Local differential quadrature method using irregularly distributed nodes for solving partial differential equations  

用非规则节点解偏微分方程的局部微分求积法(英文)

作　　者：王娟 夏利伟 马杭 

机构地区：[1]Department of Mechanics,College of Sciences,Shanghai University

出　　处：《Journal of Shanghai University(English Edition)》2008年第2期110-114,共5页上海大学学报（英文版）

摘　　要：In the conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature （LDQ） method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in the new approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directly approximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature is still kept. Numerical examples are provided to validate the LDQ method.In the conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature （LDQ） method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in the new approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directly approximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature is still kept. Numerical examples are provided to validate the LDQ method.

关 键 词：differential quadrature （DQ） method irregular node distribution INTERPOLATION MESH-FREE partial differentialequation （PDE）. 

分 类 号：O175.2[理学—数学]