##############ECHO OF PROBLEM################# ##############temp/tanpostode.ode################# diff ( y , x , 1 ) = tan ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(1.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=1; array_given_rad_poles[1][1]=c(1.570796327); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.0); array_given_ord_poles[1][2]=c(0.0); /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(20.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.11); glob_lower_ratio_limit=c(0.99); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(glob__m1 * ln(cos(c(x)))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.005008355623235254 y[1] (numeric) = 0.005008355623235254 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.471 Order of pole (given) = 0 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] = 0.2 y[1] (closed_form) = 0.02013477305240835 y[1] (numeric) = 0.02013477305240829 absolute error = 5.898059818321144e-17 relative error = 2.929290438471402e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 1.371 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.412 Order of pole (ratio test) = 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] = 0.3 y[1] (closed_form) = 0.04569165592605806 y[1] (numeric) = 0.04569165592605797 absolute error = 9.020562075079397e-17 relative error = 1.974225247970264e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 1.271 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.308 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.27 Order of pole (three term test) = 0.01257 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (closed_form) = 0.08222901907505541 y[1] (numeric) = 0.08222901907505539 absolute error = 1.387778780781446e-17 relative error = 1.687699544992427e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.171 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.205 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.171 Order of pole (three term test) = 0.0001554 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4999999999999999 y[1] (closed_form) = 0.1305842404437227 y[1] (numeric) = 0.1305842404437227 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.071 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.102 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.071 Order of pole (three term test) = 1.659e-06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = 0.1919651694194377 y[1] (numeric) = 0.1919651694194376 absolute error = 2.775557561562891e-17 relative error = 1.445865190001415e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 0.9708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9993 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9708 Order of pole (three term test) = 1.449e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000000000000001 y[1] (closed_form) = 0.2680857575679312 y[1] (numeric) = 0.2680857575679311 absolute error = 1.110223024625157e-16 relative error = 4.141298048419575e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 0.8708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8964 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8708 Order of pole (three term test) = 9.676e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000000000000002 y[1] (closed_form) = 0.3613907468113439 y[1] (numeric) = 0.3613907468113437 absolute error = 2.220446049250313e-16 relative error = 6.144169624822874e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 0.7708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7935 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7708 Order of pole (three term test) = 4.835e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000000000000002 y[1] (closed_form) = 0.4754424435858146 y[1] (numeric) = 0.4754424435858143 absolute error = 2.220446049250313e-16 relative error = 4.670273088165162e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 0.6708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6905 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.6708 Order of pole (three term test) = 1.373e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 0.6156264703860146 y[1] (numeric) = 0.6156264703860144 absolute error = 2.220446049250313e-16 relative error = 3.606807302905661e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 0.5708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5876 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5708 Order of pole (three term test) = 4.245e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 0.7905480772542323 y[1] (numeric) = 0.7905480772542318 absolute error = 4.440892098500626e-16 relative error = 5.617485167916587e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.4708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4846 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.4708 Order of pole (three term test) = 1.677e-13 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.227585804561417 y[1] (closed_form) = 1.08912116306789 y[1] (numeric) = 1.089121163067889 absolute error = 8.881784197001252e-16 relative error = 8.155001021174362e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.03813450247038645 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.3432 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3533 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.3432 Order of pole (three term test) = 8.165e-13 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.320595856086691 y[1] (closed_form) = 1.395948036901104 y[1] (numeric) = 1.395948036901102 absolute error = 1.554312234475219e-15 relative error = 1.11344562504323e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.02780005230091164 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.2502 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2576 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.2502 Order of pole (three term test) = 4.083e-13 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.406639797963243 y[1] (closed_form) = 1.811430131055812 y[1] (numeric) = 1.811430131055811 absolute error = 1.332267629550188e-15 relative error = 7.354783420620595e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.01823961431462795 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.1642 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.169 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.1642 Order of pole (three term test) = 1.361e-13 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE Finished! diff ( y , x , 1 ) = tan ( x ) ; Iterations = 38 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 100.6 %