@Article{IJNAM-16-4,
author = {Zadorin, Alexander and Tikhovskaya, Svetlana},
title = {Formulas of Numerical Differentiation on a Uniform Mesh for Functions with the Exponential Boundary Layer},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2019},
volume = {16},
number = {4},
pages = {590--608},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/2019-IJNAM-13016},
url = {https://global-sci.com/article/83078/formulas-of-numerical-differentiation-on-a-uniform-mesh-for-functions-with-the-exponential-boundary-layer}
}