I'm solving stiff ODE systems, like
y' = My + f
where M is a large constant matrix and f occasionally changes.
I know that explicit (forward) Euler, RK4 and other usual explicit methods are rarely used to solve these problems because very tiny timesteps are required to avoid instability. I know that implicit methods usually have no such problems.
However, now I would like to know that are there stable (absolutely stable?) explicit methods at all? I'm interested in them even if they are not very accurate.
Hi, some explicit codes exist as ROCK2 and ROCK4 developped by Ernst Hairer:
http://www.unige.ch/~hairer/software.html
Another approach would be to try to compute the expenential of matrix M as your system is linear.
There is an entire family of exponential integrators. Those methods are typically explicit and treat the linear part of your ODE exactly. Best place to start https://na.math.kit.edu/download/papers/acta-final.pdf
In principle at least, you may always use an explicit numerical method to solve stiff systems of ordinary differential equations. The great problem is that you must be prepared to use a very small time-stepsize if your problem is really very stiff.
Hi,
I agree with Thomas. For parallel computing of such differential systems, have a look to the PARAEXP algorithm
- Badges
- Science topic
- Similar topics
- Mathematics
- Algebra
- Matrix