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<p>In this paper, our focus is on developing a time stepping method for solving the fractional Feynman-Kac equation. We extend convolution quadrature, which is predicated on the block generalized Adams method, to approximate the fractional substantial derivative. Subsequently, the proposed algorithm is implemented to tackle the backward fractional Feynman-Kac equation within the temporal dimension. The convergence rate for the time-discrete solutions is derived by means of the Laplace transform representation. Numerical experiments with spectral collocation method in space direction verify the effectiveness of the algorithm.</p>

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Block generalized Adams convolution quadrature for the backward fractional Feynman-Kac equation

  • 期刊论文

  • 发表日期：

    2025年9月24日

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  • Ling Liu,
  • Jinrong Wang

摘要

In this paper, our focus is on developing a time stepping method for solving the fractional Feynman-Kac equation. We extend convolution quadrature, which is predicated on the block generalized Adams method, to approximate the fractional substantial derivative. Subsequently, the proposed algorithm is implemented to tackle the backward fractional Feynman-Kac equation within the temporal dimension. The convergence rate for the time-discrete solutions is derived by means of the Laplace transform representation. Numerical experiments with spectral collocation method in space direction verify the effectiveness of the algorithm.