##############ECHO OF PROBLEM################# ##############temp/divpostode.ode################# diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.0); 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(c(2.0) - ln(float_abs(cos(c(x))))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 2 y[1] (numeric) = 2 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 = 1.571 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] = 0.1 y[1] (closed_form) = 2.005008355623235 y[1] (numeric) = 2.005008355623235 absolute error = 4.440892098500626e-16 relative error = 2.214899546949879e-14 % Desired digits = 8 Estimated correct digits = 13 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) = 2.020134773052408 y[1] (numeric) = 2.020134773052408 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 = 1.371 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] = 0.3 y[1] (closed_form) = 2.045691655926058 y[1] (numeric) = 2.045691655926058 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 = 1.271 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.324 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] = 0.4 y[1] (closed_form) = 2.082229019075055 y[1] (numeric) = 2.082229019075056 absolute error = 4.440892098500626e-16 relative error = 2.132758720495265e-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 = 1.22 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] = 0.4999999999999999 y[1] (closed_form) = 2.130584240443723 y[1] (numeric) = 2.130584240443723 absolute error = 4.440892098500626e-16 relative error = 2.084354147656584e-14 % 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 = 1.115 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.071 Order of pole (three term test) = 0.0005817 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = 2.191965169419438 y[1] (numeric) = 2.191965169419438 absolute error = 4.440892098500626e-16 relative error = 2.025986617149048e-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 = 1.011 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9708 Order of pole (three term test) = 2.17e-05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000000000000001 y[1] (closed_form) = 2.268085757567931 y[1] (numeric) = 2.268085757567932 absolute error = 4.440892098500626e-16 relative error = 1.957991263638371e-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 = 0.9071 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8708 Order of pole (three term test) = 6.735e-07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000000000000002 y[1] (closed_form) = 2.361390746811344 y[1] (numeric) = 2.361390746811344 absolute error = 4.440892098500626e-16 relative error = 1.88062568827175e-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 = 0.8029 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7708 Order of pole (three term test) = 1.636e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000000000000002 y[1] (closed_form) = 2.475442443585814 y[1] (numeric) = 2.475442443585815 absolute error = 8.881784197001252e-16 relative error = 3.587958273889616e-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 = 0.6987 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.6708 Order of pole (three term test) = 2.857e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 2.615626470386014 y[1] (numeric) = 2.615626470386015 absolute error = 8.881784197001252e-16 relative error = 3.395662300240629e-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 = 0.5946 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5708 Order of pole (three term test) = 3.229e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 2.790548077254232 y[1] (numeric) = 2.790548077254233 absolute error = 4.440892098500626e-16 relative error = 1.591404976928494e-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 = 0.4904 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.4708 Order of pole (three term test) = 9.881e-14 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) = 3.089121163067888 y[1] (numeric) = 3.089121163067888 absolute error = 4.440892098500626e-16 relative error = 1.437590778760604e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.03813450247038617 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 = 0.3575 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.3432 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.32059585608669 y[1] (closed_form) = 3.395948036901098 y[1] (numeric) = 3.395948036901098 absolute error = 4.440892098500626e-16 relative error = 1.307703195174055e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02780005230091182 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 = 0.2606 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.2502 Order of pole (three term test) = 2.968e-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] = 1.406639797963242 y[1] (closed_form) = 3.811430131055801 y[1] (numeric) = 3.811430131055803 absolute error = 1.332267629550188e-15 relative error = 3.495453369838206e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.01823961431462824 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 = 0.171 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.1642 Order of pole (three term test) = 0 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 ) = sin ( x ) / cos ( x ) ; Iterations = 40 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 100.5 %