A Robust Numerical Scheme via Grid Equidistribution for Singularly Perturbed Delay Partial Differential Equations Arising in Control Theory

In this paper, a model constituting the temperature control of a continuous casting process is considered. This model gives rise to singularly perturbed delay differential equations. This motivated us to construct a robust numerical scheme to solve singularly perturbed parabolic delay convection–dif...

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Bibliographic Details
Published inInternational journal of applied and computational mathematics Vol. 10; no. 2
Main Authors Deepika, P., Das, Abhishek
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.04.2024
Springer Nature B.V
Subjects
Applications of Mathematics
Boundary layers
Computational Science and Engineering
Continuous casting
Control theory
Delay
Derivatives
Diffusion layers
Error analysis
Finite element method
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Nuclear Energy
Operations Research/Decision Theory
Original Paper
Partial differential equations
Robustness (mathematics)
Temperature control
Theoretical
Truncation errors
Uniform convergence
65M06
Control theory
Equidistribution grid
65M12
Boundary layers
Truncation error
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Summary:In this paper, a model constituting the temperature control of a continuous casting process is considered. This model gives rise to singularly perturbed delay differential equations. This motivated us to construct a robust numerical scheme to solve singularly perturbed parabolic delay convection–diffusion problems exhibiting regular boundary layers. A uniform mesh is used to discretize the domain in the temporal direction, while a non-uniform mesh is used to discretize the spatial variable, which is created by equidistributing a monitor function. For the temporal derivative, the numerical scheme uses the backward Euler scheme, while the space derivative follows the upwind scheme. The truncation error analysis is performed. It is demonstrated that the approach has an optimal error bound and converges uniformly with first-order accuracy in the discrete supremum norm. The theoretical findings are validated by numerical experiments.
ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-024-01716-6