August 16, 2025Fractal and FractionalOpen Access

Stability and Convergence Analysis of Compact Finite Difference Method for High-Dimensional Time-Fractional Diffusion Equations with High-Order Accuracy in Time

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Authors

JCJunying CaoShanghai Open University JFJie FangXi’an University of Posts and Telecommunications ZWZhongqing WangUniversity of Shanghai for Science and Technology

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Implication

This analysis reveals the stability and convergence of a high-order method for time-fractional diffusion equations, suggesting improved numerical solutions.

Key Points

The proposed scheme achieves convergence order of (3−γ) in time and 4 in space, enhancing accuracy.
Stability and convergence are established using the new norm ||·||H˜1, proving its equivalence to the standard H1-norm.
An innovative transformation introduces positive coefficients in the high-order numerical scheme, aiding in performance.
Numerical experiments confirm the theoretical accuracy of the proposed method across various diffusion equations.

Cite This Study

Cao et al. (2025) studied this question.

synapsesocial.com/papers/68a368780a429f797332d759 https://doi.org/10.3390/fractalfract9080520

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Implication

This analysis reveals the stability and convergence of a high-order method for time-fractional diffusion equations, suggesting improved numerical solutions.

Stability and Convergence Analysis of Compact Finite Difference Method for High-Dimensional Time-Fractional Diffusion Equations with High-Order Accuracy in Time

Discussion

Member takes

Implication

Key Points

Cite This Study

Stability and Convergence Analysis of Compact Finite Difference Method for High-Dimensional Time-Fractional Diffusion Equations with High-Order Accuracy in Time

Discussion

Member takes

Implication

Key Points

Cite This Study

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