##############ECHO OF PROBLEM################# ##############temp/exp_sqrtpostode.ode################# diff ( y , x , 1 ) = exp ( sqrt ( 0.1 * x + 0.2 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=16; 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) * exp(sqrt(c(0.1) * x + c(0.2))) * sqrt( c(0.1) * x + c(0.2)) - c(20.0) * exp(sqrt(c(0.1) * 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) = -13.83604079041925 y[1] (numeric) = -13.83604079041925 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 = 4.309 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.998 Order of pole (three term test) = 1.526 Radius of convergence (six term test) for eq 1 = 27.05 Order of pole (six term test) = 2.6 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = -13.6470752222473 y[1] (numeric) = -13.64744729440841 absolute error = 0.0003720721611166766 relative error = 0.00272638755965915 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 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 = 4.417 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.098 Order of pole (three term test) = 1.526 Radius of convergence (six term test) for eq 1 = 27.72 Order of pole (six term test) = 2.628 TOP MAIN SOLVE Loop x[1] = 2.199999999999999 y[1] (closed_form) = -13.45662826122465 y[1] (numeric) = -13.45737075201431 absolute error = 0.0007424907896531607 relative error = 0.005517658474616943 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 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 = 4.525 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.198 Order of pole (three term test) = 1.526 Radius of convergence (six term test) for eq 1 = 28.39 Order of pole (six term test) = 2.656 TOP MAIN SOLVE Loop x[1] = 2.299999999999999 y[1] (closed_form) = -13.26470624619314 y[1] (numeric) = -13.26581758324235 absolute error = 0.00111133704921329 relative error = 0.008378150473797599 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 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 = 4.633 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.298 Order of pole (three term test) = 1.526 Radius of convergence (six term test) for eq 1 = 29.06 Order of pole (six term test) = 2.684 TOP MAIN SOLVE Loop x[1] = 2.399999999999999 y[1] (closed_form) = -13.07131520722569 y[1] (numeric) = -13.07279389451507 absolute error = 0.001478687289383274 relative error = 0.01131245988594836 % 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 = 4.74 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.398 Order of pole (three term test) = 1.527 Radius of convergence (six term test) for eq 1 = 29.74 Order of pole (six term test) = 2.714 TOP MAIN SOLVE Loop x[1] = 2.499999999999998 y[1] (closed_form) = -12.8764608836221 y[1] (numeric) = -12.87830549705541 absolute error = 0.001844613433307885 relative error = 0.01432546916407827 % 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 = 4.848 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.498 Order of pole (three term test) = 1.527 Radius of convergence (six term test) for eq 1 = 30.43 Order of pole (six term test) = 2.744 TOP MAIN SOLVE Loop x[1] = 2.599999999999998 y[1] (closed_form) = -12.68014874048033 y[1] (numeric) = -12.68235792380656 absolute error = 0.002209183326231212 relative error = 0.01742237706706528 % 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 = 4.956 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.598 Order of pole (three term test) = 1.527 Radius of convergence (six term test) for eq 1 = 31.12 Order of pole (six term test) = 2.776 TOP MAIN SOLVE Loop x[1] = 2.699999999999998 y[1] (closed_form) = -12.48238398398448 y[1] (numeric) = -12.48495644503415 absolute error = 0.002572461049664909 relative error = 0.02060873189741242 % 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 = 5.064 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.698 Order of pole (three term test) = 1.527 Radius of convergence (six term test) for eq 1 = 31.82 Order of pole (six term test) = 2.808 TOP MAIN SOLVE Loop x[1] = 2.799999999999997 y[1] (closed_form) = -12.2831715755338 y[1] (numeric) = -12.2861060827391 absolute error = 0.0029345072052962 relative error = 0.02389046824959515 % 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 = 5.171 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.798 Order of pole (three term test) = 1.527 Radius of convergence (six term test) for eq 1 = 32.53 Order of pole (six term test) = 2.841 TOP MAIN SOLVE Loop x[1] = 2.899999999999997 y[1] (closed_form) = -12.08251624482287 y[1] (numeric) = -12.08581162399491 absolute error = 0.003295379172039148 relative error = 0.02727394778758238 % 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 = 5.279 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.898 Order of pole (three term test) = 1.528 Radius of convergence (six term test) for eq 1 = 33.24 Order of pole (six term test) = 2.875 TOP MAIN SOLVE Loop x[1] = 2.999999999999996 y[1] (closed_form) = -11.88042250197029 y[1] (numeric) = -11.88407763330962 absolute error = 0.003655131339330708 relative error = 0.03076600464945188 % 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 = 5.387 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.998 Order of pole (three term test) = 1.528 Radius of convergence (six term test) for eq 1 = 33.96 Order of pole (six term test) = 2.91 Finished! diff ( y , x , 1 ) = exp ( 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 %