An a priori harmonic mesh for singularly perturbed boundary value problems
type: Item
instance of: scholarly article
title: An a priori harmonic mesh for singularly perturbed boundary value problems
zbMATH Open document ID: 1406.65053
author: V. Ramesh
author: B. Priyanga
author: M. Prithvi
author: M. K. Kadalbajoo
published in: International Journal of Applied and Computational Mathematics
publication date: 2018-12-03T00:00:00Z
review text: The paper is concerned with the construction of a priori meshes for the numerical solution of the one-dimensional singularly pertubed two-point boundary value problems using the finite difference method. The authors decompose a domain into several subdomains such that the endpoints of the subdomains are defined using partial sums of the harmonic series and they propose a mesh that is uniform on each subdomain. The authors derive error estimates for the upwind finite difference scheme with the constructed harmonic mesh. To illustrate the efficiency and reliability of the method, numerical experiments are provided and the harmonic mesh is compared with Bakhvalov and Shishkin meshes.
reviewed by: Dana Černá
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L11
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 6987679
zbMATH Keywords: singular pertubation problem
zbMATH Keywords: boundary value problem
zbMATH Keywords: harmonic mesh
zbMATH Keywords: finite difference scheme
zbMATH Keywords: Bakhvalov mesh
zbMATH Keywords: generalized Shishkin mesh
MaRDI profile type: Publication
full work available at URL: s40819-018-0574-y
OpenAlex ID: W2898532693
cites work: Q5610080
cites work: Q3499327
cites work: Mesh patterns and the expansion of permutation statistics as sums of permutation patterns
cites work: Q3909948
cites work: Numerical methods on Shishkin mesh for singularly perturbed delay differential equations with a grid adaptation strategy
cites work: Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
cites work: Layer-adapted meshes for reaction-convection-diffusion problems
cites work: Q4379541
cites work: Combinatorial Identities for Generalized Stirling Numbers Expanding $f$-Factorial Functions and the $f$-Harmonic Numbers
cites work: Q3690992
cites work: A priori meshes for singularly perturbed quasilinear two-point boundary value problems
cites work: A modification of the Shishkin discretization mesh for one-dimensional reaction-diffusion problems
Wikidata QID: Q129031964
DOI: 10.1007/S40819-018-0574-Y
description: scientific article; zbMATH DE number 6987679