Computational Examples

Abstract

As established in the earlier part of the book, the equilibrium system governing our mathematical model is

$$\displaystyle\begin{array}{rcl} & Z_{x} \diamond u[x] = 0,\quad x \in S,&{}\end{array}$$

(5.1)

where u is the displacement vector function and Z _x is the operator defined by (4.1). The examples discussed in this chapter illustrate the numerical implementation of the direct and classical indirect methods for various boundary value problems. Since it is important to know how accurate our results are, in a majority of cases we make use, for comparison purposes, of a test solution of system (5.1). Specifically, using (4.26) and (4.27) with parameters

$$\displaystyle\begin{array}{rcl} & \lambda \rightarrow 1,\quad \mu \rightarrow 2,\quad k \rightarrow 3,\quad a_{1} = 1,\quad b_{1} = 2,\quad a_{2} = -3,\quad b_{2} = 4&{}\end{array}$$

(5.2)

in conjunction with the Mathematica ^®; function FullSimplify, we construct the particular solution