Singularly Perturbed Problems Modeling Reaction-convection-diffusion Processes

By E. O 'riordan, Maria Pickett, G. I. Shishkin. 2003

73 citations recorded by the source corpus.

Abstract In this paper, parameter - uniform numerical methods for singularly perturbed ordinary differential equations containing two small parameters are studied.Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. A numerical algorithm based on an upwind finite difference operator and an appropriate piecewise uniform mesh is constructed. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are given to illustrate the parameter-uniform convergence of numerical approximations.

Subfields: Mechanical Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/72e2bfea1145243cc84a119b4e4e3340bc2ae5d8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mechanical Engineering

1. Zorica Uzelac
2. Hans-Görg Roos
3. Volker Mehrmann
4. Pratibhamoy Das

In Numerical Analysis

1. Pratibhamoy Das
2. Zorica Uzelac
3. Hans-Görg Roos
4. Volker Mehrmann
5. Subrata Rana

Citations in the corpus

• The Sdfem for a Convection-diffusion Problem with Two Small Parameters (2003, methodology): “Recently, simple upwinding on a properly chosen Shishkin mesh was analyzed independently in [5,9].”
• Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters (2015, methodology): “From the a priori analysis [24] it follows that the boundary layers arise from the left and right singular components of the solution.”