基于微分求积法的边界值方法

摘要

This paper mainly explores the relationship between boundary value method and differential quadrature method .By using the classical differential quadrature formulae ,this paper systematically constructs three different types of boundary value methods .When selecting the uniform grid points ,the boundary value methods derived from this paper are consistent with the existing boundary value methods .The obtained results reveal the intrinsic relationship between the differential quadrature methods and boundary value methods ,and meanwhile arrive at the relation between linear multistep formulae and single-step multi-stage methods .%探究了边界值方法与微分求积法两者之间的关系.利用经典的微分求积公式,系统地构造了三类不同的边界值方法;当采用均匀网格点时,本文所导出的边界值方法与已有的边界值方法是一致的.研究结果揭示了微分求积法与边界值方法两者之间的内在关系,也建立了线性多步法与单步多级方法之间的联系.