Abstract
A high-order accuracy finite difference scheme is investigated to solve the one-dimensional extended Fisher-Kolmogorov (EFK) equation. A three level linearized compact finite difference scheme is proposed. Priori estimates and unique solvability are discussed in detail by the discrete energy method. The unconditional stability and convergence of the difference solution are proved. The new compact difference scheme has second-order accuracy in time and fourth-order accuracy in space in maximum norm. Numerical experiments demonstrate the accuracy, efficiency of our proposed technique.
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