Do Convergence Solutions of ODE/PDEs Match Their Asymptotic Solutions?

[chwala]

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 mean that if solution exists then ...when using convergence as an alternative way of getting solution of the pde/ode ...read adomian decomposition...

Does it therefore mean that convergence solution of an ode/pde EQUATION = Asymptotic solution of an ode/pde EQUATION ?
regards,
chwala

 

[HallsofIvy]

It's not at all clear what you mean by "convergenced solution" or "asymptotic solution". A "solution" to a differential equation by is a function that satisfies the differential equation. How you got that function does not matter.

 

[chwala]

It's not at all clear what you mean by "convergenced solution" or "asymptotic solution". A "solution" to a differential equation by is a function that satisfies the differential equation. How you got that function does not matter.

Hallsoflvy,
thanks for your quick response...i am reffering to adomian decomposition method of solving linear and non linear partial and ordinary differential equation...where the author has emphasised on the convergence of the equations(pde & ode) as a condition in the working of the problemto a specific solution that may also be solved by other means i.e thro..analytical means or numerical means e.g runge kutta ,finite difference method and so on...now on the analytic method..one may get a solution that is asymptotic in nature.

Are the two methods I.E asymptotic and convergence complementing each other..kindly look at adomian decomposition in general as you make a conclusion,
regards,
chwala

 

[chwala]

Hallsoflvy,
thanks for your quick response...i am reffering to adomian decomposition method of solving linear and non linear partial and ordinary differential equation...where the author has emphasised on the convergence of the equations(pde & ode) as a condition in the working of the problemto a specific solution that may also be solved by other means i.e thro..analytical means or numerical means e.g runge kutta ,finite difference method and so on...now on the analytic method..one may get a solution that is asymptotic in nature.

Are the two methods I.E asymptotic and convergence complementing each other..kindly look at adomian decomposition in general as you make a conclusion,
regards,
chwala

i have researched on the two- asymptotic and convergence...a differential equation can be solved analytically by use of asymptotic method...once solved and a solution found ...the same solution can be tested for convergence or divergence as a property of solution...thank you all...on the other hand convergence can be used as a method in solving differential equation particularly of second order...by use of what we call adomian decomposition...where a solution is found and in most cases the solutions are convergent in nature.
regards