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arXiv · 2409.10861

A Fractional spectral method for weakly singular Volterra integro-differential equations with delays of the third-kind

Borui Zhao
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Abstract

In this paper, we present a fractional spectral collocation method for solving a class of weakly singular Volterra integro-differential equations (VDIEs) with proportional delays and cordial operators. Assuming the underlying solutions are in a specific function space, we derive error estimates in the $L^2_{\omega^{\alpha,\beta,\lambda}}$ and $L^{\infty}$-norms. A rigorous proof reveals that the numerical errors decay exponentially with the appropriate selections of parameters $\lambda$. Subsequently, numerical experiments are conducted to validate the effectiveness of the method.

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Borui Zhao. 2024-09-17. A Fractional spectral method for weakly singular Volterra integro-differential equations with delays of the third-kind. https://arxiv.org/abs/2409.10861

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