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Raji Reddy, Narahari, Mohapatra, Jugal. (1401). A robust numerical scheme for singularly perturbed delay parabolic initial-boundary-value problems involving mixed space shifts. سامانه مدیریت نشریات علمی, 11(1), 42-51. doi: 10.22034/cmde.2022.50833.2109
Narahari Raji Reddy; Jugal Mohapatra. "A robust numerical scheme for singularly perturbed delay parabolic initial-boundary-value problems involving mixed space shifts". سامانه مدیریت نشریات علمی, 11, 1, 1401, 42-51. doi: 10.22034/cmde.2022.50833.2109
Raji Reddy, Narahari, Mohapatra, Jugal. (1401). 'A robust numerical scheme for singularly perturbed delay parabolic initial-boundary-value problems involving mixed space shifts', سامانه مدیریت نشریات علمی, 11(1), pp. 42-51. doi: 10.22034/cmde.2022.50833.2109
Raji Reddy, Narahari, Mohapatra, Jugal. A robust numerical scheme for singularly perturbed delay parabolic initial-boundary-value problems involving mixed space shifts. سامانه مدیریت نشریات علمی, 1401; 11(1): 42-51. doi: 10.22034/cmde.2022.50833.2109

A robust numerical scheme for singularly perturbed delay parabolic initial-boundary-value problems involving mixed space shifts

Computational Methods for Differential Equations
مقاله 4، دوره 11، شماره 1، فروردین 2023، صفحه 42-51    اصل مقاله (372.29 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.50833.2109
نویسندگان
Narahari Raji Reddy1؛ Jugal Mohapatra* 2
1Department of Mathematics and Humanities, Kakatiya Institute of Technology and Science, Warangal, India.
2Department of Mathematics, National Institute of Technology Rourkela, Odisha, India.
چکیده
This article proposes a parameter uniform numerical method for solving a singularly perturbed delay parabolic initial boundary-value problem involving mixed space shifts. The model also involves a large delay in time. Taylor’s series expansion is applied to approximate the retarded terms in the spatial direction. For the time discretization, the implicit trapezoidal scheme is applied on uniform mesh, and for the spatial discretization, we use a proper combination of the mid-point upwind and the central difference scheme on Shishkin mesh. The proposed scheme provides a second-order convergence rate uniformly with respect to the perturbation parameter. Some comparison results are presented by using the proposed method to support our claim.
کلیدواژه‌ها
Time delay parabolic problem؛ Mixed shifts؛ Singular perturbation؛ Boundary layer؛ Uniform convergence
مراجع
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