| Abstract: |
| This work addresses a class of steady-state and time-dependent degenerate singular perturbation problems with two parameters affecting the convection and diffusion terms. Due to the presence of degeneracy and multiple perturbation parameters, the continuous solution exhibits boundary layers with different widths at the boundaries of the spatial domain. To effectively capture these layers, we utilize a piecewise uniform Shishkin grid for spatial discretization and a uniform grid for time discretization. The time derivative is approximated using an implicit Euler method on the equispaced temporal grid, while upwind finite difference schemes are applied to the Shishkin mesh for spatial derivatives. To enhance solution accuracy, we incorporate the Richardson extrapolation technique. Our theoretical analysis establishes an error bound, demonstrating almost second-order convergence. Numerical experiments are conducted to corroborate the theoretical findings, confirming the predicted convergence rates. |
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