On the Structure of Time in Computational Semantics of a Variable-Step Solver for Hybrid Behavior Analysis

Hybrid dynamic systems combine continuous and discrete behavior. Often, computational approaches approximate behavior of an analytic solution, for example, numerical integration to approximate differential equation behavior. The accuracy and computational efficiency of the integration usually depend on the complexity of the method and its implicated approximation errors, especially when repeated over iterations. This work formally defines the computational semantics of a solver in a denotational sense so as to analyze discreteand continuous-time behavior of time-based block diagram models. A stream-based approach is used to analyze the numerical integration implemented by the solver. The resulting solver applies the principle of nonmonotonic time and so consecutive values may be computed in a temporally nonmonotonic manner. This allows shifting the evaluation points backward and forward in time. Stratification recovers a partially ordered structure in time. Solver dynamics are thus made explicit and can be studied in concert with behavior of discontinuous models parts.