Formulas for Numerical Differentiation on a Uniform Mesh in the Presence of a Boundary Layer

Numerical differentiation of functions with large gradients is considered. It is assumed that the original function of one variable can be decomposed into the sum of a regular component with bounded derivatives up to a certain order and a boundary layer component, which has large gradients and is kn...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2024-06, Vol.64 (6), p.1167-1175
Main Author: Zadorin, A. I.
Format: Article
Language:English
Subjects:
Boundary layers
Boundary value problems
Computational Mathematics and Numerical Analysis
Decomposition
General Numerical Methods
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical analysis
Numerical differentiation
Polynomials
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Summary:Numerical differentiation of functions with large gradients is considered. It is assumed that the original function of one variable can be decomposed into the sum of a regular component with bounded derivatives up to a certain order and a boundary layer component, which has large gradients and is known up to a factor. In particular, this decomposition is relevant for solution of a singularly perturbed boundary value problem, since the application of classical polynomial formulas of numerical differentiation to functions with large gradients can lead to significant errors. The error of numerical differentiation formulas is estimated for constructed formulas exact on the boundary layer component of the original function. The results of numerical experiments, consistent with the error estimates obtained, are presented.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542524700416