Volume 16, Issue 4
Formulas of Numerical Differentiation on a Uniform Mesh for Functions with the Exponential Boundary Layer

Alexander Zadorin and Svetlana Tikhovskaya

Int. J. Numer. Anal. Mod., 16 (2019), pp. 590-608.

Preview Full PDF BiBTex 84 523
  • 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.

  • History

Published online: 2019-02

  • AMS Subject Headings

65D25, 41A30

  • Cited by