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<p>A coefficient inverse problem for a singularly perturbed parabolic convection–diffusion equation with the final time data is studied. At first, a discretization scheme of the direct problem is constructed by using classical backward Euler method on a uniform mesh for the time derivative and an upwind finite difference scheme on a Shishkin-type mesh for the spatial derivative. Subsequently, we introduce a new fitness function about the coefficient inverse problem, which is solved by using an enhanced sine cosine algorithm (ESCA). This ESCA is constructed by using four strategies, including the tent chaos mapping, the hybrid update strategy, the improvement of random weight, and the chaotic local search. The effectiveness of ESCA is verified on 10 standard benchmark functions and a coefficient inverse problem for a singularly perturbed parabolic convection–diffusion. It is shown from these experimental results that for various performance evaluation indexes, ESCA can produce high-quality solutions with better objective values compared to the other algorithms.</p>

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An ESCA algorithm for solving the coefficient inverse problem of singularly perturbed parabolic convection–diffusion equation

  • 期刊论文

  • 发表日期：

    2025年5月6日

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  • Li-Bin Liu,
  • Tian Zhou,
  • Ling Li,
  • Xiongfa Mai,
  • Delong Guo

摘要

A coefficient inverse problem for a singularly perturbed parabolic convection–diffusion equation with the final time data is studied. At first, a discretization scheme of the direct problem is constructed by using classical backward Euler method on a uniform mesh for the time derivative and an upwind finite difference scheme on a Shishkin-type mesh for the spatial derivative. Subsequently, we introduce a new fitness function about the coefficient inverse problem, which is solved by using an enhanced sine cosine algorithm (ESCA). This ESCA is constructed by using four strategies, including the tent chaos mapping, the hybrid update strategy, the improvement of random weight, and the chaotic local search. The effectiveness of ESCA is verified on 10 standard benchmark functions and a coefficient inverse problem for a singularly perturbed parabolic convection–diffusion. It is shown from these experimental results that for various performance evaluation indexes, ESCA can produce high-quality solutions with better objective values compared to the other algorithms.