A new third-order energy stable technique and error estimate for the extended Fisher-Kolmogorov equation.

A new third-order energy stable technique, which is a convex splitting scheme with the Douglas-Dupont regularization term Aτ2(ϕn−ϕn−1), is proposed for solving the extended Fisher–Kolmogorov equation. The higher-order backward difference formula is used to deal with the time derivative term. The constructed numerical scheme is uniquely solvable and unconditionally preserves the modified discrete energy dissipative law. With the help of discrete orthogonal convolution kernels, the L2 norm error estimate of the stabilized BDF3 scheme can be established by acting the standard inner product with the error system. Several numerical experiments are used to verify the validity of the numerical method and the correctness of the theoretical analysis.