Abstract

Differential relations include both differential operators and solvers for boundary value problems. The formulas of compact finite difference approximations for first- and second-order differential relations of the form \({{P}_{1}}[u] = {{P}_{2}}[f]\) are obtained. An approximation on three-point stencils is used. Its implementation, as in the case of classical difference schemes, requires the inversion of a tridiagonal matrix. However, compact schemes provide significantly higher accuracy and the fourth order of approximation instead of the second.

中文翻译：

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逼近微分关系的紧凑有限差分方案

摘要

微分关系包括微分算子和边值问题的求解器。紧凑有限差分近似的形式的一阶和二阶微分关系的公式\（{{P} _ {1}} [U] {_ {2} {P}} [F] \ =），得到。使用三点模板的近似值。如在经典差分方案的情况下那样，其实现需要三对角矩阵的求逆。但是，紧凑的方案提供了更高的精度和近似的四阶而不是第二阶。