A Differential Quadrature as a numerical method to solve differential equations

Abstract

A Differential Quadrature proposed here can be used to solve boundary-value and initial-value differential equations with a linear or nonlinear nature. Unlike the classic Differential Quadrature Method (DQM), the newly proposed Differential Quadrature chooses the function values and some derivatives wherever necessary as independent variables. Therefore, the δ-type grid arrangement used in the classic DQM is exempt while applying the boundary conditions exactly. Most importantly, the explicit weighting coefficients can be obtained using the proposed procedures. The present method is used to solve two types of differential equations which are the single-span Bernoulli–Euler beam's buckling equation and the one-degree-of-freedom solid dynamic equation. Excellent results were obtained.