Analysis of a nonlinear singularly perturbed Volterra integro-differential equation
Sumit, Sunil 1Kumar, Sunil 1Vigo-Aguiar, Jesus2
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作者信息
1. Indian Inst Technol BHU Varanasi
2. Univ Salamanca
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Abstract
We consider a nonlinear singularly perturbed Volterra integro-differential equation. The problem is discretized by an implicit finite difference scheme on an arbitrary nonuniform mesh. The scheme comprises of an implicit difference operator for the derivative term and an appropriate quadrature rule for the integral term. We establish both a priori and a posteriori error estimates for the scheme that hold true uniformly in the small perturbation parameter. Numerical experiments are performed and results are reported for validation of the theoretical error estimates. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
NSTL
Elsevier