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Reliability and Accuracy of ODE Systems Solution for Modeling Environment of Heterogeneous Dynamic Systems PA10  

 Zhuk D.M.
 Kozhevnikov D.Yu.
 Manichev V.B.
Date of publication

 For solving some problems of simulation heterogeneous dynamic systems, it is necessary to use interdisciplinary or multiphysics analysis at the concentrated and distributed level of simulation (simulation of MEMS, for example). Such approach will correspond to requirements of reliability and adequacy of simulator, even at very complex products design. Needs for precision simulation dynamic systems with ill-conditioned mathematical models (with stiff and super-stiff ODE set) are increased now continuously. There are many challenges of mathematical simulation in the time domain on the basis of a solution the stiff ODE sets: in chemistry (for example, problems of a chemical kinetics), in physics (problems of mechanics, an isotope kinetics, laser technics, etc.), in microelectronics and nanoelectronics, in CAE systems. It is increased importance of adequate and precision simulation of heterogeneous dynamic systems. Time-domain simulation and analysis of electronic circuits (by Intel and our firms) is now realized by programs using solvers ODE of SPICE simulator. In EDA software of the foreign companies the basic attention now is given the user-friendly interface and convenience of using the programs. However with increase in the complexity of solved problems there is a necessity of mathematical simulation of wave effects and solutions of the super-rigid ODE sets. EDA software mentioned above companies do not solve these problems now. The basic weakness of known programs for numerical simulation of dynamic systems (for example, MATLAB_SIMULINK) consists in deriving incorrect outcome for numerical simulation of dynamic systems at the low set requirements to a mathematical accuracy (parameter - eps) to integration of corresponding ODE set as model of dynamic system (by default eps=0.001 in MATLAB-SIMULINK). Low requirements to a mathematical accuracy for a solution of mathematical models of dynamic systems result from a low measurement accuracy of initial interior parameters of dynamic systems and accordingly numerical values of different factors, as a rule, and it is necessary to consider also a technological variety of these parameters and aging of modelled products. To disadvantages of known programs for simulation of dynamic systems we can add also its orientation for mathematicians-programmers and the design engineers of the top skills knowing mathematical English language (for example, MATLAB_SIMULINK is not localized). Development of software product PA10 (Program for Analysis, version 10) is directed on elimination of these disadvantages. Problems of reliable and accurate simulation of heterogeneous dynamic systems and objects with program PA10, surpassing similar foreign software products, are considered in this paper. Base function of PA10 is an reliable and accurate simulation and an engineering time-domain analysis of systems and objects for designing products of microelectronics, nanoelectronics and, in the main, mechatronics (MEMS). Experience of development of mathematical kernel PA10 - program solver the ODE set manzhuk is considered. This solver surpasses in reliability and accuracy of calculations corresponding solvers in a package of mathematical programs MATLAB and furthermore surpass solvers ODE of SPICE simulator (Gear and Trapezoid methods).
 Electronic Design Automation (EDA), simulation, Computer Aided Engineering (CAE), dynamic systems, Ordinary Differential Equations (ODE), Differential Algebraic Equations (DAE).
Library reference
 Zhuk D.M., Kozhevnikov D.Yu., Manichev V.B. Reliability and Accuracy of ODE Systems Solution for Modeling Environment of Heterogeneous Dynamic Systems PA10 // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2018. Issue 1. P. 97-102.
URL of paper

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