What question did this study set out to answer?

The aim is to explore the nonlinear time-fractional Sine-Gordon equation using the Fourier spectral method.

March 7, 2026Open Access

Fourier Spectral Method for Nonlinear Time-Fractional Sine-Gordon Equations

Q: What does this research mean for the field?

The Fourier spectral method provides a stable and convergent numerical solution for the nonlinear time-fractional Sine-Gordon equation. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Key Points

The aim is to explore the nonlinear time-fractional Sine-Gordon equation using the Fourier spectral method.
Utilized the Fourier spectral method for spatial discretization.
Applied L1 approximation scheme for time-fractional derivative.
Proved existence and uniqueness of numerical solution.
Analyzed stability and convergence of the proposed method.
Validated theoretical results through numerical experiments.
The method demonstrated stability and convergence properties.
Numerical experiments confirmed the theoretical findings.
Existence and uniqueness of solutions were established.

Abstract

In this paper, the nonlinear time-fractional Sine-Gordon equation is investigated via the Fourier spectral method. The time-fractional derivative is approximated by the L1 approximation scheme, and the spatial component is discretized using the Fourier spectral method. The existence and uniqueness of the numerical solution are proven, and the stability and convergence of the proposed method are analyzed, respectively. Theoretical results are validated by numerical experiment.

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