Numerical Scheme for Singularly Perturbed Mixed Delay Differential Equation on Shishkin Type Meshes

Two non-uniform meshes used as part of the finite difference method to resolve singularly perturbed mixed-delay differential equations are studied in this article. The second-order derivative is multiplied by a small parameter which gives rise to boundary layers at x=0 and x=3 and strong interior la...

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Vydáno v:Fractal and fractional Ročník 7; číslo 1; s. 43
Hlavní autoři: Elango, Sekar, Unyong, Bundit
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.01.2023
Témata:
Analysis
Bakhvalov–Shishkin mesh
Boundary conditions
Boundary layer
Boundary layers
Boundary value problems
Convergence
Decomposition
Delay
Differential equations
Finite difference method
finite difference scheme
fractional calculus
mixed-delay differential equations
Ordinary differential equations
Shishkin mesh
singular perturbation problems
ISSN:2504-3110, 2504-3110
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Shrnutí:Two non-uniform meshes used as part of the finite difference method to resolve singularly perturbed mixed-delay differential equations are studied in this article. The second-order derivative is multiplied by a small parameter which gives rise to boundary layers at x=0 and x=3 and strong interior layers at x=1 and x=2 due to the delay terms. We prove that this method is almost first-order convergent on Shishkin mesh and is first-order convergent on Bakhvalov–Shishkin mesh. Error estimates are derived in the discrete maximum norm. Some examples are provided to validate the theoretical result.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract7010043