In this paper, several families of schemes are obtained based on the idea of nth order polynomial. Each family has different schemes with different types and orders. Also, the error terms, which determine the order of the scheme, of each scheme in all families are computed using the same methodology. Traditional finite different schemes beside backward, central, and forward compact schemes at each family are introduced. This work proposes a clear and simple method of constructing finite difference schemes, and it presents the flexibility and the properties of compact schemes. Beside the feature of the high order accuracy, which are gained by compact schemes without increasing the width of points set, compact schemes achieve better spectrum resolution compared to the traditional noncompact ones. Additionally, comparing the numerical dissipation of many schemes illustrates the favor of compact schemes when using problems with high frequency. Finally, there is an effort to solve and compare solutions of some standard problems from Computational Fluid Dynamics (CFD) using compact and noncompact schemes.
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机译：本文基于Nth阶多项式的思想获得了几个方案系列。每个家庭都有不同类型和订单的不同方案。此外，使用相同的方法计算确定所有家庭中的每个方案的顺序的错误术语。介绍了每个家庭的后向，中央和前向紧凑型方案旁边的传统有限不同方案。这项工作提出了一种明确而简单的构造有限差分方案的方法，它呈现了紧凑方案的灵活性和性质。除了高阶精度的特征旁边，通过紧凑的方案获得而不增加点集的宽度，与传统的非融合器相比，紧凑的方案实现了更好的频谱分辨率。另外，比较许多方案的数值耗散说明了在使用高频率问题时的紧凑方案的支持。最后，努力使用Compact and Noncompact方案来解决和比较一些标准问题的解决方案来自计算流体动力学（CFD）。
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