The direct numerical integration of linear matrix differential equations using pade approximations

Abstract

Abstract A class of approximations to the matrix linear differential equation is presented. The approximations range, in accuracy, from the simplest forward difference scheme to the exact solution. The infinite series defining the exponential matrix is used to ascertain the accuracy of the various approximations. A clear distinction is made between approximations to the system equations and the forcing function, with the forcing term being represented by a piecewise linear function. Special application is given to the equations arising in structural dynamics of the form equation image For these structural dynamic equations, the measure of the energy of the system is used to analyse the stability of the numerical approximations.