A M\"untz-collocation spectral method for weakly singular Volterra delay-integro-differential equations
<|reference_start|>A M\"untz-collocation spectral method for weakly singular Volterra delay-integro-differential equations: A M\"untz spectral collocation method is implemented for solving weakly singular Volterra integro-differential equations (VDIEs) with proportional delays. After constructing the numerical scheme to seek an approximate solution, we derive error estimates in a weighted $L^2$ and $L^{\infty}$-norms. A rigorous proof reveals that the proposed method can handle the weak singularity of the exact solution at the initial point $t=0$, with the numerical errors decaying exponentially in certain cases. Moreover, several examples will illustrate our convergence analysis.<|reference_end|>
@article{zhao2024a,
    title={A M\"untz-collocation spectral method for weakly singular Volterra
  delay-integro-differential equations},
    author={Borui Zhao},
    journal={arXiv preprint arXiv:2410.02784},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.02784},
    primaryClass={math.NA cs.NA}
}