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Calculation of nth Derivative with Minimum Error Based on Function’s Measurement
- Authors: Kochurov A.S.1,2, Demidov A.S.1,3,4
-
Affiliations:
- Moscow State University
- Moscow Center of Fundamental and Applied Mathematics
- Moscow Institute of Physics and Technology
- Peoples’ Friendship University of Russia (RUDN University)
- Issue: Vol 63, No 9 (2023)
- Pages: 1428-1437
- Section: General numerical methods
- URL: https://ogarev-online.ru/0044-4669/article/view/136179
- DOI: https://doi.org/10.31857/S0044466923090077
- EDN: https://elibrary.ru/XMHVDC
- ID: 136179
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Abstract
A solution of the problem that arises in all cases where it is required to approximately calculate the derivatives of an a priori smooth function by its experimental discrete values is proposed. The problem is reduced to finding an “optimal” step of difference approximation. This problem has been studied by many mathematicians. It turned out that to find an optimal approximation step for the kth-order derivative, it is required to know a highly accurate estimate of the modulus of the derivative of order k+1. The proposed algorithm, which gives such an estimate, is applied to the problem of thrombin concentration, which determines the dynamics of blood coagulation. This dynamics is represented by plots and provides a solution of the thrombin concentration problem, which is of interest to biophysicists.
About the authors
A. S. Kochurov
Moscow State University; Moscow Center of Fundamental and Applied Mathematics
Email: kchrvas@yandex.ru
119234, Moscow, Russia; 119991, Moscow, Russia
A. S. Demidov
Moscow State University; Moscow Institute of Physics and Technology; Peoples’ Friendship University of Russia (RUDN University)
Author for correspondence.
Email: demidov.alexandre@gmail.com
119234, Moscow, Russia; 123098, Moscow; 115419, Moscow, Russia
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