We propose four conservative schemes for the regularized long-wave (RLW) equation. The RLW equation has three invariants: mass, momentum, and energy. Our schemes are designed by using the discrete variational derivative method to inherit appropriate conservation properties from the equation. Two of our schemes conserve mass and momentum, while the other two schemes conserve mass and energy. With one of our schemes, we prove the numerical solution stability, the existence of the solutions, and the convergence of the solutions. Through some numerical computation examples, we demonstrate the efficiency and robustness of our schemes.

中文翻译：

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正则化长波方程的非线性和线性保守有限差分格式

我们为正则化长波 (RLW) 方程提出了四种保守方案。RLW 方程具有三个不变量：质量、动量和能量。我们的方案是通过使用离散变分导数方法从方程中继承适当的守恒性质而设计的。我们的两个方案守恒质量和动量，而另外两个方案守恒质量和能量。使用我们的一种方案，我们证明了数值解的稳定性、解的存在性和解的收敛性。通过一些数值计算示例，我们证明了我们方案的效率和稳健性。