##############ECHO OF PROBLEM################# ##############temp/tanh_sqrtpostode.ode################# diff ( y , x , 1 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.1; glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-1.5); 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(0.0)); } /* 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 y[1] (numeric) = 0 absolute error = 0 relative error = -1 % Desired digits = 8 Estimated correct digits = -16 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 1.765 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.616 Order of pole (three term test) = 1.118 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 0 y[1] (numeric) = 0.09470611835872972 absolute error = 0.09470611835872972 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 1.874 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.717 Order of pole (three term test) = 1.093 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (closed_form) = 0 y[1] (numeric) = 0.1899474278336102 absolute error = 0.1899474278336102 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 1.983 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.819 Order of pole (three term test) = 1.068 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (closed_form) = 0 y[1] (numeric) = 0.2856578963298885 absolute error = 0.2856578963298885 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.093 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.922 Order of pole (three term test) = 1.044 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4999999999999999 y[1] (closed_form) = 0 y[1] (numeric) = 0.3817812721810266 absolute error = 0.3817812721810266 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.202 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.024 Order of pole (three term test) = 1.021 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = 0 y[1] (numeric) = 0.478269378504024 absolute error = 0.478269378504024 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.31 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.126 Order of pole (three term test) = 0.9983 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.57508075106371 absolute error = 0.57508075106371 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.419 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.228 Order of pole (three term test) = 0.9761 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000000000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.6721795411526518 absolute error = 0.6721795411526518 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.528 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.33 Order of pole (three term test) = 0.9544 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000000000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.7695346250323301 absolute error = 0.7695346250323301 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 2.4 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.636 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.433 Order of pole (three term test) = 0.9332 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 0 y[1] (numeric) = 0.8671188758796048 absolute error = 0.8671188758796048 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.745 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.535 Order of pole (three term test) = 0.9125 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 0 y[1] (numeric) = 0.9649085646711759 absolute error = 0.9649085646711759 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 2.6 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.853 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.638 Order of pole (three term test) = 0.8922 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = 0 y[1] (numeric) = 1.062882864175196 absolute error = 1.062882864175196 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 2.7 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.962 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.74 Order of pole (three term test) = 0.8724 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = 0 y[1] (numeric) = 1.161023435990771 absolute error = 1.161023435990771 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 2.8 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.07 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.843 Order of pole (three term test) = 0.853 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.400000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 1.259314084926895 absolute error = 1.259314084926895 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 2.9 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.178 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.945 Order of pole (three term test) = 0.834 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.500000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 1.357740468323631 absolute error = 1.357740468323631 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 3 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.286 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.048 Order of pole (three term test) = 0.8154 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.600000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 1.456289850460983 absolute error = 1.456289850460983 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.394 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.15 Order of pole (three term test) = 0.7971 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.700000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 1.554950894169228 absolute error = 1.554950894169228 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.502 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.253 Order of pole (three term test) = 0.7792 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.800000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 1.653713483290072 absolute error = 1.653713483290072 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.61 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.356 Order of pole (three term test) = 0.7617 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 1.752568570844403 absolute error = 1.752568570844403 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.718 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.458 Order of pole (three term test) = 0.7444 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.000000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 1.851508048716674 absolute error = 1.851508048716674 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.825 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.561 Order of pole (three term test) = 0.7275 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y[1] (closed_form) = 0 y[1] (numeric) = 1.950524635425405 absolute error = 1.950524635425405 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 3.933 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.664 Order of pole (three term test) = 0.7108 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 0 y[1] (numeric) = 2.049611779157317 absolute error = 2.049611779157317 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 4.041 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.767 Order of pole (three term test) = 0.6945 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = 0 y[1] (numeric) = 2.148763573732148 absolute error = 2.148763573732148 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 4.148 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.87 Order of pole (three term test) = 0.6784 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.399999999999999 y[1] (closed_form) = 0 y[1] (numeric) = 2.247974685561298 absolute error = 2.247974685561298 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 4.255 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.973 Order of pole (three term test) = 0.6625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.499999999999999 y[1] (closed_form) = 0 y[1] (numeric) = 2.347240289985686 absolute error = 2.347240289985686 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 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 = 4.363 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.076 Order of pole (three term test) = 0.6469 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.599999999999999 y[1] (closed_form) = 0 y[1] (numeric) = 2.446556015641446 absolute error = 2.446556015641446 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 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 = 4.47 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.179 Order of pole (three term test) = 0.6316 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.699999999999998 y[1] (closed_form) = 0 y[1] (numeric) = 2.545917895718183 absolute error = 2.545917895718183 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 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 = 4.577 