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<p>In this paper, we introduce new schemes for solving space-fractional reaction–diffusion equations, based on the nonstandard compact finite difference for time variable and Fourier spectral method for space variable. The introduced methods are explicit schemes of second-order accurate in time, unconditionally stable, which have dynamical consistency and are simple to implement. We also provide the proof of theorems concerning the stability and convergence of the schemes. Some numerical tests are included that confirm our theoretical discussions and also illustrate the effectiveness of the methods in application.</p>

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An Explicit Unconditional Stable Compact Nonstandard Finite Difference Method for the Space-Fractional Reaction–Diffusion Equations

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • Maryam Pouladi,
  • Seyed Mohammad Hosseini

摘要

In this paper, we introduce new schemes for solving space-fractional reaction–diffusion equations, based on the nonstandard compact finite difference for time variable and Fourier spectral method for space variable. The introduced methods are explicit schemes of second-order accurate in time, unconditionally stable, which have dynamical consistency and are simple to implement. We also provide the proof of theorems concerning the stability and convergence of the schemes. Some numerical tests are included that confirm our theoretical discussions and also illustrate the effectiveness of the methods in application.