What does this research mean for the field?

The fast finite difference scheme for variable-order time-fractional diffusion equations achieves optimal convergence rates while significantly reducing computational costs compared to existing methods. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to develop a fast scheme for solving fractional diffusion equations with optimal error estimates and to demonstrate its computational advantages.

March 12, 2026Mathematical Methods in the Applied Sciences

Optimal Error Estimates of Fast L1 Scheme for Variable‐Order Fractional Diffusion Equations

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Authors

JZJ. ZhangShanghai Medical College of Fudan University XHXuefei HeNorthwest A&F University TLTianyi LiUniversity of Macau

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Implication

Develops a fast finite difference scheme, showing optimal convergence rates in fractional diffusion equations, highlighting computational efficiency.

Key Points

The aim is to develop a fast scheme for solving fractional diffusion equations with optimal error estimates and to demonstrate its computational advantages.
Developed a finite difference scheme on graded meshes.
Combined 1 approximation with sum-of-exponentials for kernel approximation.
Proved numerical stability and convergence using maximum principle analysis.
Conducted numerical experiments to validate theoretical findings.
Achieved high accuracy and computational efficiency with the proposed method.
Established sharp error estimates and rigorous proofs of stability and convergence.
Demonstrated optimal convergence rates while significantly reducing computational costs compared to existing methods.

Cite This Study

Zhang et al. (2026) studied this question.

synapsesocial.com/papers/69b257a296eeacc4fcec6635 https://doi.org/10.1002/mma.70646

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Implication

Develops a fast finite difference scheme, showing optimal convergence rates in fractional diffusion equations, highlighting computational efficiency.

Optimal Error Estimates of Fast L1 Scheme for Variable‐Order Fractional Diffusion Equations

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Member takes

Implication

Key Points

Cite This Study

Optimal Error Estimates of Fast L1 Scheme for Variable‐Order Fractional Diffusion Equations

Discussion

Member takes

Implication

Key Points

Cite This Study

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