Path: news.mathworks.com!not-for-mail
From: <HIDDEN>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Solving Implicit Integral
Date: Fri, 5 Jul 2013 06:59:09 +0000 (UTC)
Organization: The MathWorks, Inc.
Lines: 70
Message-ID: <kr5qrt$orp$1@newscl01ah.mathworks.com>
References: <kr1onj$eql$1@newscl01ah.mathworks.com> <kr3513$plo$1@newscl01ah.mathworks.com> <kr4epu$n7i$1@newscl01ah.mathworks.com> <kr5pim$m7r$1@newscl01ah.mathworks.com>
Reply-To: <HIDDEN>
NNTP-Posting-Host: www-00-blr.mathworks.com
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
X-Trace: newscl01ah.mathworks.com 1373007549 25465 172.30.248.45 (5 Jul 2013 06:59:09 GMT)
X-Complaints-To: news@mathworks.com
NNTP-Posting-Date: Fri, 5 Jul 2013 06:59:09 +0000 (UTC)
X-Newsreader: MATLAB Central Newsreader 3799640
Xref: news.mathworks.com comp.soft-sys.matlab:798811

"Torsten" wrote in message <kr5pim$m7r$1@newscl01ah.mathworks.com>...
> "Mayur" wrote in message <kr4epu$n7i$1@newscl01ah.mathworks.com>...
> > Hi Torsten
> > 
> > I guess I made a slight error in writing up the equation.
> > The integral is raised to power (negative) 1
> > 
> > Maybe this was not clear in my original post.
> > 
> > The right equation looks like:
> > 
> > U(t) = C^-1
> > 
> > where C = integral(0-1) [dz/tanh(A*z + arctanh(1-A*y(t)))]
> > 
> > Please let me know how to go about solving it.
> > 
> > Thanks
> > Mayur
> > 
> > "Torsten" wrote in message <kr3513$plo$1@newscl01ah.mathworks.com>...
> > > "Mayur" wrote in message <kr1onj$eql$1@newscl01ah.mathworks.com>...
> > > > Hi
> > > > 
> > > > I want to solve the following equation using MATLAB but do not know or understand how to do it.
> > > > 
> > > > I would really appreaciate your help on this.
> > > > 
> > > > The equation is :
> > > > 
> > > > U(t) = integral(0-1) [dz/tanh(A*z + arctanh(1-A*y(t)))]^-1
> > > > 
> > > > where y(t) = integral (0-t) U(t)dt and A is a constant
> > > > 
> > > > y(0)=0
> > > > 
> > > > or same can be written as :
> > > > 
> > > > dy/dt = integral(0-1) [dz/tanh(A*z + arctanh(1-A*y(t)))]^-1
> > > > 
> > > > Please let me know if someone can help me with this. I am just not sure how to go about it.
> > > > 
> > > > Thanks
> > > 
> > > I don't understand what you mean by
> > > [dz/tanh(A*z + arctanh(1-A*y(t)))]^-1.
> > > Do you want to take "dz" in the denominator ? 
> > > 
> > > Best wishes
> > > Torsten.
> 
> In this case, you have a simple differential equation of the form
> dy/dt= 1/integral(0-1) [dz/tanh(A*z + arctanh(1-A*y(t)))]
> with initial condition y(0)=0.
> Use ODE45 which solves equations of the form
> dy/dt=f(t,y).
> In the function routine where you have to supply f(t,y), call MATLAB's 
> quad function to evaluate the integral for the y-value supplied by ODE45.
> 
> Best wishes
> Torsten.
>  

Or even simpler (because the integral can be evaluated analytically):
dy/dt = A/(log(sinh(A+arctanh(a-A*y)))-log(sinh(arctanh(a-A*y))))
with initial condition 
y(0)=0.

Best wishes
Torsten.