No abstract

Known mathematical packages, MATLAB, Maple, Mathematica, MathCAD and others may get wrong, often plausible, the result of numerical solution of ODE systems with low, given by default, the requirements for mathematical accuracy of the results of the numerical solution of ODE systems. Since ODE system parameters obtained usually experimental, with a low mathematical precision, so the requirements for the precision of the results of mathematical solutions of ODE systems is low (for example, in MATLAB package required precision is 0.001). The article offers a basic set of tests to assess the range of applicability of the relevant solvers. The basic set of test problems for ODE solvers systems include linear ODE systems with the known analytic solution and nonlinear systems with known graphics solution. Presented comparative results of solutions for proposed problems using MATLAB solvers and manzhuk program from a library of standard mathematical programs SADEL (Sets of Algebraic and Differential Equations solvers Library), which has been designed for reliable and accurate solving of systems of linear algebraic equations (LAE) and ODE systems. The results can be used in mathematical modeling of dynamic systems described by ODE systems.

In the manual classical numerical methods are considered and algorithms for the decision of systems of the ordinary differential equations (ODE), nonlinear and linear algebraic equations (NAU and LAU), and also ways of ensuring reliability and demanded accuracy of results of the decision. Ideas, which still not are stated are reflected in textbooks on calculus mathematics, namely: decision systems the ODE without reduction to a normal form of Cauchy resolved rather derivative, and refusal from any numerical an equivalent - nykh of transformations of the initial equations of mathematical models and is- the hodnykh of data because such transformations can change properties of models at a variation of coefficients in corresponding urav- neniyakh. It is intended for students, graduate students and teachers of higher education institutions in the direction of preparation "Informatics and computer facilities". The grant will also be useful for engineers and scientists on the corresponding specialties.