##############ECHO OF PROBLEM################# ##############temp/tan_sqrt_linpostode.ode################# diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; ! /* 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(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=c(0.001); 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 = 1.225 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.19 Order of pole (three term test) = 0.0007514 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) = -0.4250951536638883 absolute error = 0.4250951536638883 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 = 1.387 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.347 Order of pole (three term test) = 0.0001216 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) = -0.7652943064368829 absolute error = 0.7652943064368829 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 = 1.536 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.493 Order of pole (three term test) = 0.001092 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) = -1.048790649058352 absolute error = 1.048790649058352 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 = 1.678 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.63 Order of pole (three term test) = 0.003232 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) = -1.291476382650868 absolute error = 1.291476382650868 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 = 1.814 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.762 Order of pole (three term test) = 0.007307 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) = -1.503202813299885 absolute error = 1.503202813299885 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 = 1.945 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.889 Order of pole (three term test) = 0.0139 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) = -1.690503838656562 absolute error = 1.690503838656562 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 = 2.073 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.012 Order of pole (three term test) = 0.02332 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) = -1.857938450917818 absolute error = 1.857938450917818 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 = 2.198 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.133 Order of pole (three term test) = 0.03566 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) = -2.008815659861942 absolute error = 2.008815659861942 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 = 2.32 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.25 Order of pole (three term test) = 0.05075 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 0 y[1] (numeric) = -2.145614225576715 absolute error = 2.145614225576715 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 = 2.44 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.366 Order of pole (three term test) = 0.06829 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) = -2.270239499340557 absolute error = 2.270239499340557 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 = 2.559 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.48 Order of pole (three term test) = 0.0879 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) = -2.384187816046955 absolute error = 2.384187816046955 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 = 2.677 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.592 Order of pole (three term test) = 0.1092 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) = -2.488655715724144 absolute error = 2.488655715724144 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 = 2.793 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.703 Order of pole (three term test) = 0.1317 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) = -2.584614831865499 absolute error = 2.584614831865499 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 = 2.908 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.812 Order of pole (three term test) = 0.1552 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) = -2.67286464153998 absolute error = 2.67286464153998 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 = 3.023 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.921 Order of pole (three term test) = 0.1793 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) = -2.754070498293336 absolute error = 2.754070498293336 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 = 3.136 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.028 Order of pole (three term test) = 0.2037 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) = -2.828791618233164 absolute error = 2.828791618233164 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 = 3.249 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.135 Order of pole (three term test) = 0.2282 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) = -2.897502046004885 absolute error = 2.897502046004885 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 = 3.362 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.242 Order of pole (three term test) = 0.2526 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) = -2.960606613356697 absolute error = 2.960606613356697 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 = 3.474 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.347 Order of pole (three term test) = 0.2768 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) = -3.018453259621699 absolute error = 3.018453259621699 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 = 3.586 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.453 Order of pole (three term test) = 0.3006 Radius of convergence (six term test) for eq 1 = 3.272 Order of pole (six term test) = -0.3232 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y[1] (closed_form) = 0 y[1] (numeric) = -3.07134266492409 absolute error = 3.07134266492409 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 = 3.697 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.557 Order of pole (three term test) = 0.3241 Radius of convergence (six term test) for eq 1 = 3.358 Order of pole (six term test) = -0.3336 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 0 y[1] (numeric) = -3.119535868513665 absolute error = 3.119535868513665 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 = 3.808 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.661 Order of pole (three term test) = 0.3471 Radius of convergence (six term test) for eq 1 = 3.439 Order of pole (six term test) = -0.344 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = 0 y[1] (numeric) = -3.163260355675606 absolute error = 3.163260355675606 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 = 3.919 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.765 Order of pole (three term test) = 0.3695 Radius of convergence (six term test) for eq 1 = 3.516 Order of pole (six term test) = -0.3546 TOP MAIN SOLVE Loop x[1] = 2.399999999999999 y[1] (closed_form) = 0 y[1] (numeric) = -3.202714966056181 absolute error = 3.202714966056181 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 = 4.029 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.869 Order of pole (three term test) = 0.3914 Radius of convergence (six term test) for eq 1 = 3.588 Order of pole (six term test) = -0.3653 TOP MAIN SOLVE Loop x[1] = 2.499999999999999 y[1] (closed_form) = 0 y[1] (numeric) = -3.238073884461082 absolute error = 3.238073884461082 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 = 4.139 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.972 Order of pole (three term test) = 0.4127 Radius of convergence (six term test) for eq 1 = 3.654 Order of pole (six term test) = -0.3764 TOP