Numerical solutions for the general Rosenau-RLW equation are considered and an energy conservative linearized finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence, and a priori error estimate of the scheme are proved using energy method. Numerical results demonstrate that the scheme is efficient and reliable.
In this paper, numerical solutions for the Rosenau-KdV equation coupling with the Rosenau-RLW equation are considered and a new C-N pseudo-compact conservative numerical scheme, which preserves the original conservative properties is designed. The proposed scheme is based on a finite difference method. The existence of the difference solutions has been shown by the Brouwer fixed point theorem. Unconditional stability, second-order convergence, and a prior error estimate of the scheme are proved by the discrete energy method. Numerical examples have been given to verify the theoretical results.
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