Journal
NUMERICAL ALGORITHMS
Volume -, Issue -, Pages -Publisher
SPRINGER
DOI: 10.1007/s11075-023-01620-y
Keywords
Singular perturbation; A posteriori mesh; Mesh refinement; Delay differential equations; Volterra integro-differential equations
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This article presents a numerical analysis of a class of singularly perturbed delay Volterra integro-differential equations with multiple boundary layers. The problem is discretized 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: an a priori error estimate for robust convergence on specific meshes, and a maximum norm a posteriori error estimate involving difference derivatives of the approximate solution. Numerical experiments confirm the theoretical findings.
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.
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