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**Numerical solutions of a class of singular neutral functional differential equations on graded meshes.**
*(English)*
Zbl 1404.65329

Summary: In this paper, we present case studies to illustrate the dependence of the rate of convergence of numerical schemes for singular neutral equations (SNFDEs) on the particular mesh employed in the computation. Previously, a semigroup theoretical framework was used to show convergence of semi- and fully-discrete methods for a class of SNFDEs with weakly singular kernels. On the other hand, numerical experiments demonstrated a “degradation” of the expected rate of convergence when uniform meshes were considered. In particular, it was numerically observed that the degradation of the rate of convergence was related to the strength of the singularity in the kernel of the SNFDE. Following the idea used for Volterra equations with weakly singular kernels, we investigate graded meshes associated with the kernel of the SNFDE in attempting to restore convergence rates.

### MSC:

65R20 | Numerical methods for integral equations |

34K40 | Neutral functional-differential equations |

45D05 | Volterra integral equations |

45J05 | Integro-ordinary differential equations |

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\textit{P. Perez-Nagera} and \textit{J. Turi}, J. Integral Equations Appl. 30, No. 3, 447--472 (2018; Zbl 1404.65329)

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