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 $\textbf{D}=\ln\rho(h\lambda)$. Dynamic characteristic is considered in three forms:

$\textbf{D}$ – Complex dynamic characteristic;

$\textbf{D}_{R}$ – Real dynamic characteristics;

$\textbf{D}_{I}$ – 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.

References

1. Kosteltsev V.I. Dynamic properties of numerical methods of integration of systems of ordinary differential equations. – Preprint N23. – L.: LIIAN, 1986.
2. Dekker K., Verver J. Stability of Runge–Kutta methods for stiff nonlinear differential equations. / trans. from engl. – M.: Mir, 1988.

See also

• Euler's method
• Runge–Kutta methods
• Runge–Kutta method (SDE)
• List of Runge–Kutta methods

External links

• Dynamic properties and characteristics of RK-methods