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<p>The paper proposes both numerical and analytical methods for solving the inverse problem of identifying the coefficient on the left-hand side of the time-dependent fractional diffusion equation, with initial-periodic boundary and over-determination conditions. First, we investigate a theoretical approach to clarify the existence and uniqueness of the inverse problem. In the numerical process, the finite difference method and numerical techniques for fractional integrals and derivatives are employed. Numerical results for several test examples are presented and discussed to illustrate the accuracy and stability of the numerical inversion.</p>

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NUMERICAL ANALYSIS OF INVERSE PROBLEMS FOR THE DIFFUSION EQUATION WITH INITIAL-BOUNDARY AND OVERDETERMINATION CONDITIONS

  • 期刊论文

  • 发表日期：

    2025年1月14日

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  • Jonibek J. Jumaev

摘要

The paper proposes both numerical and analytical methods for solving the inverse problem of identifying the coefficient on the left-hand side of the time-dependent fractional diffusion equation, with initial-periodic boundary and over-determination conditions. First, we investigate a theoretical approach to clarify the existence and uniqueness of the inverse problem. In the numerical process, the finite difference method and numerical techniques for fractional integrals and derivatives are employed. Numerical results for several test examples are presented and discussed to illustrate the accuracy and stability of the numerical inversion.