Analysis of a nonlinear singularly perturbed Volterra integro-differential equation. (English) Zbl 1481.65271
Summary: 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.
MSC:
| 65R20 | Numerical methods for integral equations |
| 45J05 | Integro-ordinary differential equations |
| 45D05 | Volterra integral equations |
| 65L11 | Numerical solution of singularly perturbed problems involving ordinary differential equations |
| 65L50 | Mesh generation, refinement, and adaptive methods for ordinary differential equations |
Keywords:
singularly perturbed; Volterra integro-differential equation; adaptive mesh generation; equidistribution principle; a posteriori analysisReferences:
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