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 Post subject: STODOLA-VIANELLO itteration problemPosted: Mon, 26 Dec 2011 08:42:54 UTC
 S.O.S. Newbie

Joined: Mon, 26 Dec 2011 07:35:15 UTC
Posts: 3
I don't know where to post this calculation problem in this forum,So I m posting it here.
I hope you people would have a look at it and would help me to understand it.

The following problem is part of the Stodola-Vianello iteration method.After doing some calculation the following three equations are found,from which four variables are to be calculated.

The above image shows the calculation which has been carried out on above 3 equations ( these three equations has got 4 unknowns ,they are Wn^2 ,a1n,a2n and a3n )

In order to simplify we can represent the above three equation as follows

x*p = (95049*x) - (47524.5* y)
y*p = - (47524.5*x) + (95049*y) - (47524.5*z)
z*p = - (47524.5*y ) + (47524.5*z)

where p = Wn^2
x = a1n
y = a2n
z = a3n

I have tried to solve these 3 equation but failed to get any result,infact I got struck in the middle of calculation.So I m asking you people to help me in solving this problem.

For the calculation ,the author of this example has taken "x" as 1 (i.e. a1n = 1) as assumption
and has tabulated the result ,but in table I found that all values x,y and z are assumed (at first cycle) except Wn .

If any understand this procedure or know how to do this calculation ,then please explain me.

Thanking you in advance
Regards

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 Post subject: Re: STODOLA-VIANELLO itteration problemPosted: Mon, 26 Dec 2011 08:50:30 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6009
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
Moved from Proposed Problems to Differential Equations.

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 Post subject: Re: STODOLA-VIANELLO itteration problemPosted: Mon, 26 Dec 2011 11:32:02 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6009
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
I don't know where to post this calculation problem in this forum,So I m posting it here.
I hope you people would have a look at it and would help me to understand it.

The following problem is part of the Stodola-Vianello iteration method.After doing some calculation the following three equations are found,from which four variables are to be calculated.

The above image shows the calculation which has been carried out on above 3 equations ( these three equations has got 4 unknowns ,they are Wn^2 ,a1n,a2n and a3n )

In order to simplify we can represent the above three equation as follows

x*p = (95049*x) - (47524.5* y)
y*p = - (47524.5*x) + (95049*y) - (47524.5*z)
z*p = - (47524.5*y ) + (47524.5*z)

where p = Wn^2
x = a1n
y = a2n
z = a3n

I have tried to solve these 3 equation but failed to get any result,infact I got struck in the middle of calculation.So I m asking you people to help me in solving this problem.

For the calculation ,the author of this example has taken "x" as 1 (i.e. a1n = 1) as assumption
and has tabulated the result ,but in table I found that all values x,y and z are assumed (at first cycle) except Wn .

If any understand this procedure or know how to do this calculation ,then please explain me.

Thanking you in advance
Regards

No! What you have is an iterative scheme.

and the normalisation . We use the starting condition , to iteratively find

(maybe in the last equation instead of the updated value ).

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 Post subject: Re: STODOLA-VIANELLO itteration problemPosted: Mon, 26 Dec 2011 12:38:47 UTC
 S.O.S. Newbie

Joined: Mon, 26 Dec 2011 07:35:15 UTC
Posts: 3
Thanks for the quick reply.
Yes it is iterative scheme.

Will you please tell me why and
why not any other values like 2,3,etc.Why -1.3 and 0.7
can we use any other value,will the final result change after iteration based on new values for a2n and a3n
thanks for the reply,i hope you will reply and explain me again.

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 Post subject: Re: STODOLA-VIANELLO itteration problemPosted: Mon, 26 Dec 2011 13:01:50 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6009
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
Thanks for the quick reply.
Yes it is iterative scheme.

Will you please tell me why and
why not any other values like 2,3,etc.Why -1.3 and 0.7
can we use any other value,will the final result change after iteration based on new values for a2n and a3n
thanks for the reply,i hope you will reply and explain me again.

The starting values -1.3 and 0.7 are chosen to be close to the exact solution, so that the scheme will hopefully converge to the exact solution (with prescribed tolerance) within a few iterations.

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 Post subject: Re: STODOLA-VIANELLO itteration problemPosted: Thu, 5 Jan 2012 10:45:17 UTC
 S.O.S. Newbie

Joined: Mon, 26 Dec 2011 07:35:15 UTC
Posts: 3
thanks,it was very helpful.

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