Does convergence imply asymptotic relation

[chwala]

hello,
does convergence imply asymptotic relation of an ordinary differential equation?

 

[dacruick]

sounds right.

 

[chwala]

kindly expound ...are there cases where a convergent solution might not be asymptotic?
regards

 

[dacruick]

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.

 

[chwala]

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.

Hi,
well let me put the question a bit clear...my concern area is on ode and pde...my question is when you solve a pde/ode analytically and get a solution by asymptotic means does this imply that if solution exists then if using convergence of the pde/ode as an alternative method for solving the same...read adomian decomposition...does it mean convergence amounts to asymptotic and vice versa?
regards,
chwala-MSC APPLIED MATHEMATICS FINALIST,NAIROBI KENYA