A Müntz-collocation spectral method for weakly singular Volterra delay-integro-differential equations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929526571794432 |
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| author | Zhao, Borui |
| author_facet | Zhao, Borui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02784 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Müntz-collocation spectral method for weakly singular Volterra delay-integro-differential equations Zhao, Borui Numerical Analysis 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. |
| title | A Müntz-collocation spectral method for weakly singular Volterra delay-integro-differential equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2410.02784 |