Example [1] Find у ’ (1) and у ’’ (1) for function у ( х ), given tabular: Values of function у ( х )
S o l u t i o n . According to the table we’ll receive: h = 0.02, х = 1, х _{ 0 } = 1, hence, q = 0. Having made final differences of function у ( х ) and using underlined values, from formula (9) we’ll receive:
Similarly, using blacked out values from formula (10) we’ll receive:
For comparison with exact values we’ll notice, that tabulated function is Bessel’s function at which the first derivative at х = 1 is equal to – 0.4400506, and the second, accordingly, – 0.325147. From here it is visible, that numerical finding of the second derivative gives greater error, than for the first derivative. |