Abstract:
We consider a nonlinear singularly perturbed Volterra integro-differential equation. The problem is discretized by an implicit finite difference scheme on an arbitrary non-uniform 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.
Description:
his research was supported by the Science and Engineering Research Board (SERB), India under the Project No.ECR/2017/000564. The first author gratefully acknowledges the support of University Grants Commission, India , for research fellowship with Reference No: 20/12/2015(ii)EU-V. The authors gratefully acknowledge the valuable comments and suggestions from the anonymous referees.
