Neutron Diffusion: Concepts and Uncertainty Analysis for Engineers and Scientists by S. Chakraverty & Sukanta Nayak

Author:S. Chakraverty & Sukanta Nayak [Chakraverty, S.]
Language: eng
Format: azw3
ISBN: 9781351667494
Publisher: CRC Press
Published: 2017-04-21T04:00:00+00:00

From Equation 5.42, Equation 5.43 and Equation 5.44, it follows that

and

To compute the first derivative of f, one has the following:

(5.45)

At xi = 0, we have

Hence, Equation 5.45 will be

(5.46)

which is same as the second-order accurate forward difference expression obtained by using Taylor series expansion. Here, one may note that this approximation is classified as second-order accurate for ∂f/∂x, since ∂3f/∂x3 vanishes just as in the accuracy analysis of the Taylor series expansion. The second derivative of f may be calculated as

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