The basic set of test problems for ODE system solvers

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.

Research and Development of Digital Educational Products Powered by MARS Simulating Environment

“…Original software is also being developed [12][13][14]. Among the Russian modeling systems the most famous are MVTU [15], SiminTech [16,17], PA10 [18]. The software for education applications, based on component circuit method [19] and simulation system MARS [20], is discussed in this article.…”