A new stable finite difference scheme and its convergence for time-delayed singularly perturbed parabolic PDEs (original) (raw)
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Abstract
In this study, we consider the time-delayed singularly perturbed parabolic PDEs (SPPPDEs). We know that the classical finite difference scheme will not produce good results for singular perturbation problems on a uniform mesh. Here, we propose a new stable finite difference (NSFD) scheme, which produces good results on a uniform mesh and also on an adaptive mesh. The NSFD scheme is constructed based on the stability of the analytical solution. Results are compared with the results available in the literature and observed that the proposed method is efficient over the existing methods for solving SPPPDEs.
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Authors and Affiliations
- Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, 440010, India
Pramod Chakravarthy Podila & Kamalesh Kumar
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- Pramod Chakravarthy Podila
- Kamalesh Kumar
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Correspondence toPramod Chakravarthy Podila.
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Communicated by Frederic Valentin.
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Podila, P.C., Kumar, K. A new stable finite difference scheme and its convergence for time-delayed singularly perturbed parabolic PDEs.Comp. Appl. Math. 39, 140 (2020). https://doi.org/10.1007/s40314-020-01170-2
- Received: 15 November 2019
- Revised: 12 March 2020
- Accepted: 16 April 2020
- Published: 14 May 2020
- Version of record: 14 May 2020
- DOI: https://doi.org/10.1007/s40314-020-01170-2