Computational study for a class of time-dependent singularly perturbed parabolic partial differential equation through tension spline

This article contributes a numerical technique for a class of singularly perturbed time delayed parabolic partial differential equation. A priori results of maximum principle, stability and bounds are discussed. The continuous problem is semi-discretized by the Crank–Nicolson based scheme in the tem...

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Bibliographic Details
Published in:Computational & applied mathematics 2020-09, Vol.39 (3), Article 233
Main Authors: Kumar, P. Murali Mohan, Ravi Kanth, A. S. V.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Discretization
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Maximum principle
Parabolic differential equations
Partial differential equations
Time dependence
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Summary:This article contributes a numerical technique for a class of singularly perturbed time delayed parabolic partial differential equation. A priori results of maximum principle, stability and bounds are discussed. The continuous problem is semi-discretized by the Crank–Nicolson based scheme in the temporal direction and then discretized by the tension spline scheme on non-uniform Shishkin mesh. Error estimation for the discretized problem is derived. To validate the theoretical findings, the numerical outcomes for linear and nonlinear problems are tested.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-020-01278-5