After solving #19, the evaluation history of ContinuousRK is always one element shorter than the state history.
This means that at least two timesteps of delay are necessary for the correct interpolation to be given.
This is a conceptual quibble that is intrinsic in the Natural Continuous Extension method. Suppose that the system is composed of just two oscillators, with heavily asymmetrical conduction speeds that give for the delay matrix:
D = [[0, 0.1], [1.0, 0]]
and suppose dt=0.1.
Then to evolve the second oscillator from t to t+dt I need the interpolation of the first oscillator in [t, t + dt], that requires the evaluation at t to be done, that requires that the step from t to t+dt for the first oscillator is already been done.
One possible zeroth-order solution could be to abolish (selectively, maybe) the propose-then-fix strategy for the update of the network.
After solving #19, the evaluation history of
ContinuousRKis always one element shorter than the state history. This means that at least two timesteps of delay are necessary for the correct interpolation to be given.This is a conceptual quibble that is intrinsic in the Natural Continuous Extension method. Suppose that the system is composed of just two oscillators, with heavily asymmetrical conduction speeds that give for the delay matrix: D = [[0, 0.1], [1.0, 0]] and suppose dt=0.1.
Then to evolve the second oscillator from t to t+dt I need the interpolation of the first oscillator in [t, t + dt], that requires the evaluation at t to be done, that requires that the step from t to t+dt for the first oscillator is already been done.
One possible zeroth-order solution could be to abolish (selectively, maybe) the propose-then-fix strategy for the update of the network.