Abstract
The stability of the order of symmetric formulas for derivative approximation used in finite-difference methods for solving differential equations is analyzed. The stability of the order of a numerical differentiation formula with respect to the shift of the application point (at which this formula is applied) is defined. The conditions of numerical experiments determining the behavior of the order of the simplest symmetric approximation formulas for the first and second derivatives in the case of point shifts are described, and some numerical results are presented. The instability of the maximum order of these formulas is shown in examples. A family of rectangular quadrature rules is examined in a similar manner, and the instability of the second order of the quadrature midpoint formula is demonstrated.
Similar content being viewed by others
References
N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobel’kov, Numerical Methods (Laboratoriya Bazovykh Znanii, Moscow, 2001) [in Russian].
V. M. Verzhbitskii, Fundamentals of Numerical Methods (Vysshaya Shkola, Moscow, 2009) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Verzhbitskii, V.M. On the instability of symmetric formulas for numerical differentiation and integration. Comput. Math. and Math. Phys. 55, 917–921 (2015). https://doi.org/10.1134/S0965542515060123
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542515060123