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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Published in:Fractal and fractional Vol. 7; no. 1; p. 43
Main Authors: Elango, Sekar, Unyong, Bundit
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.01.2023
Subjects:
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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Abstract 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.
AbstractList 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.
Audience Academic
Author Elango, Sekar
Unyong, Bundit
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StartPage 43
SubjectTerms 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
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Title Numerical Scheme for Singularly Perturbed Mixed Delay Differential Equation on Shishkin Type Meshes
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