Robust Numerical Method for Singularly Perturbed Convection-Diffusion Type Problems With Non-Local Boundary Condition

Abstract

This paper presents the study of singularly perturbed differential equations of convection diffusion type with non-local boundary condition. The proposed numerical scheme is a combination of classical finite difference method for the initial boundary condition and nonstandard finite difference method for the differential equations at the interior points. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical examples considered. The method is shown to be first-order convergence independent of the perturbation parameter ε.

Richardson Extrapolation Technique for Singularly Perturbed Convection-diffusion Problem with Non-local Boundary Conditions

“…One of the main objectives of their research is to address the numerical approximation of derivatives, especially in the context of problems with disparate scales or SPP. The research conducted by Debela and Duressa [11] presents a significant advancement in the field of numerical methods for solving SPCDPs with non-local boundary conditions. Later, Debela and Duressa proposed a computational method for the class of SPCDE with IBC using the Richardson extrapolation technique in [9].…”