An interactive system for modeling

  • I. Galligani
  • L. Moltedo
Associated Software Problems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 40)


Recently some authors have proposed to introduce a pattern recognition approach in the modeling process, especially for the study of populations of species, within a compartimental representation, in aquatic ecosystems and for the water pollution control.

In order to implement this approach on a computer, it is necessary to develop "interactive systems" which are composed by a special language for modeling, a collection of data management procedures and a collection of numerical procedures. These systems give the possibility of integrating the data base handling techniques with mathematical methods for constructing models in an interactive manner in order to take into account the analyst's appreciation and understanding of the determining features of the prototype system during the different stages of the modeling process.

In this paper, we describe the main characteristics of such an interactive system with graphical facilities designed for a minicomputer which includes different algorithms for integrating ordinary differential equations. These algorithms have been chosen after an analysis which was not only oriented to the selection of the most significant methods but also to the study of their feasibility within a procedure which gives local and global error estimations. Some "standardization" problems in the implementation of this system have been taken into account.


Interactive System Numerical Procedure Lump Parameter Model Pattern Recognition Approach Global Error Estimation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [1]
    Sage A.P., Melsa J.L.: System Identification. Academic Press, New York (1971).Google Scholar
  2. [2]
    Karplus W.J.: System Identification and Simulation. A pattern Recognition Approach. Comp. Sc. Dept. Report, Univ. of California (1971), Los Angeles.Google Scholar
  3. [3]
    Smith L.B.: An example of a pragmatic approach to portable interactive graphics. Comput. & Graphics 1 (1975), 49–53.Google Scholar
  4. [4]
    Dalle Rive L., Merli C.: FALCON-A conversational polyalgorithm for ordinary differential equation problems. Information Processing 74, North-Holland Publ. Comp., Amsterdam (1974).Google Scholar
  5. [5]
    Edsberg L.: Integration Package for Chemical Kinetics. Stiff Differential Systems (ed. R.A. Willoughby). Plenum Press, New York (1974).Google Scholar
  6. [6]
    Stetter H.J.: Local estimation of the global discretization error. SIAM J. Numer. Anal. 8 (1971), 512–523.Google Scholar
  7. [7]
    Lawson J.D.: Generalized Runge-Kutta processes for stable systems with large Lipschitz constants. SIAM J. Numer. Anal. 4 (1967), 372–380.Google Scholar
  8. [8]
    Ralston A.: Runge-Kutta methods with minimum error bounds. Math. Comput. 16 (1962), 431–437.Google Scholar
  9. [9]
    Lapidus L., Seinfeld J.H.: Numerical Solution of Ordinary Differential Equations, Academic Press, New York (1971)Google Scholar
  10. [10]
    Dahlquist G.: Stability and error bounds in the numerical integration of ordinary differential equations. The Royal Inst. of Technology n.130, Stockholm (1959).Google Scholar
  11. [11]
    Gear C.W.: Numerical Initial Value Problems in Ordinary Differential Equations. Prentice Hall, N.J. (1971).Google Scholar
  12. [12]
    Jain R.K.: Some A-stable methods for stiff ordinary differential equations. Math. Comput. 26 (1972), 71–78.Google Scholar
  13. [13]
    Hull T.E. et al.: Comparing numerical methods for ordinary differential equations. SIAM J. Numer. Anal. 9 (1972), 603–637.Google Scholar
  14. [14]
    Caruthers L.C., Bergeron R.D.: Device independent graphics, SEAS 1974 Session Report.Google Scholar
  15. [15]
    Gear C.W.: The automatic integration of ordinary differential equations. Comm. ACM 14 (1971), 176–179Google Scholar
  16. [16]
    Hull T.E.: Numerical solutions of initial value problems for ordinary differential equations. Numerical Solution of Boundary Value Problems for Ordinary Differential Equations (ed. A.K. Aziz), Academic Press, New York (1975).Google Scholar
  17. [17]
    Ortega J.M., Rheinboldt W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970).Google Scholar
  18. [18]
    Argentesi F., Di Cola G., Verheyden N.: Parameter estimation of mass transfer in compartimented aquatic ecosystems. Identification and System Parameter Estimation Part 1 (ed. P. Eykhoff), North-Holland Publ. Comp., Amsterdam (1973).Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • I. Galligani
    • 1
  • L. Moltedo
    • 1
  1. 1.Istituto per le Applicazioni del Calcolo "M. Picone, CNRRomeItaly

Personalised recommendations