August 24, 2026 Thesis Open Access

Shegaye Lema Cheru

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    "description": "<p>Abstract This dissertation investigates two-parameter singularly perturbed parabolic problems, including models with and without time delay, and involving both continuous and discontinuous coefficients. The interaction of small perturbation parameters in the diffusion and convection terms induces complex multiscale layer structures, characterized by dual boundary layers of unequal thickness and sharp interior layers arising from temporal delay and non-smooth data. These features pose significant challenges for both analytical and numerical treatment. Since such problems frequently arise in scientific and engineering applications, the development of reliable numerical methods is essential for understanding the physical phenomena. To overcome the limitations of classical approaches, which often fail to capture the layer behavior accurately, parameter-uniform numerical schemes based on fitted-operator and fitted-mesh techniques are developed. The fitted-operator approach constructs discrete schemes on uniform meshes, while fitted-mesh strategy employs layer adapted non-uniform meshes. The proposed methods are rigorously analyzed for stability, consistency, and uniform convergence. Numerical experiments validate the theoretical results, demonstrating high accuracy, improved convergence behavior, and enhanced robustness compared to existing methods. The numerical results, presented through tables and surface plots clearly illustrate the influence of perturbation parameters, delay, and discontinuities on the solution structure. Key words: Singularly perturbed problem; Two parameter; Parameter-uniform; Non-smooth data; Boundary and interior layers, Time delay.</p>", 
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    "title": "Numerical Treatment of Various Classes of Two-Parameter Singularly Perturbed Parabolic Problems", 
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