Path: news.mathworks.com!newsfeed-00.mathworks.com!nlpi057.nbdc.sbc.com!prodigy.net!news.glorb.com!postnews.google.com!d38g2000prn.googlegroups.com!not-for-mail
From: Peter <petersamsimon2@hotmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: symbolic computation
Date: Fri, 8 May 2009 15:41:01 -0700 (PDT)
Organization: http://groups.google.com
Lines: 35
Message-ID: <80cd7c70-2c48-4035-bb89-a154702eb83d@d38g2000prn.googlegroups.com>
References: <gu1vfk$km4$1@fred.mathworks.com>
NNTP-Posting-Host: 173.51.90.82
Mime-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable
X-Trace: posting.google.com 1241822461 9253 127.0.0.1 (8 May 2009 22:41:01 GMT)
X-Complaints-To: groups-abuse@google.com
NNTP-Posting-Date: Fri, 8 May 2009 22:41:01 +0000 (UTC)
Complaints-To: groups-abuse@google.com
Injection-Info: d38g2000prn.googlegroups.com; posting-host=173.51.90.82; 
	posting-account=SC1WwgkAAABiObOlxxQD3J1U2fKBEJiV
User-Agent: G2/1.0
X-HTTP-UserAgent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.9.0.10) 
	Gecko/2009042316 Firefox/3.0.10 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe)
Xref: news.mathworks.com comp.soft-sys.matlab:538576


On May 8, 12:00 pm, "devi " <rama...@gmail.com> wrote:
> Hello,
>
> I have an equation
> y = b*sech(b*acosh(1/x))*tanh(b*acosh(1/x))/(sqrt((1/x)-1)*sqrt(1+(1/x)=
)*(x^2));
>
> where b varies from 2 to 101,as b = M+1 ; M varies from 1 : 100
> x = 1.001:0.001:1.01
>
> The problem is I am simulating a chain network with M routers.For M =1 =
and 2 that is b = 2 and 3 the analytical and simulated results are almost=
 concordant with 4 and 9 respectively which are the limits.But when I incre=
ase the b values they tend to hit numerical stability issues and lose accur=
acy.
>
> I need help to compute the limits analytically using symbolic computation=
 or maple
>
> Thanks
> devi

The following power series in the variable dx = x - 1 should provide
sufficient accuracy (about 6 to 8 significant digits) for your desired
range 0.001 <= dx <= 0.01

    b^2 + (5*b*(-b + b^3)*dx)/3. +
       (b*(64*b - 125*b^3 + 61*b^5)*dx^2)/
        30. + (b*(-312*b + 889*b^3 - 854*b^5 +
            277*b^7)*dx^3)/126. +
       (b*(62136*b - 229000*b^3 + 324093*b^5 -
            207750*b^7 + 50521*b^9)*dx^4)/
        22680

--Peter