Arbitrary high-order linear structure-preserving schemes for the regularized long-wave equation

In this paper, a class of arbitrarily high-order linear momentum-preserving and energy-preserving schemes are proposed, respectively, for solving the regularized long-wave equation. For scheme, key idea is based on extrapolation/prediction-correction technique symplectic Runge-Kutta method in time, together with standard Fourier pseudo-spectral space. We show that scheme linear, high-order, unconditionally stable preserves discrete momentum system. it mainly energy quadratization approach analogous linearized strategy used construction scheme. The proposed can preserve both mass quadratic exactly. Numerical results addressed to demonstrate accuracy efficiency