MaplePrimes - answers and comments on Question, Once again an Asymptotic series problem

guess, that can not work

Axel Vogt — Sat, 02 Jul 2011 18:15:56 Z

# using the notations in your sheet

Digits:=15;
combine(((subs(S0=S01,parvals,A0))),exp):
v:=convert(%, rational);

eval(v, l=0) indicates there is a division by l

series(v, l=0, 1);

This gives fct(R3)/l + terms of higher orders

But something like R/a does not give a reasonable result
for asympt(%, a)

Guess you need to work with v*l ...

PS: you should avoid variables like l (lower case L)
they are easily mixed up with the constant 1 (=2/2)

some experiment / plot

Axel Vogt — Sun, 03 Jul 2011 12:52:04 Z

Here some animated plot, it seems that for increasing lambda (=your lower case L)
there may be no solution for negativ R3 - could that be?

Re: some explanation of a few points

kh2n — Sun, 03 Jul 2011 23:14:45 Z

1. "By plotting it is 'obvious', that for r=0 this is always negative (so r
must decrease to have a chance to fullfill F=0."

The above point you mentioned should be understood as

when R3=r=0, this means that the gravity factor is ignored, so it is now

 irrelavant that whether liquid is above vapour or vapour is above liquid.

 Bcoz If gravity is zero then the problem, instead of a vertical through flow

becomes a  horizental flow problem. which is always stable thats why we have

sigma<0, for all l=lambda.

2. "

For lambda = 10^3 and 10^4 compute solutions for F=0 with an initial
guess of r = -2*lambda which then defines a line equation

Lin := lambda -> -1.591517842027199990210998791356366512040*lambda
                 +2.229559088349405643936812337536203057778

This means that for large l=lambda the system is marignally stable, i.e., sigma=0

 for large lambda. to me thats fine.

Thx

kh2n — Tue, 05 Jul 2011 00:06:13 Z

I really appreciate your help and patients. Do you use Tecplot or have any information about it?

analytical solution ?

Axel Vogt — Sat, 09 Jul 2011 11:28:48 Z

in reply to http://www.mapleprimes.com/questions/123502-Once-Again-An-Asymptotic-Series-Problem#comment123641
(because comments do not give updates to a thread ...)

Khan,

I guess you mean eq (3) in your attached pdf?

Sorry, my knowledge about DEs is too much limited for a reasonable answer,
may be others can help - but for that it would be better to open a new thread
with a specific question (this one here is becoming quite long now and usually
nobody would step in, as s/he would have to read everything before).

For checking symbolical solutions there commands in Maple like ?odetest

But best would be to start a new thread

oops

Axel Vogt — Sat, 02 Jul 2011 19:52:14 Z

I mixed up while dividing :-(

Anyway, find it attached Kopie_von_R3Infintyp.mws