August 21, 2025AxiomsOpen Access

High-Order Time–Space Compact Difference Methods for Semi-Linear Sobolev Equations

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Numerical analysis demonstrates improved accuracy of semi-linear Sobolev equation methods, indicating effectiveness of high-order techniques.

The proposed high-order compact difference methods achieve fourth-order accuracy in space and time, enhancing numerical solutions.
Using Richardson extrapolation improves temporal accuracy, transforming second-order methods into fourth-order ones.
The methods are validated through numerical experiments, confirming the robustness of the proposed solution techniques.
A proof of convergence is provided, ensuring the reliability of the fully fourth-order methods developed.

Hou et al. (2025) studied this question.

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Numerical analysis demonstrates improved accuracy of semi-linear Sobolev equation methods, indicating effectiveness of high-order techniques.