Conference rusure::math

1128.0. "General Numerical Integrator/Simulator" by COMPLX::LUKSIC () Fri Sep 22 1989 17:00

         General Numerical Integrator Software.....

         I have recently completed a home grown numerical integrator
         called GENUS (GEneral NUmerical Simulator). GENUS is suited
         for a large class of deterministic continuous time dynamic
         systems including systems with hysteresis, discontinuities
         in derivatives, finite time delays and Dirac delta function.
         The package is written in FORTRAN, it is very compact, fast
         and portable. It produces numerical and graphical outputs
         which configure during execution, and thus it provides an
         environment for interactive simulation and parametric
         analysis.  Version 1.0, introduced here, is still very
         simple in terms of user interface capabilities. It is
         intended primarily to generate interest among users and to
         provide the first step in gaining the experience in numerical
         simulation of nonstandard dynamical events. The software
         support of GENUS is expected to become an ongoing process
         reflecting growing users' needs.
         
         Simulating the types of dynamical problems listed above is not
         simple. For this reason, I have prepared a User's Manual that
         can be obtained from

            Mladen Luksic
            Mechanical CAD and Engineering
            DEC, Colorado Springs
            CXO1-1/Q13
            DTN: 522-3592
            E-mail: COMPLX::LUKSIC

         The manual describes in detail all the functions of GENUS, it
         provides basic theoretical background and relevant references,
         and introduces six completely worked out problems that
         illustrate applications in the areas of

            o  solving linear ODE systems
            
            o  solving systems of nonlinear ODE's
               (example with calculating a limit cycle)
               
            o  solving an ODE over discontinuous vector fields,
               i.e., an ODE with multivalued right hand side
               (example with the motion of bouncing elastic ball)
               
            o  solving systems with multivalued states
               (example with the position servomechanism with
               hysteretic controller)

            o  solving systems with discrete components
               (example with sampled control system)

            o  solving time delay equations
               (example with calculating blood cell density and
               investigation of the related chaos)            

         The program is also capable of solving delay equations with
         state dependent delays and all combinations of the above
         categories. Also, the selection of numerical algorithms
         allows for integration of stiff problems.

         By its numerical capabilities, GENUS is comparable with
         similar commercial software (except for the size of problems,
         but this was purposely kept small in the experimantal phase).
         What gives it an advantage in comparison with ACSL (a well
         known continuous simulation language capable of dealing with
         discontinuities) is that in GENUS, discontinuities are dealt
         with via the system of switch functions and the mechanism
         called differential automaton. This makes the switching logic
         transparent to the user and eliminates the cumbersome scheduling
         of events (as it is done in ACSL). The choice of integration step
         size is independent of the sampling rate for systems with discrete
         components. This was found very useful in continuous-dicrete
         type simulations.

         In closing, GENUS is in essence a general mathematical software
         tool and I would be very interested to see to what kind of
         problems the users are applying it. If you find this interesting,
         please send me a message requesting a copy of the manual. The
         location of the software is there. Also, the software will be
         soon installed in the software tools clearing house catalog.

         Thanks.
         Mladen Luksic