An efficient computational approach for solving two-dimensional extended Fisher–Kolmogorov equation

Ismail, Kaouther; Rahmeni, Mohamed; Omrani, Khaled

doi:10.1080/00036811.2022.2134123

Cited by 4 publications

(1 citation statement)

References 18 publications

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“…The numerical methods, including finite element Galerkin method [5,8], collocation method [25] and pseudo-spectral method [16] for solving the EFK model had attracted many researchers. The numerical research in [11,12,13,14,15] are mainly focused on the Crank-Nicolson (CN) type schemes with uniform time-step. However, it is well known that the BDF method is a class of implicit methods for solving rigid differential equation numerical integrals.…”

Section: Introductionmentioning

confidence: 99%

A New Multi-Step BDF Energy Stable Technique for the Extended Fisher-Kolmogorov Equation

Sun,

Hu,

et al. 2024

Mathematical Modelling and Analysis

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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.

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