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A new three-point linearized conservative compact difference scheme based on reduction order method for the RLW equation
  • Ruihua Zhong,
  • X.F. Wang
Ruihua Zhong
Minnan Normal University

Corresponding Author:[email protected]

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X.F. Wang
Minnan Normal University
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Abstract

In this paper, a new fourth-order compact difference scheme based on the reduction order method is proposed for solving the regularized long wave (RLW) equation. The compact finite difference scheme is three-level and linear. The discrete mass and discrete energy, boundedness and uniqueness of the present compact scheme are proved. Convergence and stability of the compact scheme are also analyzed by using the discrete energy method. Our compact scheme has the rates of convergence of second-order in temporal direction and fourth-order in spatial direction, respectively. Numerical examples are carried out to verify the reliability of the theory analysis.