Abstract
A second-order difference method on graded meshes is proposed for the multi-term fourth-order evolution equation (FOEE). We handle the Riemann–Liouvile fractional integral by the product integration rule on the graded meshes and the spatial derivatives by the second order central difference formula. Stability and convergence of the \(L^2\)-norm is provided. Finally, some numerical examples are given to verify the theoretical analysis and the validity of the proposed method.
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We thank the anonymous referees for their valuable comments and suggestions which helped us to improve the manuscript a lot.
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Communicated by Hui Liang.
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The work was supported by National Natural Science Foundation of China (12126321), Scientific Research Fund of Hunan Provincial Education Department (21B0550), Hunan Provincial Natural Science Foundation of China (2022JJ50083, 2021JJ30209), and Scientific research and innovation Foundation of Hunan University of Technology (CX2115, CX2114)
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Wu, L., Zhang, H., Yang, X. et al. A second-order finite difference method for the multi-term fourth-order integral–differential equations on graded meshes. Comp. Appl. Math. 41, 313 (2022). https://doi.org/10.1007/s40314-022-02026-7
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DOI: https://doi.org/10.1007/s40314-022-02026-7