Abstract

In this paper, a new conservative fourth-order finite difference scheme is proposed for solving the generalized Rosenau–KdV–RLW equation. The solvability, convergence, and conservation of the numerical solution are discussed by the discrete energy method. The scheme is convergent of $$O(\tau ^{2}+h^{4})$$ and unconditionally stable. Several numerical experiment results show that the proposed scheme is efficient and reliable.

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