##############ECHO OF PROBLEM################# ##############temp/sinh_sqrtpostode.ode################# diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(2.0); x_end=c(3.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.01); glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-2.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.5); 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(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * cosh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * sinh( sqrt(c(0.1) * c(x) + c(0.2)))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 1.754980921980319 y[1] (numeric) = 1.754980921980319 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 = 4 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 4.308 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.504 Radius of convergence (six term test) for eq 1 = 6.086 Order of pole (six term test) = -0.7346 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = 1.82300372306918 y[1] (numeric) = 1.822765518099698 absolute error = 0.0002382049694813482 relative error = 0.01306662002205405 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 h = 0.05 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 4.416 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.1 Order of pole (three term test) = 1.504 Radius of convergence (six term test) for eq 1 = 6.24 Order of pole (six term test) = -0.7342 TOP MAIN SOLVE Loop x[1] = 2.199999999999999 y[1] (closed_form) = 1.891973042977408 y[1] (numeric) = 1.891498497347698 absolute error = 0.0004745456297103878 relative error = 0.0250820502687286 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 h = 0.05 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 4.523 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.2 Order of pole (three term test) = 1.504 Radius of convergence (six term test) for eq 1 = 6.394 Order of pole (six term test) = -0.7339 TOP MAIN SOLVE Loop x[1] = 2.299999999999999 y[1] (closed_form) = 1.961881674429918 y[1] (numeric) = 1.961172571793153 absolute error = 0.0007091026367649356 relative error = 0.03614400633876077 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 h = 0.05 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 4.631 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.3 Order of pole (three term test) = 1.505 Radius of convergence (six term test) for eq 1 = 6.548 Order of pole (six term test) = -0.7335 TOP MAIN SOLVE Loop x[1] = 2.399999999999999 y[1] (closed_form) = 2.032722718061869 y[1] (numeric) = 2.031780766209076 absolute error = 0.0009419518527935544 relative error = 0.04633941680406233 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 h = 0.05 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 4.739 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.4 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.499999999999998 y[1] (closed_form) = 2.104489564422327 y[1] (numeric) = 2.103316399690561 absolute error = 0.001173164731765652 relative error = 0.05574580894097619 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 h = 0.05 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 4.846 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.5 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.599999999999998 y[1] (closed_form) = 2.177175877402352 y[1] (numeric) = 2.175773068735962 absolute error = 0.001402808666389976 relative error = 0.06443249169486968 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 h = 0.05 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 4.954 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.6 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.699999999999998 y[1] (closed_form) = 2.250775578946399 y[1] (numeric) = 2.249144631645573 absolute error = 0.001630947300826691 relative error = 0.07246156907345451 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 h = 0.05 Radius of convergence (given) for eq 1 = 4.7 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 5.062 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.7 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.799999999999997 y[1] (closed_form) = 2.325282834922707 y[1] (numeric) = 2.323425194109388 absolute error = 0.001857640813319072 relative error = 0.07988881117684857 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 h = 0.05 Radius of convergence (given) for eq 1 = 4.8 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 5.17 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.8 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.899999999999997 y[1] (closed_form) = 2.400692042042527 y[1] (numeric) = 2.398609095870451 absolute error = 0.002082946172076383 relative error = 0.08676440524642205 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 h = 0.05 Radius of convergence (given) for eq 1 = 4.9 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 5.277 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.9 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.999999999999996 y[1] (closed_form) = 2.476997815730758 y[1] (numeric) = 2.474690898363237 absolute error = 0.002306917367521422 relative error = 0.09313360524061827 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 h = 0.05 Radius of convergence (given) for eq 1 = 5 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 5.385 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5 Order of pole (three term test) = 1.505 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 21 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 110 %