Section STARTWERTE

In this section, first the values of initial time and final time have to be provided by

E(1) = value of the initial time
E(2) = value of the final time

If either initial or final time are free and not fixed (see Section GENERAL of the input file) then an estimated value has to be used here.

Next the initial estimates of the control parameters have to be supplied (if there are any) by

P(i) = estimate of the value of the i-th control parameter

Then a list of the multiple shooting nodes follows where each multiple shooting node is accompanied by a list of estimates of the values of the state variables and at the multiple shooting nodes.

The list of multiple shooting nodes must have at least two entries, namely for the initial time and for the final time.

The (constant) values of the multiple shooting nodes can be provided in two different ways:

• By using the absolute value t where

  T = absolute value of the multiple shooting node

• or by using the corresponding normalized value
  (where )

  TAU = normalized value of the multiple shooting node

Example: Consider the case of a time period of . A multiple shooting node (absolute value) can now be selected either by

T = 2.0

or by the normalized value

TAU = 0.4

A list of estimates of the values of the state variables has to accompany each multiple shooting node in the form of

Y( 1) = estimated value of

Y(NY) = estimated value of
V( 1) = estimated value of

V(NV) = estimated value of

In the case of a free final time it is recommended to select multiple shooting nodes by normalized values. Then their relative position in will be constant for any value of while their absolute values will vary depending on the current value of .

Remarks:

• If the functions of the right hand side of the differential-algebraic equations are only piecewise differentiable (for example, if they are piecewise defined), it is absolutely necessary to place a multiple shooting node at such a matching point of the functions of the right hand side. Otherwise uncontrollable errors may occur in the integration method and in the computation of the gradients that will cause the method to fail.
• Please note that the first and last multiple shooting nodes always have to be equal to initial time and final time.