This analysis demonstrates the stability and convergence of a new numerical method for specific equations, supporting advanced computational techniques.
In this paper, the nonlinear time-fractional convection-diffusion equations are solved by the Legendre spectral method. The Caputo time-fractional derivative is discretized by the L2–1σ scheme. A priori estimates of the fully discrete scheme are derived, and the existence and uniqueness of the numerical solution are analyzed. It is rigorously proved that the fully discrete scheme is unconditionally stable, and the convergence order of the numerical scheme is O(N1−m+τ2). Finally, numerical results are presented to verify the theoretical analysis.
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Lu et al. (2026) studied this question.
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