Parameter overspecification.

The number of specified parameter indices is allowed to be be greater than the generic number. In such case there will be ``overspecified'' parameters, whose values will appear in the screen and fort.7 output, but which are not part of the continuation process. A simple example is provided by demo opt, where the first three runs have overspecified parameters whose values, although constant, are printed.

There is, however, a more useful application of parameter overspecification. In the user-supplied routine PVLS one can define solution measures and assign these to otherwise unused parameters. Such parameters can then be overspecified, in order to print them on the screen and in the fort.7 output. It is important to note that such overspecified parameters must appear at the end of the ICP list, as they cannot be used as true continuation parameters.

For an example of using parameter overspecification for printing user-defined solution measures, see demo pvl. This is a boundary value problem (Bratu's equation) which has only one true continuation parameter, namely PAR(1). Three solution measures are defined in the routine PVLS, namely, the $L_2$-norm of the first solution component, the minimum of the second component, and the left boundary value of the second component. These solution measures are assigned to PAR(2), PAR(3), and PAR(4), respectively. In the constants-file c.pvl we have NICP=4, with PAR(1)-PAR(4) specified as parameters. Thus, in this example, PAR(2)-PAR(4) are overspecified. Note that PAR(1) must appear first in the ICP list; the other parameters cannot be used as true continuation parameters.