I have a discrete time system of the form $$\mathbf{y}[k+1] = f(\mathbf{y}[k])$$ that I want to step until a specific condition $$g(\mathbf{y}[K]) < 0,$$ usually $K\sim1000$.

Evaluations of $f$ are expensive, but $f$ is pretty well-behaved: for example there are lots of cases where $f$ is constant, or close to linear in $k$, for $50 < k < K-50$. In that region I could easily extrapolate over several steps to avoid having to calculate $f$ at each step, but close to the ends I need to be more careful.

So my question is: are there any adaptive stepping algorithms for cases like this, which tell me how many steps I can extrapolate over? e.g. a discrete version of Dormand-Price?

New contributor
Tino Sulzer is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.

Your Answer

Tino Sulzer is a new contributor. Be nice, and check out our Code of Conduct.

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.