Manichev

To solve problems of modeling of dynamic systems, in some cases it is necessary to use a multidiscipline analysis of dynamical systems on the level of concentrated and distributed simulation. This approach will meet the requirements of accuracy, even for highly complex products. At the same time, the complexity of designed objects increases. The growth of claims on the part of manufacturers of complex modern equipment creates new generations of engineering analysis systems. The most popular programs such as ANSYS, MSC.Nastran, NX.Nastran, COMSOL, etc. They have a high precision, but they can not be used for the simulation of complex dynamic systems in the early stages of design. In this paper, multilevel Multiphysics simulation platform based on the original ODE solver with very high complexity and reliability of been proposed. As a result, the requirements for this platform are formulated. Object-oriented approach to the creation of new models for the various components of the objects have been proposed.

The main drawback of known software products for numerical modeling of continuous dynamic systems, for example - MATLAB-SIMULINK, Maple-MapleSim, WolframSys-temModeler, OpenModelica, etc. consists in receiving incorrect, often likelihood, results of numerical modeling of continuous dynamic systems at the low set requirements to the mathematical accuracy of the numerical solution of the ODE systems modeling such systems. Application of AL-stable (A(π/2)-stable) methods for the ODE systems solution for reliable modeling of continuous dynamic systems at low requirements to the mathematical accuracy for simulation results is proved in this article. Algorithms and program realization of these methods are considered. The comparative results of the "difficult" test solution and practical tasks confirming efficiency of the developed programs are given.

In this paper the authors present a comparison of various modern solvers of stiff systems of ordinary differentsial equations with C-solvers from SADEL library developed by the authors. A set of test caseswas  prepared by the authors; is consists of 6 stiff ODE systems with known analytical or asymptotic solutions. The test results are given in the article. The authors also present the basic theoretical information about the methods used in the testing of the numerical integration of systems of ordinary differential equations and considered various options of problem statement.