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.

See also

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

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.

External links

• Dynamic properties and characteristics of RK-methods