4.5 Two Further Examples

In Section 2.3, we gave an example. An SEIF file for this example is given in Figure |refF3.3.1. The problem is again given the name DOC. The two types of nonlinear element were assigned the names ELEMENT1/2 by the previous SDIF file. The elemental variables were given names beginning with V and the internal variables for the second nonlinear element started with U. The constant 0.0 occurs in the derivatives of both elements, so an auxiliary variable is assigned to hold its value (although, we could have just not specified these particular components, which would then have taken their default zero value). The function value and derivatives of the second element type use both sines and cosines of $u_2$ and again auxiliary variables are assigned to hold these values, this time as variables local to ELEMENT2. The second derivatives are sufficiently straightforward to compute that we provide them.

Figure 4.6: SEIF file for the element types for the example
of Section 2.3

Figure 4.7: SEIF file for the element types for the example
of Section 2.4

We gave a second example in Section 2.4. An SEIF file for this example is given in Figure 4.7 on page . The problem is again given the name DOC2. The only type of nonlinear element was assigned the name SQUARE in the previous SDIF file, its elemental variable was called V and there was no useful range transformation.