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

Author(s)	Desta Sodano Sheiso
Country	Ethiopia
Abstract	This study presents the Richardson extrapolation techniques for solving singularly perturbed convection -diffusion problems (SPCDP) with non-local boundary conditions. A numerical approach is presented using an upwind finite difference scheme a piecewise-uniform (Shishkin) mesh. To handle the non-local boundary conditions, the trapezoidal rule is applied. The study establishes an error bound for numerical solutions and determines the numerical approximation for scaled derivatives. To enhance convergence and accuracy, we utilize Richardson extrapolation. This elevates accuracy from firs-order to second order convergence
Keywords	Singularly perturbed problems, Richardson extrapolation, Upwind scheme, Nonlocal boundary condition, Scaled derivatives, Piecewise-uniform mesh.
Field	Mathematics
Published In	Volume 5, Issue 6, November-December 2023
Published On	2023-11-27
DOI	https://doi.org/10.36948/ijfmr.2023.v05i06.9377

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