The discussion centers on the relationship between convergence and asymptotic behavior in the context of ordinary differential equations (ODEs) and partial differential equations (PDEs). Participants explore whether convergence of solutions implies an asymptotic relation, particularly when using methods like Adomian decomposition.
Participants express differing views on whether convergence implies asymptotic relations, with no consensus reached on the matter. Some participants agree with the notion that convergence suggests an asymptotic limit, while others raise questions about exceptions and the relationship between different solution methods.
Participants have not fully defined the terms "convergence" and "asymptotic" in this context, and the discussion lacks resolution on the conditions under which convergence might not imply asymptotic behavior.
dacruick said:well are you talking about the convergence of f(x) as x goes from 0 to infinity?
If it converges, that means that there is a value that f(x) cannot exceed. That sounds like an asymptote to me.
I am by no means an expert in this kind of thing, your statement just seemed right to me.
someone else may be able to help you more thoroughly.