Does first order ODE always have numerical solutions?

[CRquantum]

Thank you very much!

By any chance, do you think the Gear-Hindmarsh method may have already included in the latest DVODE solver by G.D. Byrne & S. Thompson?

Has anyone used DVODE and is it good?

Thank you very much for the message @nicholaswogan , true, strangely, the original link does not work any more. Fortunately, I have downloaded their whole website (the latest version) of dvode before. Now I pushed it to a new gitlab repo, you could download it from the link below, In the folder VODE_F90 Support Page , double click index.html, then you should see the whole original website, and you can download all the corresponding files locally. Hope that helps

Sinces GEARS seems to be an old solver, probably the later vode or DVODE already included the method.

Also, what do you think the stiff ODE solver by Hairer?
http://www.unige.ch/~hairer/software.html
Hairer has two ODE books, one for non-stiff one for stiff ODE,

Solving Ordinary Differential Equations I: Nonstiff Problems (Springer Series in...

Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic...