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This research examines the time-fractional diffusion equation regarding variable coefficients, considering second-kind Steklov nonlocal boundary conditions that include three real parameters. The Caputo’s definition of the time-fractional derivative is used. A difference scheme of temporal order \(3-\delta \) , where \(\delta \) represents the order of the time-fractional derivative, is developed using an L2 type approach. In the spatial direction a second-order approximation is employed. The stability and convergence of the proposed difference scheme are analyzed through the method of energy inequalities, which results in the establishment of the a priori estimates for the scheme.

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Stability Analysis of an L2 Type Numerical Scheme for the Steklov Nonlocal Boundary Value Problems in Time-Fractional Diffusion Equations

  • 会议论文

  • 发表日期：

    2025年

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  • Anatoly A. Alikhanov,
  • Mohammad Shahbazi Asl,
  • Adam A. Alikhanov,
  • Ruslan A. Chernobrovkin

摘要

This research examines the time-fractional diffusion equation regarding variable coefficients, considering second-kind Steklov nonlocal boundary conditions that include three real parameters. The Caputo’s definition of the time-fractional derivative is used. A difference scheme of temporal order \(3-\delta \) , where \(\delta \) represents the order of the time-fractional derivative, is developed using an L2 type approach. In the spatial direction a second-order approximation is employed. The stability and convergence of the proposed difference scheme are analyzed through the method of energy inequalities, which results in the establishment of the a priori estimates for the scheme.