High-order finite difference schemes are widely used in the field of numerical solutions of partial differential equations. Although the importance of their local conservation property is well recognized, especially for solving hyperbolic conservation laws, the importance of their global conservation property (GCP) is seldom considered. To show that in some cases the GCP is indeed important in improving performance of finite difference schemes, we make a comparative study of two fifth-order schemes with boundary closures satisfying the GCP or not. For some toy models considered in this short note, we show that the scheme satisfying the GCP does perform better than its counterpart without the GCP.

高阶有限差分格式广泛用于偏微分方程数值解的领域。尽管已充分认识到其本地保护性的重要性，尤其是对于解决双曲线保护法，但很少考虑其全局保护性（GCP）的重要性。为了表明在某些情况下GCP在提高有限差分方案的性能方面确实很重要，我们对边界封闭是否满足GCP的两个五阶方案进行了比较研究。对于本简短说明中考虑的某些玩具模型，我们表明满足GCP的方案的确比不具有GCP的方案表现更好。