A novel mid-point upwind scheme for fractional-order singularly perturbed convection-diffusion delay differential equation

Abstract

This study presents a numerical approach for solving temporal fractionalorder singularly perturbed parabolic convection-diffusion differential equations with a delay using a uniformly convergent scheme. We use the asymptotic analysis of the problem to offer a priori bounds on the exact solution and its derivatives. To discretize the problem, we use the implicit Euler technique on a uniform mesh in time and the midpoint upwind finite difference approach on a piece-wise uniform mesh in space. The proposed technique has a nearly first-order uniform convergence order in both spatial and temporal dimensions. To validate the theoretical analysis of the scheme, two numerical test situations for various values of ε are explored.

Keywords

• caputo–fabrizio derivative operator
• midpoint upwind scheme
• fractional-order differential equation
• delay differential equation
• singularly perturbed problem