Meshless scheme for solving backward higher-order time-fractional parabolic equations with an extremely long time span

Chih-Wen Chang

Chaos, Solitons & Fractals, 2025, vol. 201, issue P1

Abstract: This study developed a regularization-free method for solving backward higher-order time-fractional parabolic equations with an extremely long time span, which are severely-ill-posed equations. In this method, two boundary conditions and a terminal time-wave function are used to establish the group symmetry. The constructed governing equation is then transformed into a linear combination of basis functions to acquire the complete solution. Furthermore, the method constructs an alternative symmetry group basis, which allows the governing equation to be transformed into a linear system and solved completely. When several numerical experiments are examined, we clearly show that the proposed approach can effectively handle the backward higher-order time-fractional parabolic equations. In addition, the proposed method remains robust even when the terminal data are extremely small and contaminated with significant noise, with the corresponding numerical results being highly accurate and stable. The proposed method has three advantages: (i) it does not require the estimation of additional data, (ii) it avoids the use of regularization parameters, and (iii) it does not involve any complex process.

Keywords: Anomalous diffusion modeling; Interface dynamics; Symmetry-based computational methods; Retrospective analysis; Parameter identification (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012044

DOI: 10.1016/j.chaos.2025.117191

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