- 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 . Dynamic characteristic is considered in three forms:
- – Complex dynamic characteristic;
- – Real dynamic characteristics;
- – 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.
- Kosteltsev V.I. Dynamic properties of numerical methods of integration of systems of ordinary differential equations. – Preprint N23. – L.: LIIAN, 1986.
- Dekker K., Verver J. Stability of Runge–Kutta methods for stiff nonlinear differential equations. / trans. from engl. – M.: Mir, 1988.
First order methodsEuler method · Backward Euler · Semi-implicit Euler · Exponential Euler Second order methods Higher order methods
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