求解RLW-KdV方程的一个高精度平均隐式守恒差分格式OA北大核心

In this paper,a three-level high-accuracy conservative difference scheme is proposed for the initial boundary value problem of RLW-KdV equation.Combining the Taylor expansion with the partial extrapola-tion in the spatial layer of difference scheme,the second-order term of the truncation error is removed.The averaged implicit scheme is applied in the temporal layer of difference scheme.The difference scheme pos-sesses fourth-order accuracy in the spatial direction and second-order accuracy in the temporal direction and reasonably simulates a conservative property of the original problem.Using the discrete Sobolev embedding inequality and the discrete functional analysis method,the convergence and stability of the difference scheme are given.Numerical examples demonstrate the effectiveness of the difference scheme.