Parameter-uniform convergence analysis on a Bakhvalov-type mesh with a smooth mesh-generating function using the preconditioning approach

Authors

  • Thái Anh Nhan Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, CA 95053, USA
  • Relja Vulanovic Department of Mathematical Sciences, Kent State University at Stark, 6000 Frank Ave. NW, North Canton, OH 44720, USA

Keywords:

singular perturbation, convection-diffusion, boundary-value problem, Bakhvalov-type mesh, finite differences, uniform convergence, preconditioning

Abstract

The linear singularly perturbed convection-diffusion problem in one dimension is considered and its discretization on a Bakhvalov-type mesh generated by a smooth mesh-generating function is analyzed. The preconditioning technique is used to obtain the first-order pointwise convergence uniform in the perturbation parameter.

Additional Files

Published

25-03-2023

Issue

Vol. 2 No. 1 (2024)

Section

Research Article

License

Copyright (c) 2024 Letters on Applied and Pure Mathematics

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Parameter-uniform convergence analysis on a Bakhvalov-type mesh with a smooth mesh-generating function using the preconditioning approach. (2023). Letters on Applied and Pure Mathematics, 2(1), 21-34. https://lapmjournal.com/index.php/lapm/article/view/v2n1a16