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Finite difference scheme for singularly perturbed reaction diffusion problem of partial delay differential equation with nonlocal boundary condition.
- Source :
- Advances in Difference Equations; 3/4/2021, Vol. 2021 Issue 1, p1-20, 20p
- Publication Year :
- 2021
-
Abstract
- This paper investigates singularly perturbed parabolic partial differential equations with delay in space, and the right end plane is an integral boundary condition on a rectangular domain. A small parameter is multiplied in the higher order derivative, which gives boundary layers, and due to the delay term, one more layer occurs on the rectangle domain. A numerical method comprising the standard finite difference scheme on a rectangular piecewise uniform mesh (Shishkin mesh) of N r × N t elements condensing in the boundary layers is suggested, and it is proved to be parameter-uniform. Also, the order of convergence is proved to be almost two in space variable and almost one in time variable. Numerical examples are proposed to validate the theory. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16871839
- Volume :
- 2021
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Advances in Difference Equations
- Publication Type :
- Academic Journal
- Accession number :
- 149070562
- Full Text :
- https://doi.org/10.1186/s13662-021-03296-x