An a posteriori based convergence analysis for a nonlinear singularly perturbed system of delay differential equations on an adaptive mesh

The present work considers a nonlinear system of singularly perturbed delay differential equation whose each component of the solution has multiple layers. Here, we provide an a posteriori based convergence analysis for the adaptation of these layer phenomena. We derive a parameter uniform a posteri...

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Bibliographic Details
Published in:Numerical algorithms Vol. 81; no. 2; pp. 465 - 487
Main Author: Das, Pratibhamoy
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2019
Springer Nature B.V
Subjects:
Algebra
Algorithms
Computer Science
Convergence
Differential equations
Error analysis
Exact solutions
Mesh generation
Nonlinear systems
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Partial differential equations
Theory of Computation
35F25
65L05
A posteriori based convergence analysis
Nonlinear equations
Optimal convergent solution
35F20
Singular perturbation
34A34
Multiple layer phenomena
65Y20
Interior layer
34L30
Multi-scale phenomena
Moving mesh algorithm
A priori and a posteriori meshes
65L50
Delay problem
System of differential equations
65J15
65L10
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Description
Summary:The present work considers a nonlinear system of singularly perturbed delay differential equation whose each component of the solution has multiple layers. Here, we provide an a posteriori based convergence analysis for the adaptation of these layer phenomena. We derive a parameter uniform a posteriori error estimate which will lead to a layer adaptive mesh by moving a fixed number of mesh points. It is theoretically shown that the layer adaptive solution on the a posteriori generated mesh will uniformly converge to the exact solution with optimal order accuracy where the optimality is measured with respect to the continuous problem discretization. The comparison results with the existing methods based on a priori meshes show that the proposed method on the a posteriori mesh is highly effective.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-018-0557-4