The Questionnaire

1.

Generalities.

(a)

Which are the Research and Development activities of your enterprise?. Please include a short description of them.

(b)

Does your enterprise deal with practical problems of a mathematical character by using Scientific Computing techniques?. Describe such problems briefly.

(c)

Which kind of mathematical software is used in your enterprise?. Classify it according its character: numeric, symbolic, statistics, CAD/CAM, etc.

(d)

For your purposes, are the functionalities of the used mathematical software enough or you are obligated to extend them in order to solve your problems?. If the answer is no, please include a short description of one or several examples of such situation.

2.

The generation of the equations: synthesis of the mathematical model.

(a)

Has your staff the responsibility of generating the mathematical model corresponding to the considered real-world problem?. If the answer is no, please include a short description of how the mathematical model is provided.

(b)

If the equations, inside the mathematical model and coming from the real-world problem, to consider are very difficult to solve or have a very complicated (or not useful) solution with the available techniques, how do you proceed?. Do you try to generate new simpler mathematical model by using a less accurate approximation to the real-world problem or do you contact with some expertise center?. If possible, please provide some example of the previous situations.

(c)

Do you need to perform parameter estimation with the equations inside the mathematical model?. In other words, do the equations to solve contain parameters to fix in order the solution verifies some restrictions?. If possible, please provide some example of such situations.

3.

About the equations inside the mathematical model.

(a)

Which is the kind of equations your staff has to investigate/solve/manage?. The following items can be used as a first choice:

• Differential Equations: Ordinary/Partial.
• Integral Equations: Uni/Multidimensional.
• Non-[Differential/Integral] Equations: Linear/Algebraic/Non-Algebraic.
• Others (please specify).

Please do indicate in your answer which is the number of equations, unknowns and parameters appearing in such equations.

(b)

The numbers/coefficients appearing in the equations, are they known exactly or approximately?, do they come from experimental data?. A concrete example could be very useful.

4.

About the solving of nonlinear equations.

(a)

If a nonlinear system of equations (in one or several unknowns) arises from the considered real-world problem you are dealing with, which of the following problems need to be treated?

• The existence of a solution with complex or real coordinates.
• The computation of an approximation for one (all) real (or complex) solution.
• The existence of a finite number of complex (real) solutions.
• The same problems than before but the solutions searched inside a prescribed region in ${\rm C\kern -4.6pt \vrule height 6.8pt width 0.3pt depth -0.5pt}\hskip4pt^n$ or ${\rm I\kern -2.2pt R\hskip 1pt}^n$.

(b)

If a nonlinear system of equations (in one or several unknowns) containing parameters arises from the considered real-world problem you are dealing with, do you need to describe the properties of the solution depending on the values of the parameters?.

5.

About the solutions.

(a)

Do you need to solve the equations inside the mathematical model once or do they need to be solved (by the corresponding method) many times during the production process?. In the second case please indicate which maximum real time you can accept in solving your equations?.

(b)

Does your staff perform simulation of the production process involving the considered equations before using the obtained solutions?. If the answer is yes, please provide some example indicating how such simulation is done?.