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

Abstract

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.