A new three-point linearized conservative compact difference scheme
based on reduction order method for the RLW equation
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.