An a priori harmonic mesh for singularly perturbed boundary value problems
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.
scientific article; zbMATH DE number 6987679
scientific article