A two-grid spectral deferred correction method for the generalized multi-order fractional differential equations

Quen-Yi Lin and Ming-Cheng Shiue

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 245, issue C, 1-20

Abstract: Spectral deferred correction (SDC) methods constitute a class of numerical schemes that achieve arbitrarily high-order accuracy by iteratively applying a low-order method. These methods combine high accuracy with low computational cost, making them attractive for numerically solving differential equations. In this paper, the explicit two-grid SDC method for the generalized multi-order fractional differential equations and its theoretical analysis are studied. The analysis demonstrates that the proposed scheme is stable, provided that the time step size is sufficiently small, and that it achieves high-order convergence under the same condition. Numerical experiments are provided to validate and illustrate the theoretical findings.

Keywords: Spectral deferred corrections; Stability; Convergence; Fractional differential equations (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:245:y:2026:i:c:p:1-20

DOI: 10.1016/j.matcom.2025.12.021

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