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A higher-order accurate difference approximation of singularly perturbed reaction-diffusion problem using grid equidistribution
- Source :
- Ain Shams Engineering Journal, Vol 12, Iss 4, Pp 4211-4221 (2021)
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- This paper proposes a higher-order numerical approximation scheme to solve singularly perturbed reaction–diffusion boundary value problems. The proposed scheme is a combination of a fourth-order numerical difference method and classical central difference method applied on a non-equidistant grid. The non-equidistant grid is generated by equi-distributing a non-negative monitor function. The theoretical and empirical error analysis demonstrate that the proposed scheme has fourth-order uniform convergence with respect to the perturbation parameter.
- Subjects :
- 020209 energy
Uniform convergence
020208 electrical & electronic engineering
General Engineering
Finite difference
Hybrid difference scheme
Perturbation (astronomy)
02 engineering and technology
Engineering (General). Civil engineering (General)
Grid
Robust discretization
Boundary value problems
Grid equidistribution
Scheme (mathematics)
Reaction–diffusion system
0202 electrical engineering, electronic engineering, information engineering
Applied mathematics
Order (group theory)
Boundary value problem
TA1-2040
Singular perturbation
Higher-order approximation
Mathematics
Subjects
Details
- ISSN :
- 20904479
- Volume :
- 12
- Database :
- OpenAIRE
- Journal :
- Ain Shams Engineering Journal
- Accession number :
- edsair.doi.dedup.....558692898cec1cd2d6f86fff1d4c9f7e