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From: Jennifer Young on 16 Jun 2010 04:20
Hi all,

I know this is a simple question, but I am not well-versed in MATLAB and just need to solve a (complicated) equation and then plot it. The equation is:

44.0526*exp(-2*k*t)=-(log(1-(A/(B*Qm-C)))+A/(B*Qm-C)+X*(A/(B*Qm-C))^2)/((A/(B*Qm-C))^(1/3)-(A/(B*Qm-C)))

where A, B, C, k and X are all constants for which I have values.

I just need to solve for Qm over a given range of t, but am not sure how to approach this because I keep receiving error messages about syms or ezplot issues for various methods I have attempted. Any help would be extremely appreciated! Thanks so much. :)

Jenn
From: Gang-Gyoo on 16 Jun 2010 07:11
Hi Jenn

If you give me the parameter values except Qm, i'll try.

Gang-Gyoo JIN


"Jennifer Young" <jnnyoung(a)gmail.com> wrote in message <hva1go$h59$1(a)fred.mathworks.com>...
> Hi all,
>
> I know this is a simple question, but I am not well-versed in MATLAB and just need to solve a (complicated) equation and then plot it. The equation is:
>
> 44.0526*exp(-2*k*t)=-(log(1-(A/(B*Qm-C)))+A/(B*Qm-C)+X*(A/(B*Qm-C))^2)/((A/(B*Qm-C))^(1/3)-(A/(B*Qm-C)))
>
> where A, B, C, k and X are all constants for which I have values.
>
> I just need to solve for Qm over a given range of t, but am not sure how to approach this because I keep receiving error messages about syms or ezplot issues for various methods I have attempted. Any help would be extremely appreciated! Thanks so much. :)
>
> Jenn
From: Gang-Gyoo on 16 Jun 2010 07:40
hi Jenn

try to tune the following program with your parameters
wish your success

Gang-Gyoo JIN

function test
x0=10; x1= 100; nmax= 70; eps= 1e-5; buf= [];
for t= 5:0.1:10
y= bisect(@fun, t, x0, x1, eps, nmax);
buf= [buf;t y];
end
plot(buf(:,1),buf(:,2))

function x= bisect(fun, t, x0, x1, eps, nmax)
x2= 0;
if x1 < x0 | fun(t,x0)*fun(t,x1) > 0
disp('Bound error in bisect');
x= 0;
return;
end
for i= 1: nmax
x2= (x0+x1)/2.0;
if abs(x2-x1) <= eps
x= x2;
return;
end
fx0= fun(t,x0);
fx2= fun(t,x2);
if fx0*fx2 < 0
x1= x2;
else
x0= x2;
end
end
disp('Completed unsuccessfully');
x= x2;

function fval= fun(t,Qm)
A= 1; B= 2; C= 0.1; X= 11;k=1;
f1= 44.0526*exp(-2*k*t)+log(1-(A/(B*Qm-C)));
f2= A/(B*Qm-C)+X*(A/(B*Qm-C))^2/(A/(B*Qm-C))^(1/3);
f3= -A/(B*Qm-C);
fval= f1+f2+f3;

%44.0526*exp(-2*k*t)=-(log(1-(A/(B*Qm-C)))+A/(B*Qm-C)+
%X*(A/(B*Qm-C))^2)/((A/(B*Qm-C))^(1/3)-(A/(B*Qm-C)))
From: Torsten Hennig on 16 Jun 2010 03:41
> Hi all,
>
> I know this is a simple question, but I am not
> well-versed in MATLAB and just need to solve a
> (complicated) equation and then plot it. The equation
> is:
>
> 44.0526*exp(-2*k*t)=-(log(1-(A/(B*Qm-C)))+A/(B*Qm-C)+X
> *(A/(B*Qm-C))^2)/((A/(B*Qm-C))^(1/3)-(A/(B*Qm-C)))
>
> where A, B, C, k and X are all constants for which I
> have values.
>
> I just need to solve for Qm over a given range of t,
> but am not sure how to approach this because I keep
> receiving error messages about syms or ezplot issues
> for various methods I have attempted. Any help would
> be extremely appreciated! Thanks so much. :)
>
> Jenn

Hi Jennifer,

I doubt that you can get a symbolic solution for Qm
in terms of the other parameters involved.
So you will have to use a numerical method.

Write your equation as
44.0526*exp(-2*k*t)-(-(log(1-(A/(B*Qm-C)))+A/(B*Qm-C)+X
*(A/(B*Qm-C))^2)/((A/(B*Qm-C))^(1/3)-(A/(B*Qm-C))))=0
and use fzero or fsolve to solve for the unknown Qm
given a value for t.

Best wishes
Torsten.
From: Torsten Hennig on 16 Jun 2010 03:59
> > Hi all,
> >
> > I know this is a simple question, but I am not
> > well-versed in MATLAB and just need to solve a
> > (complicated) equation and then plot it. The
> equation
> > is:
> >
> >
> 44.0526*exp(-2*k*t)=-(log(1-(A/(B*Qm-C)))+A/(B*Qm-C)+X
>
> > *(A/(B*Qm-C))^2)/((A/(B*Qm-C))^(1/3)-(A/(B*Qm-C)))
> >
> > where A, B, C, k and X are all constants for which
> I
> > have values.
> >
> > I just need to solve for Qm over a given range of
> t,
> > but am not sure how to approach this because I
> keep
> > receiving error messages about syms or ezplot
> issues
> > for various methods I have attempted. Any help
> would
> > be extremely appreciated! Thanks so much. :)
> >
> > Jenn
>
> Hi Jennifer,
>
> I doubt that you can get a symbolic solution for Qm
> in terms of the other parameters involved.
> So you will have to use a numerical method.
>
> Write your equation as
> 44.0526*exp(-2*k*t)-(-(log(1-(A/(B*Qm-C)))+A/(B*Qm-C)+
> X
> *(A/(B*Qm-C))^2)/((A/(B*Qm-C))^(1/3)-(A/(B*Qm-C))))=0
> and use fzero or fsolve to solve for the unknown Qm
> given a value for t.
>
> Best wishes
> Torsten.

Or go the reverse way:
Insert values for Qm and solve for t (this can be
done easily in an explicit way).
Afterwards, for the graphics, reverse the roles
of Qm and t.

Best wishes
Torsten.
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