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A priori and a posteriori error estimation for singularly perturbed delay integro-differential equations.
- Source :
-
Numerical Algorithms . Apr2024, Vol. 95 Issue 4, p1561-1582. 22p. - Publication Year :
- 2024
-
Abstract
- This article deals with the numerical analysis of a class of singularly perturbed delay Volterra integro-differential equations exhibiting multiple boundary layers. The discretization of the considered problem is done using an implicit difference scheme for the differential term and a composite numerical integration rule for the integral term. The analysis of the discrete scheme consists of two parts. First, we establish an a priori error estimate that is used to prove robust convergence of the discrete scheme on Shishkin and Bakhvalov type meshes. Next, we establish the maximum norm a posteriori error estimate that involves difference derivatives of the approximate solution. The derived a posteriori error estimate gives the computable and guaranteed upper bound on the error. Numerical experiments confirm the theory. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10171398
- Volume :
- 95
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Numerical Algorithms
- Publication Type :
- Academic Journal
- Accession number :
- 176120252
- Full Text :
- https://doi.org/10.1007/s11075-023-01620-y