MAIN SOLVE Loop x[1] = 2.599999999999999 y[1] (closed_form) = 0 y[1] (numeric) = -3.269489909695652 absolute error = 3.269489909695652 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 = 4.249 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.075 Order of pole (three term test) = 0.4335 Radius of convergence (six term test) for eq 1 = 3.713 Order of pole (six term test) = -0.3877 TOP MAIN SOLVE Loop x[1] = 2.699999999999998 y[1] (closed_form) = 0 y[1] (numeric) = -3.297097149635089 absolute error = 3.297097149635089 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 = 4.359 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.178 Order of pole (three term test) = 0.4537 Radius of convergence (six term test) for eq 1 = 3.764 Order of pole (six term test) = -0.3993 TOP MAIN SOLVE Loop x[1] = 2.799999999999998 y[1] (closed_form) = 0 y[1] (numeric) = -3.321013255987241 absolute error = 3.321013255987241 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 = 4.469 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.281 Order of pole (three term test) = 0.4733 Radius of convergence (six term test) for eq 1 = 3.805 Order of pole (six term test) = -0.4113 TOP MAIN SOLVE Loop x[1] = 2.899999999999998 y[1] (closed_form) = 0 y[1] (numeric) = -3.341341286454356 absolute error = 3.341341286454356 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 = 4.578 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.383 Order of pole (three term test) = 0.4924 Radius of convergence (six term test) for eq 1 = 3.836 Order of pole (six term test) = -0.4235 TOP MAIN SOLVE Loop x[1] = 2.999999999999997 y[1] (closed_form) = 0 y[1] (numeric) = -3.358171262682098 absolute error = 3.358171262682098 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 = 4.688 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.485 Order of pole (three term test) = 0.5109 Radius of convergence (six term test) for eq 1 = 3.855 Order of pole (six term test) = -0.4357 TOP MAIN SOLVE Loop x[1] = 3.099999999999997 y[1] (closed_form) = 0 y[1] (numeric) = -3.371581477742251 absolute error = 3.371581477742251 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 = 4.797 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.588 Order of pole (three term test) = 0.5288 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) = -3.381639595687293 absolute error = 3.381639595687293 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 = 4.906 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.69 Order of pole (three term test) = 0.5462 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) = -3.388403577053429 absolute error = 3.388403577053429 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 = 5.015 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.791 Order of pole (three term test) = 0.5632 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) = -3.391922457433473 absolute error = 3.391922457433473 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 = 5.124 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.893 Order of pole (three term test) = 0.5796 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) = -3.392237000924812 absolute error = 3.392237000924812 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 = 5.233 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.995 Order of pole (three term test) = 0.5955 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) = -3.389380246036214 absolute error = 3.389380246036214 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 = 5.342 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.096 Order of pole (three term test) = 0.611 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) = -3.383377958253782 absolute error = 3.383377958253782 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 = 5.451 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.198 Order of pole (three term test) = 0.626 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) = -3.374249000728091 absolute error = 3.374249000728091 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 = 5.56 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.299 Order of pole (three term test) = 0.6406 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) = -3.362005632305073 absolute error = 3.362005632305073 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 = 5.668 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.4 Order of pole (three term test) = 0.6548 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) = -3.34665374026997 absolute error = 3.34665374026997 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 = 5.777 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.501 Order of pole (three term test) = 0.6686 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) = -3.328193013619784 absolute error = 3.328193013619784 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 = 5.885 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.603 Order of pole (three term test) = 0.682 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) = -3.306617061356352 absolute error = 3.306617061356352 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 = 5.994 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.704 Order of pole (three term test) = 0.6951 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) = -3.281913479145194 absolute error = 3.281913479145194 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 = 6.102 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.805 Order of pole (three term test) = 0.7078 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) = -3.254063866670188 absolute error = 3.254063866670188 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 = 6.211 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.906 Order of pole (three term test) = 0.7201 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) = -3.223043797094337 absolute error = 3.223043797094337 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 = 6.319 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.007 Order of pole (three term test) = 0.7322 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) = -3.188822739181195 absolute error = 3.188822739181195 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 = 6.428 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.107 Order of pole (three term test) = 0.7439 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) = -3.151363931812287 absolute error = 3.151363931812287 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 = 6.536 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.208 Order of pole (three term test) = 0.7554 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) = -3.11062420982811 absolute error = 3.11062420982811 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 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 = 6.644 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.309 Order of pole (three term test) = 0.7666 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) = -3.066553779299857 absolute error = 3.066553779299857 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 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 = 6.753 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.41 Order of pole (three term test) = 0.7773 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) = -3.019095939481848 absolute error = 3.019095939481848 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 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 = 6.861 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.511 Order of pole (three term test) = 0.7873 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = tan ( 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 %