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A new multi-step BDF energy stable technique for the extended Fisher-Kolmogorov equation

    Qihang Sun   Affiliation
    ; Xiuling Hu Affiliation
    ; Xin Li Affiliation
    ; Yang Li Affiliation
    ; Luming Zhang Affiliation

Abstract

The multi-step backward difference formulas of order k (BDF-k) for 3 ≤ k ≤ 5 are proposed for solving the extended Fisher–Kolmogorov equation. Based upon the careful discrete gradient structures of the BDF-k formulas, the suggested numerical schemes are proved to preserve the energy dissipation laws at the discrete levels. The maximum norm priori estimate of the numerical solution is established by means of the energy stable property. With the help of discrete orthogonal convolution kernels techniques, the L2 norm error estimates of the implicit BDF-k schemes are established. Several numerical experiments are included to illustrate our theoretical results.

Keyword : extended Fisher-Kolmogorov equation, multi-step BDF method, discrete orthogonal convolution kernels, stability and convergence

How to Cite
Sun, Q., Hu, X., Li, X., Li, Y., & Zhang, L. (2024). A new multi-step BDF energy stable technique for the extended Fisher-Kolmogorov equation. Mathematical Modelling and Analysis, 29(1), 125–140. https://doi.org/10.3846/mma.2024.17430
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Feb 23, 2024
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