A Linear Fully Discrete Spectral Scheme for the Time Fractional Allen–Cahn Equation
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This paper considers the numerical approximation of the time fractional Allen–Cahn equation with initial and periodic boundary conditions, and a linear fully discrete scheme is constructed with the finite difference method in time and the Fourier spectral method in space. Based on a temporal–spatial error splitting argument, the boundedness of numerical solutions in the L∞ norm is rigorously proved and the unconditional convergence of the proposed scheme is obtained. Numerical examples illustrate the theoretical results.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Advanced Numerical Methods in Computational Mathematics
Numerical Solvers for Ordinary Differential Equations
Publication details
- Journal / source
- Mathematics
- Volume
- 14
- Issue
- 6
- Pages
- 1006–1006
- Publication date
- 16 March 2026
- Language
- EN