- #1

Kortirion

- 8

- 0

As I'm pretty green I was reading this page http://reference.wolfram.com/mathematica/tutorial/NDSolvePlugIns.cdf and its section on the Adams method. I don't have the skill to make a more efficient algorithm than the one prescribed in there, so I just copy-pasted all the necessary code into my Mathematica notebook. With this I could use it within NDSolve by adding "Method -> AdamsBM".

It works, rolls ok with my system and when I take the difference in solutions of the "regular" unspecified method of NDSolve with this AdamsBM method, there's some difference depending on the working precision I tell AdamsBM to work in. So they really are different and this "working precision" plays some role.

**What I'm really interested in**at this point is the error of this numerical AdamsBM method. So in short - how do I calculate this error? How do I know that this AdamsBM is better than the other for example? I've read around a bit on the internet but couldn't find anything that fits my level of understanding regarding this subject.

Actually I have some other questions as well, but they are tied in with this question about the error of the method at hand. I think it's a good starting point.

Any advice or help is most appreciated, whether it's about the Adams method in general or any of its specifics. Thanks in advance!