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<p>In this paper, we propose two kinds of efficient numerical methods for solving VIEs of second kind with a composite oscillatory kernel. We first describe the oscillatory structure of the original solution and then give the fully discrete multi-oscillation-preserving spectral method and the spectral-element method, respectively. We establish that these two approximate methods reach the optimal convergence order, independent of the wave numbers. Finally, three numerical examples are presented to demonstrate the efficiency and accuracy of the proposed methods.</p>

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Spectral algorithms for second kind VIEs with a composite oscillatory kernel

  • 期刊论文

  • 发表日期：

    2026年2月23日

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  • Xiaowen Zhang,
  • Haotao Cai

摘要

In this paper, we propose two kinds of efficient numerical methods for solving VIEs of second kind with a composite oscillatory kernel. We first describe the oscillatory structure of the original solution and then give the fully discrete multi-oscillation-preserving spectral method and the spectral-element method, respectively. We establish that these two approximate methods reach the optimal convergence order, independent of the wave numbers. Finally, three numerical examples are presented to demonstrate the efficiency and accuracy of the proposed methods.