A new DQ-based method and its application to the stability of columns

摘要

A numerical Picard–like method, which combines successive approximations with differential quadrature, is discussed for application to the stability of columns.Unlike other methods, the present method satisfies all the boundary conditions without any additional computation for each iteration and it does not require any subdivision of the problem domain. Despite of its recursive nature, the approximate solution can be expressed by operational matrices and vectors of known quantities, such as the solution obtained by advanced polynomial expansions. Several examples show the satisfactorily behaviour of the proposed method in comparison to the existing methods both in the linear and nonlinear range.