Open AccessNumerical differentiation on the Bakhvalov mesh in the presence of an exponential boundary layer
Author(s) -
Н. А. Задорин
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1546/1/012108
Subject(s) - mathematics , exponential function , boundary (topology) , numerical differentiation , boundary layer , layer (electronics) , polynomial , finite difference , mathematical analysis , physics , mechanics , materials science , composite material
The question of the application of formulas of the numerical differentiation of functions in the presence of the exponential boundary layer is investigated. The problem is that the application of classical formulas, wich are based on the differentiation of the Lagrange polynomial on the uniform mesh in this case leads to significant errors. It is proposed to study the formulas for derivatives on the Bakhvalov mesh, which is widely used in the construction of difference schemes for singularly perturbed problems. It is proved that applying of classical difference formulas for derivatives on a Bakhvalov mesh have error estimate that is uniform with respect to a small parameter. The results of numerical experiments are presented.