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

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 $L^2$ 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.

27 pages, 16 figures, 8 tables. arXiv admin note: substantial text overlap with arXiv:2409.10861