# Does convergence imply asymptotic relation

• chwala
In summary, the conversation discusses the relationship between convergence and asymptotic solutions of ordinary and partial differential equations. The participants suggest that if a solution is obtained through asymptotic means, then it may also converge. They also mention Adomian decomposition as an alternative method for solving these equations. However, there is uncertainty about whether convergence always implies asymptotic solutions and vice versa.

#### chwala

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

sounds right.

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

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.

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.

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

## 1. What is convergence?

Convergence refers to the idea that as a series of values or variables approach a certain point or value, they become increasingly closer and eventually equal to that point or value.

## 2. How does convergence relate to asymptotic relation?

Convergence implies asymptotic relation in that as a series of values or variables converge to a certain point or value, they also approach an asymptote (a line that a graph approaches but never touches).

## 3. Can convergence exist without an asymptote?

Yes, convergence can exist without an asymptote. It simply means that the series of values or variables are approaching a certain point or value, but may not necessarily reach it or have an asymptote associated with it.

## 4. Is convergence the same thing as an asymptote?

No, convergence and an asymptote are not the same thing. Convergence refers to the process of approaching a certain point or value, while an asymptote is a line that a graph approaches but never touches.

## 5. How is convergence used in science?

Convergence is commonly used in science to analyze and understand patterns and relationships between data points. It helps to determine if a series of values or variables are approaching a certain point or value, and if there is an asymptotic relation involved.