The authors present a numerical technique for simulator coupling of modular dynamical systems. In general case a module of the system is presented by nonlinear state and output (systems of) equations. The state and output equations depend on the state and input vectors and on time. The global system is formed by the interconnection between the modules introduced by the coupling equations that specify how the inputs are computed from outputs.
The modeling of modules is independent of the global system structure. An important property of methods of numerical integration of the state equations of each module to ensure convergence is zero-stability (D-stability) [cf. E. Hairer, S. Nørsett and G. Wanner, Solving ordinary differential equations. I: Nonstiff problems. (Springer, Berlin) (1987; Zbl 0638.65058)]. The authors give the definition of zero-stability of the coupled integration and analyze its properties. Two methods of simulator coupling which guarantee zero-stability for a global system including algebraic loops are considered. The core of the first method is iteration (there are two variants of iterative simulator coupling: (a) iteration of the output equations and (b) iteration of the global integration step). The second method is based on introducing of addition filters in the mathematical model.
The sections of the paper are: 1. Introduction, 2. Modular description of dynamic systems, 3. Modular numerical integration, 4. Methods of simulator coupling, 5. Example, 6. Conclusion. The main steps of the authors approach are illustrated by figures.
The paper contains few misprints (e.g. on page 96 formula (4), read “(2)”, formula (5), read “(3)”).
The example of a double pendulum is considered. A detailed consideration, analytical and numerical results that illustrate the main statements of the paper on the example are given.