### Dynamic Errors of Numerical Methods of ODE Discretization

The dynamical characteristic of the numerical method of ordinary differential equations (ODE) discretization – is the natural logarithm of its function of stability $\textbf\left\{D\right\}=\ln\rho\left(h\lambda\right)$. Dynamic characteristic is considered in three forms:

$\textbf\left\{D\right\}$ – Complex dynamic characteristic;
$\textbf\left\{D\right\}_\left\{R\right\}$ – Real dynamic characteristics;
$\textbf\left\{D\right\}_\left\{I\right\}$ – Imaginary dynamic characteristics.

The dynamic characteristic represents the transformation operator of eigenvalues of a Jacobian matrix of the initial differential mathematical model (MM) in eigenvalues of a Jacobian matrix of mathematical model (also differential) whose exact solution passes through the discrete sequence of points of the initial MM solution received by given numerical method.