Analogy of the Approximate Methods

Abstract

So far we have seen that calculus of variations and the finite element method both refer to the integral equations. The finite difference method on the other hand deals primarily with the differential equations. At any stage of the problem however, these three methods follow very analogous paths. In order to illustrate the similarities between them, let us consider an elementary problem such as a simple prismatic beam subject to a distributed transverse load p (x). The integral and the differential equations of this problem are, respectively,

$$$$

(5.1)

and

$$$$

(5.2)

.