Numerical Analysis For Singularly Perturbed Delay Differential Equations
| dc.contributor.author | Hazarika, Pradyut | |
| dc.date.accessioned | 2026-11-05T06:52:17Z | |
| dc.date.available | 2026-11-05T06:52:17Z | |
| dc.date.issued | 2025 | |
| dc.description.abstract | This thesis investigates a singularly perturbed delay differential equation modeled as a parabolic partial differential equation (PDE). Such problems are characterized by the presence of a small perturbation parameter and a delay term, which together induce boundary and interior layers, making both analysis and numerical approximation challenging. We begin by decomposing the solution and the differential operator into regular and singular components, enabling precise characterization of the solution structure. Rigorous bounds are derived for both components, shedding light on their respective behaviors and interactions. To approximate the solution numerically, the domain is discretized, and a weak formulation of the model problem is developed. This formulation is further employed to construct a finite element method (FEM) tailored to handle the singular perturbation and delay effects efficiently. Stability and accuracy of the FEM are established through analytical and numerical validation. The methodology ensures robustness in capturing sharp gradients and delayed responses in the solution. Overall, the thesis provides a comprehensive framework for understanding and approximating singularly perturbed delay PDEs. The results lay the groundwork for future research in higher dimensions, nonlinear models, and applications in science and engineering involving time delays and rapid transitions. | |
| dc.identifier.uri | http://nits.ndl.gov.in/handle/123456789/275 | |
| dc.language.iso | en | |
| dc.publisher | Department of Mathematics, NITS | |
| dc.relation.ispartofseries | D2413 | |
| dc.title | Numerical Analysis For Singularly Perturbed Delay Differential Equations | |
| dc.type | Thesis |