Runge–Kutta Methods for Dissipative and Gradient Dynamical Systems
Runge–Kutta Methods for Dissipative and Gradient Dynamical Systems
The numerical approximation of dissipative initial value problems by fixed time-stepping Runge–Kutta methods is considered and the asymptotic features of the numerical and exact solutions are compared. A general class of ordinary differential equations, for which dissipativity is induced through an inner product, is studied throughout. This class arises naturally …