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High-order smoothness and high-order collocation approximation for Volterra integral equation with multiscale and nonlinear exponent kernel

  • Wenlin Qiu
  • Chuanwei Su
  • Xiangcheng Zheng
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Abstract

We consider a Volterra integral equation with multiscale and nonlinear exponent kernel. We propose the high-order smoothing conditions, under which the initial singularity of the solutions can be eliminated up to any prescribed order. This indicates the application of the multiscale nature of the kernel on local modification of the solutions. Then a discontinuous high-order collocation method with arbitrary polynomial degree is developed and analyzed on uniform or graded meshes based on the solution regularity. This work serves as a comprehensive extension and complement to [Zheng, Qiu and Stynes, SIAM J. Numer. Anal., to appear] in both mathematical and numerical aspects.

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Cite

BibTeXRIS
BibTeX
@misc{qiu2026highorder,
  title = {{High-order smoothness and high-order collocation approximation for Volterra integral equation with multiscale and nonlinear exponent kernel}},
  author = {Wenlin Qiu and Chuanwei Su and Xiangcheng Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05851},
  eprint = {2609.05851},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05851},
}
RIS
TY  - UNPB
TI  - High-order smoothness and high-order collocation approximation for Volterra integral equation with multiscale and nonlinear exponent kernel
AU  - Wenlin Qiu
AU  - Chuanwei Su
AU  - Xiangcheng Zheng
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.05851
UR  - https://arxiv.org/abs/2609.05851
AB  - We consider a Volterra integral equation with multiscale and nonlinear exponent kernel. We propose the high-order smoothing conditions, under which the initial singularity of the solutions can be eliminated up to any prescribed order. This indicates the application of the multiscale nature of the kernel on local modification of the solutions. Then a discontinuous high-order collocation method with arbitrary polynomial degree is developed and analyzed on uniform or graded meshes based on the solution regularity. This work serves as a comprehensive extension and complement to [Zheng, Qiu and Stynes, SIAM J. Numer. Anal., to appear] in both mathematical and numerical aspects.
ER  -