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March 8, 2026IMA Journal of Numerical Analysis

A hybrid polynomial spectral collocation method for weakly singular Volterra integral equations with variable exponent

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Authors

ZMZheng MaMSMartin Stynes

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Overview

Demonstrates a numerical method to solve weakly singular Volterra integral equations, implying improved accuracy in approximations.

Key Points

  • The aim is to develop a hybrid method for solving weakly singular Volterra integral equations with variable exponents.
  • Analytical techniques based on previous works are applied on a small interval.
  • Polynomial spectral collocation is utilized at Jacobi-Gauss points on a larger interval.
  • Estimates for best approximations of functions by polynomials are derived in the L∞ norm.
  • Sharp error bounds for the hybrid method are established.
  • Numerical experiments confirm the accuracy of the error bounds.

Cite This Study

Ma et al. (2025) studied this question.

synapsesocial.com/papers/69ada8b2bc08abd80d5bbeb3https://doi.org/10.1093/imanum/draf144
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