Solutions to Periodic Differential Equations

Abstract

Closed form solutions of periodic differential equations are, in general, difficult to find. Whilst series expansions can be determined in some cases [1] they are generally of little value in most applications, especially when many solutions are required. There are, however, a few specific types of periodic equation that can be solved analytically and for which the solutions appear in an easily used form. So useful and simple in fact are these special cases that they form the essence of modelling techniques which can be used to generate very good approximations to the solutions of intractable periodic differential equations. These modelling methods are the subject of Chap. 5. In this chapter equations which are tractable are treated in depth using the matrix approach laid down in Chap. 2. Methods for handling homogeneous equations are dealt with first whilst particular integrals are considered in a later section.