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arXiv · 2410.02784

A M\"untz-collocation spectral method for weakly singular Volterra delay-integro-differential equations

Borui Zhao
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Abstract

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.

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Borui Zhao. 2024-09-18. A M\"untz-collocation spectral method for weakly singular Volterra delay-integro-differential equations. https://arxiv.org/abs/2410.02784

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