Formulas of Numerical Differentiation on a Uniform Mesh for Functions with the Exponential Boundary Layer
Year: 2019
Author: Alexander Zadorin, Svetlana Tikhovskaya
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 4 : pp. 590–608
Abstract
It is known that the solution of a singularly perturbed problem corresponds to the function with large gradients in a boundary layer. The application of Lagrange polynomial on a uniform mesh to interpolate such functions leads to large errors. To achieve the error estimates uniform with respect to a small parameter, we can use either a polynomial interpolation on a mesh which condenses in a boundary layer or we can use special interpolation formulas which are exact on a boundary layer component of the interpolating function. In this paper, we construct and study the formulas of numerical differentiation based on the interpolation formulas which are exact on a boundary layer component. We obtained the error estimates which are uniform with respect to a small parameter. Some numerical results validating the theoretical estimates are discussed.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-IJNAM-13016
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 4 : pp. 590–608
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Function of one variable exponential boundary layer formulas of numerical differentiation an error estimate.