A Müntz-collocation spectral method for weakly singular Volterra delay-integro-differential equations

2024/09/18 by Zhao, Borui
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2410.02784

openalex publication_date 2024/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Müntz 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 L² and L^∞-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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