A novel fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation. (English) Zbl 1221.65213
The authors present a robust fitted operator finite difference method for the numerical solution of a singularly perturbed delay parabolic partial differential equation. This method is unconditionally stable and is convergent with order \(\mathcal O(k+h^2)\), where \(k\) and \(h\) are respectively the time and space step-sizes. The performance of the presented method is illustrated through some numerical experiments.
Reviewer: Petr Sváček (Praha)
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35R10 | Partial functional-differential equations |
| 35B25 | Singular perturbations in context of PDEs |
| 35K10 | Second-order parabolic equations |
Keywords:
delay parabolic partial differential equation; singular perturbations; fitted operator finite difference methods; stability; convergence; numerical experimentsReferences:
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