute error = 2.002842336423782e-12 relative error = 9.729492720973287e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 1.700032000001934 y[1] (closed_form) = 2.257752455010806 y[1] (numeric) = 2.257752455008951 absolute error = 1.854516540333861e-12 relative error = 8.213994125963581e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 1.80000000000186 y[1] (closed_form) = 2.454404189389797 y[1] (numeric) = 2.454404189388086 absolute error = 1.711519814762141e-12 relative error = 6.973259832919578e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 1.900096000001787 y[1] (closed_form) = 2.646760820367509 y[1] (numeric) = 2.64676082036594 absolute error = 1.568967178400271e-12 relative error = 5.927876694889327e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.000064000001713 y[1] (closed_form) = 2.832410061463417 y[1] (numeric) = 2.832410061461987 absolute error = 1.429523166507352e-12 relative error = 5.047020507224021e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.100032000001813 y[1] (closed_form) = 3.009747454085339 y[1] (numeric) = 3.009747454083737 absolute error = 1.602273869139026e-12 relative error = 5.323615664045661e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.200000000001913 y[1] (closed_form) = 3.177002234513785 y[1] (numeric) = 3.177002234512012 absolute error = 1.7732482149313e-12 relative error = 5.581513905364569e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.300096000002013 y[1] (closed_form) = 3.332695211822769 y[1] (numeric) = 3.332695211820837 absolute error = 1.932676241267473e-12 relative error = 5.799138890383028e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.400064000002113 y[1] (closed_form) = 3.474873887352032 y[1] (numeric) = 3.474873887349955 absolute error = 2.077449323678593e-12 relative error = 5.978488402817052e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.500032000002213 y[1] (closed_form) = 3.602325532493362 y[1] (numeric) = 3.602325532491156 absolute error = 2.206235194535111e-12 relative error = 6.124474800055223e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.600000000002313 y[1] (closed_form) = 3.713777506740279 y[1] (numeric) = 3.713777506737965 absolute error = 2.314148872528676e-12 relative error = 6.231253402576319e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.700096000002413 y[1] (closed_form) = 3.808226332641135 y[1] (numeric) = 3.808226332638727 absolute error = 2.40785169580704e-12 relative error = 6.322764157079689e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.800064000002513 y[1] (closed_form) = 3.884487555962848 y[1] (numeric) = 3.884487555960364 absolute error = 2.48423503990125e-12 relative error = 6.395270944008682e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 2.900032000002613 y[1] (closed_form) = 3.941931641263237 y[1] (numeric) = 3.941931641260702 absolute error = 2.535305299034007e-12 relative error = 6.431631823583678e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 3.000000000002713 y[1] (closed_form) = 3.979984993201657 y[1] (numeric) = 3.979984993199076 absolute error = 2.581046487648564e-12 relative error = 6.485065878533045e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 3.100096000002813 y[1] (closed_form) = 3.998278274825938 y[1] (numeric) = 3.998278274823345 absolute error = 2.592592807104666e-12 relative error = 6.484273051798857e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 3.200064000002913 y[1] (closed_form) = 3.996582075609797 y[1] (numeric) = 3.996582075607204 absolute error = 2.592592807104666e-12 relative error = 6.487025058053109e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 3.300032000003013 y[1] (closed_form) = 3.974949443081176 y[1] (numeric) = 3.974949443078608 absolute error = 2.567723811353062e-12 relative error = 6.459764704234062e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 3.400000000003113 y[1] (closed_form) = 3.933596385157331 y[1] (numeric) = 3.933596385154799 absolute error = 2.531752585355207e-12 relative error = 6.43622867589641e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 3.500096000003214 y[1] (closed_form) = 3.87284601556934 y[1] (numeric) = 3.872846015566865 absolute error = 2.474465077284549e-12 relative error = 6.389267911341893e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 3.600064000003314 y[1] (closed_form) = 3.793460186375535 y[1] (numeric) = 3.793460186373145 absolute error = 2.390532216622887e-12 relative error = 6.301719536186627e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 3.700032000003413 y[1] (closed_form) = 3.696166153035732 y[1] (numeric) = 3.696166153033439 absolute error = 2.293276679665723e-12 relative error = 6.20447400012635e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 3.800000000003513 y[1] (closed_form) = 3.581935423824534 y[1] (numeric) = 3.581935423822355 absolute error = 2.179589841944107e-12 relative error = 6.084950129047545e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 3.900096000003614 y[1] (closed_form) = 3.451732550602756 y[1] (numeric) = 3.451732550600709 absolute error = 2.047251257408789e-12 relative error = 5.931083093478054e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 4.000064000003714 y[1] (closed_form) = 3.307190368324945 y[1] (numeric) = 3.307190368323043 absolute error = 1.901589996577968e-12 relative error = 5.749865549896065e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 4.100032000003814 y[1] (closed_form) = 3.149595522736577 y[1] (numeric) = 3.149595522734833 absolute error = 1.744382416291046e-12 relative error = 5.538433121645445e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 4.200000000003913 y[1] (closed_form) = 2.980521642674577 y[1] (numeric) = 2.980521642673002 absolute error = 1.575184427338172e-12 relative error = 5.284928667468682e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 4.300096000004014 y[1] (closed_form) = 2.801422436599245 y[1] (numeric) = 2.801422436597851 absolute error = 1.393996029719347e-12 relative error = 4.976029361039787e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 4.400064000004114 y[1] (closed_form) = 2.6145439336248 y[1] (numeric) = 2.614543933623599 absolute error = 1.200817223434569e-12 relative error = 4.592836280129965e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 4.500032000004214 y[1] (closed_form) = 2.421529036709947 y[1] (numeric) = 2.421529036708936 absolute error = 1.010302952408892e-12 relative error = 4.172169472646748e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 4.600000000004314 y[1] (closed_form) = 2.224305053861537 y[1] (numeric) = 2.224305053860726 absolute error = 8.109068971862143e-13 relative error = 3.645664050344298e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 4.700096000004414 y[1] (closed_form) = 2.024585341537623 y[1] (numeric) = 2.02458534153701 absolute error = 6.128431095930864e-13 relative error = 3.027005565137832e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 4.800064000004514 y[1] (closed_form) = 1.824874524400666 y[1] (numeric) = 1.824874524400254 absolute error = 4.118927421359331e-13 relative error = 2.257101716465732e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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] = 4.900032000004614 y[1] (closed_form) = 1.626912384369575 y[1] (numeric) = 1.626912384369367 absolute error = 2.082778394196794e-13 relative error = 1.280203171484164e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (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 ) = sin ( x ) + sin ( x ) ; Iterations = 78125 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %