Computational methods for singularly perturbed differential equations with advanced argument of convection-diffusion type

Abstract

This study investigates singularly perturbed differential equations through advanced convection-diffusion techniques. We employ a finite difference approach utilizing a piecewise uniform Shishkin-type mesh to tackle this problem. Our analysis demonstrates that the approach achieves virtually first-order convergence. Error estimates are computed using discrete norms, and numerical experiments are conducted to validate these theoretical results.

Keywords

• error analysis
• finite difference method
• convection-diffusion type
• boundary layer