A.V. Kosteltsev, Abstract etc requested June 28 Operating Modeling Environment on Multi-syntax Language Base New way of constructing Environments for solution the ordinary differential equations (ODE), recurrence, analog machine scheme, etc. are considered. Proposed the new (object oriented) struct of algorithmic (computer) model (computer object file format), that support: the different forms of mathematic models (ODE, recurrence, analog machine scheme, etc.), transformation (for example, ODE system to computer model, analog machine scheme to ODE system, etc.). New multi-syntax language that support the new object file format and different forms of mathematical models (which can write in the natural mathematic languages or different graphic forms (analog machine schemes, for example)). In the part of technology and mathematics support I'm considered: * The fundamental questions of the new - dynamic theory of errors of numerical methods of discretization of ordinary differential equations (ODE). * Terms of dynamic errors, dynamic characteristics, areas of dynamic correlation of numerical methods of discretization; sources are shown and character of disturbance of structure of fundamental matrix (system of solutions) of ODE system (mathematical model) at its transformation to algorithmic (computer) model. * Characteristic of the new way of constructing and new methods of ODE discretization. Its advantages from existing ways of constructing and methods of ODE discretization are considered in details from the point of view of dynamic theory of errors.