Abstract
For more complex problems analytical derivatives are not always available and have to be approximated by numerical methods. Numerical differentiation is also very important for the discretization of differential equations. The simplest approximation uses a forward difference quotient and is not very accurate. A symmetric difference quotient improves the quality. Even higher precision is obtained with the extrapolation method. Approximations to higher order derivatives can be obtained systematically with the help of polynomial interpolation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
L.F. Richardson, Philos. Trans. R. Soc. Lond. Ser. A 210, 307–357 (1911)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Scherer, P.O.J. (2013). Numerical Differentiation. In: Computational Physics. Graduate Texts in Physics. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00401-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-00401-3_3
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00400-6
Online ISBN: 978-3-319-00401-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)