##############ECHO OF PROBLEM################# ##############temp/lin_arccospostode.ode################# diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ; ! /* BEGIN FIRST INPUT BLOCK */ max_terms=30; Digits=32; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-0.8; x_end=0.8; 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=0.1; 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) * arccos(0.1 * x + 0.2 ) - 10.0 * sqrt(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 = 1.6 estimated_steps = 1600000 step_error = 6.249999999999999e-17 est_needed_step_err = 6.249999999999999e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.939391627071972e-185 estimated_step_error = 2.939391627071972e-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 = 1.972592334120113e-177 estimated_step_error = 1.972592334120113e-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 = 1.323784313061802e-169 estimated_step_error = 1.323784313061802e-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 = 8.883766227384433e-162 estimated_step_error = 8.883766227384433e-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 = 5.961794708790758e-154 estimated_step_error = 5.961794708790758e-154 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 = 4.00089285498247e-146 estimated_step_error = 4.00089285498247e-146 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 = 2.684953948705062e-138 estimated_step_error = 2.684953948705062e-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 = 1.801842367504157e-130 estimated_step_error = 1.801842367504157e-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 = 1.209196311066124e-122 estimated_step_error = 1.209196311066124e-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 = 8.114784005153489e-115 estimated_step_error = 8.114784005153489e-115 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 = 5.445745969319524e-107 estimated_step_error = 5.445745969319524e-107 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (analytic) = -8.187131183512555 y[1] (numeric) = -8.187131183512555 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 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 9.957 Order of pole (six term test) = -1.357 TOP MAIN SOLVE Loop x[1] = -0.7 y[1] (analytic) = -8.042584387278817 y[1] (numeric) = -8.042584387236165 absolute error = 4.265210407083941e-11 relative error = 5.303283374720128e-10 % Correct digits = 12 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 = 9.945 Order of pole (six term test) = -1.357 TOP MAIN SOLVE Loop x[1] = -0.5999999999999999 y[1] (analytic) = -7.899046158670194 y[1] (numeric) = -7.899046158581291 absolute error = 8.890221891988404e-11 relative error = 1.125480433131824e-09 % Correct digits = 11 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 = 9.931 Order of pole (six term test) = -1.357 TOP MAIN SOLVE Loop x[1] = -0.4999999999999998 y[1] (analytic) = -7.756517885615279 y[1] (numeric) = -7.756517885476488 absolute error = 1.387903125760204e-10 relative error = 1.789337878449447e-09 % Correct digits = 11 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 = 9.917 Order of pole (six term test) = -1.356 TOP MAIN SOLVE Loop x[1] = -0.3999999999999997 y[1] (analytic) = -7.615001065253674 y[1] (numeric) = -7.61500106506131 absolute error = 1.923643466739122e-10 relative error = 2.526123700121953e-09 % Correct digits = 11 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 = 9.901 Order of pole (six term test) = -1.355 TOP MAIN SOLVE Loop x[1] = -0.2999999999999996 y[1] (analytic) = -7.474497305362258 y[1] (numeric) = -7.474497305112574 absolute error = 2.496838291676795e-10 relative error = 3.340476542664007e-09 % Correct digits = 11 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 = 9.885 Order of pole (six term test) = -1.354 TOP MAIN SOLVE Loop x[1] = -0.1999999999999995 y[1] (analytic) = -7.33500832589932 y[1] (numeric) = -7.335008325588524 absolute error = 3.107958335135663e-10 relative error = 4.237157201528612e-09 % Correct digits = 11 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 = 9.868 Order of pole (six term test) = -1.353 TOP MAIN SOLVE Loop x[1] = -0.09999999999999942 y[1] (analytic) = -7.19653596067085 y[1] (numeric) = -7.196535960295092 absolute error = 3.757580913088532e-10 relative error = 5.221374469083117e-09 % Correct digits = 11 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 = 9.849 Order of pole (six term test) = -1.352 TOP MAIN SOLVE Loop x[1] = 6.591949208711867e-16 y[1] (analytic) = -7.059082159123578 y[1] (numeric) = -7.059082158678934 absolute error = 4.446443213623752e-10 relative error = 6.298897099358595e-09 % Correct digits = 11 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 = 9.829 Order of pole (six term test) = -1.352 TOP MAIN SOLVE Loop x[1] = 0.1000000000000007 y[1] (analytic) = -6.922648988269866 y[1] (numeric) = -6.922648987752352 absolute error = 5.175131434498326e-10 relative error = 7.47565194085005e-09 % Correct digits = 11 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 = 9.808 Order of pole (six term test) = -1.352 TOP MAIN SOLVE Loop x[1] = 0.2000000000000008 y[1] (analytic) = -6.787238634749932 y[1] (numeric) = -6.78723863415549 absolute error = 5.944418290937392e-10 relative error = 8.758227919823843e-09 % Correct digits = 11 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 = 9.785 Order of pole (six term test) = -1.354 TOP MAIN SOLVE Loop x[1] = 0.3000000000000009 y[1] (analytic) = -6.652853407037465 y[1] (numeric) = -6.652853406361952 absolute error = 6.755138670655469e-10 relative error = 1.015374645638487e-08 % Correct digits = 10 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 = 9.762 Order of pole (six term test) = -1.355 TOP MAIN SOLVE Loop x[1] = 0.400000000000001 y[1] (analytic) = -6.519495737795036 y[1] (numeric) = -6.519495737034229 absolute error = 7.608065288877697e-10 relative error = 1.16697143381381e-08 % Correct digits = 10 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 = 9.737 Order of pole (six term test) = -1.356 TOP MAIN SOLVE Loop x[1] = 0.500000000000001 y[1] (analytic) = -6.387168186386496 y[1] (numeric) = -6.387168185536086 absolute error = 8.504104087592168e-10 relative error = 1.331435753596981e-08 % Correct digits = 10 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 = 9.711 Order of pole (six term test) = -1.357 TOP MAIN SOLVE Loop x[1] = 0.6000000000000011 y[1] (analytic) = -6.255873441553934 y[1] (numeric) = -6.255873440609518 absolute error = 9.444161008786978e-10 relative error = 1.509647069593065e-08 % Correct digits = 10 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 = 9.685 Order of pole (six term test) = -1.357 TOP MAIN SOLVE Loop x[1] = 0.7000000000000012 y[1] (analytic) = -6.125614324267577 y[1] (numeric) = -6.125614323224641 absolute error = 1.042935515727095e-09 relative error = 1.702581097205782e-08 % Correct digits = 10 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 = 9.657 Order of pole (six term test) = -1.357 Finished! diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ; Iterations = 1600 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %