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<p>In this paper, a generalized quasi-boundary value regularization method is proposed to reconstruct the source term of diffusion equation. The convergence rates of the regularized solution are proven by the eigenfunction expansion method under the a prior and posterior regularization parameter selection strategies, respectively. The corresponding inversion algorithm of discrete version is proposed. Several numerical examples are tested to show the efficiency of the inversion algorithm.</p>

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A generalized quasi-boundary value regularization method for an inverse source problem of diffusion equation

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • Zhousheng Ruan,
  • Zhenzhen Xie,
  • Zhenxing Chen,
  • Wen Zhang

摘要

In this paper, a generalized quasi-boundary value regularization method is proposed to reconstruct the source term of diffusion equation. The convergence rates of the regularized solution are proven by the eigenfunction expansion method under the a prior and posterior regularization parameter selection strategies, respectively. The corresponding inversion algorithm of discrete version is proposed. Several numerical examples are tested to show the efficiency of the inversion algorithm.