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.282 Order of pole (three term test) = 0.6164 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.799999999999998 y[1] (closed_form) = 0 y[1] (numeric) = 2.645322325152652 absolute error = 2.645322325152652 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 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 = 4.684 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.385 Order of pole (three term test) = 0.6015 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.899999999999998 y[1] (closed_form) = 0 y[1] (numeric) = 2.744766022948123 absolute error = 2.744766022948123 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 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 = 4.792 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.488 Order of pole (three term test) = 0.5868 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.999999999999997 y[1] (closed_form) = 0 y[1] (numeric) = 2.844245998932189 absolute error = 2.844245998932189 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 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 = 4.899 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.591 Order of pole (three term test) = 0.5723 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.099999999999997 y[1] (closed_form) = 0 y[1] (numeric) = 2.943759524367886 absolute error = 2.943759524367886 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 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 = 5.006 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.694 Order of pole (three term test) = 0.5579 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.199999999999997 y[1] (closed_form) = 0 y[1] (numeric) = 3.04330410591849 absolute error = 3.04330410591849 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 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 = 5.112 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.797 Order of pole (three term test) = 0.5438 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.299999999999996 y[1] (closed_form) = 0 y[1] (numeric) = 3.142877462538104 absolute error = 3.142877462538104 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 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 = 5.219 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.9 Order of pole (three term test) = 0.5298 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.399999999999996 y[1] (closed_form) = 0 y[1] (numeric) = 3.242477504920588 absolute error = 3.242477504920588 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 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 = 5.326 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.003 Order of pole (three term test) = 0.516 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.499999999999996 y[1] (closed_form) = 0 y[1] (numeric) = 3.342102317190486 absolute error = 3.342102317190486 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 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 = 5.433 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.107 Order of pole (three term test) = 0.5024 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.599999999999995 y[1] (closed_form) = 0 y[1] (numeric) = 3.441750140562886 absolute error = 3.441750140562886 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 5.1 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 5.539 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.21 Order of pole (three term test) = 0.4889 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.699999999999995 y[1] (closed_form) = 0 y[1] (numeric) = 3.541419358735916 absolute error = 3.541419358735916 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 5.2 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 5.646 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.313 Order of pole (three term test) = 0.4756 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.799999999999994 y[1] (closed_form) = 0 y[1] (numeric) = 3.641108484810981 absolute error = 3.641108484810981 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 5.3 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 5.753 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.416 Order of pole (three term test) = 0.4624 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.899999999999994 y[1] (closed_form) = 0 y[1] (numeric) = 3.740816149562592 absolute error = 3.740816149562592 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 5.4 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 5.859 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.52 Order of pole (three term test) = 0.4494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.999999999999994 y[1] (closed_form) = 0 y[1] (numeric) = 3.840541090902619 absolute error = 3.840541090902619 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 5.5 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 5.966 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.623 Order of pole (three term test) = 0.4365 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.099999999999993 y[1] (closed_form) = 0 y[1] (numeric) = 3.940282144403506 absolute error = 3.940282144403506 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 5.6 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 6.072 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.727 Order of pole (three term test) = 0.4237 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.199999999999993 y[1] (closed_form) = 0 y[1] (numeric) = 4.040038234761949 absolute error = 4.040038234761949 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 5.7 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 6.178 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.83 Order of pole (three term test) = 0.411 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.299999999999993 y[1] (closed_form) = 0 y[1] (numeric) = 4.139808368099168 absolute error = 4.139808368099168 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 5.8 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 6.285 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.933 Order of pole (three term test) = 0.3985 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.399999999999992 y[1] (closed_form) = 0 y[1] (numeric) = 4.239591625006606 absolute error = 4.239591625006606 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 5.9 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 6.391 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.037 Order of pole (three term test) = 0.3861 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.499999999999992 y[1] (closed_form) = 0 y[1] (numeric) = 4.339387154256781 absolute error = 4.339387154256781 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 6 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 6.497 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.14 Order of pole (three term test) = 0.3739 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.599999999999992 y[1] (closed_form) = 0 y[1] (numeric) = 4.439194167108626 absolute error = 4.439194167108626 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 6.1 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 6.603 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.244 Order of pole (three term test) = 0.3617 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.699999999999991 y[1] (closed_form) = 0 y[1] (numeric) = 4.539011932144878 absolute error = 4.539011932144878 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 6.2 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 6.709 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.347 Order of pole (three term test) = 0.3497 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.799999999999991 y[1] (closed_form) = 0 y[1] (numeric) = 4.638839770586322 absolute error = 4.638839770586322 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 6.3 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 6.815 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.451 Order of pole (three term test) = 0.3377 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.899999999999991 y[1] (closed_form) = 0 y[1] (numeric) = 4.738677052034015 absolute error = 4.738677052034015 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 6.4 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 6.921 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.554 Order of pole (three term test) = 0.3259 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.99999999999999 y[1] (closed_form) = 0 y[1] (numeric) = 4.838523190596121 absolute error = 4.838523190596121 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.05 Radius of convergence (given) for eq 1 = 6.5 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 7.027 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.658 Order of pole (three term test) = 0.3141 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 99 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 102 %