SUMMARY
Numerical solution methods of the main forms of differential equations for mathematical modeling of single-domain and multidomain dynamic systems in universal mathematical processors, in computer-aided design and engineering programs (CAS, CAD and CAE, respectively),were investigated in this work. The contradictions between the performance of numerical integration algorithms (accuracy, stability, economical) and the ways of their optimal matching when configuring the parameters of simulation have been analyzed. The methods, which most commonly used in solvers, can be combined into three groups: based on the Runge-Kutta algorithm, backward differentiation formulas and complex algorithms; for each of the group the adequate fields of application have been given. The factors of modeling stage (features of DS mathematical model, including structural singularity and stiffness), which have the most influence at the quality indicators (criteria) of thesimulation process (the adequacy, accuracy, cost-effectiveness) have been determined. Features of mathematical model, including structuralsingularity and stiffness, have been determined as the factors of modeling stage, which have the most influence at the quality indicators(criteria) of the simulation process (the adequacy, accuracy, cost-effectiveness). Recommendations for prevention of algorithmic failures during simulation of structurally singular systems, which presented as high-index DAE, are given. By the results of test circuit modeling, the optimal algorithm for robust simulation of dynamic systems with varying degrees of stiffness has been defined. The universal procedure of choosing the optimal algorithm of simulation, which takes into account the features of the models, has been designed. The recommendations for choosing of solver and related software for the simulation of causal and a-causal models of DS have been presented in this paper.