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Sat, 14 Feb 2009 09:55:57 +0000
How to solve transecedental equation using matlab
http://www.mathworks.com/matlabcentral/newsreader/view_thread/244498#628251
vinneelaero@gmail.com
Hi friends.....<br>
when i was doing a vibration problem i got a equation tanh(ax)+tan<br>
(ax)=0, which is a transecedental equation....i want the roots of this<br>
equation..... could any body help me to find out the roots of this<br>
equation by using matlab

Sat, 14 Feb 2009 17:22:01 +0000
Re: How to solve transecedental equation using matlab
http://www.mathworks.com/matlabcentral/newsreader/view_thread/244498#628286
Matt Fig
You could use fzero to find the roots one at a time. This will find many at a time:<br>
<br>
<a href="http://www.mathworks.com/matlabcentral/fileexchange/6924">http://www.mathworks.com/matlabcentral/fileexchange/6924</a><br>
<br>
a = 2;<br>
f = @(x) tanh(a*x) + tan(a*x);<br>
rt = newtzero(f);<br>
xx = 20:.1:20;<br>
plot(xx,f(xx),'b',rt,f(rt),'*r');<br>
ylim([1 1])<br>
xlim([min(xx) max(xx)])<br>
<br>
<br>
<br>
<br>
<br>
cadz\U`bUYUsj_ic\sY.sczis\hcWh"U]s`aV4cWms[UVsb]UY9dshcYMAU

Sat, 14 Feb 2009 20:07:02 +0000
Re: How to solve transecedental equation using matlab
http://www.mathworks.com/matlabcentral/newsreader/view_thread/244498#628298
Roger Stafford
vinneelaero@gmail.com wrote in message <3e609bfa176d4203883a6e51a6dca80d@g1g2000pra.googlegroups.com>...<br>
> Hi friends.....<br>
> when i was doing a vibration problem i got a equation tanh(ax)+tan<br>
> (ax)=0, which is a transecedental equation....i want the roots of this<br>
> equation..... could any body help me to find out the roots of this<br>
> equation by using matlab<br>
<br>
It should be pointed out that for this particular equation there is no need to resort to matlab for roots. Ordinary calculus should suffice. It is clear that there is one root at x = 0. The derivative of the left side with respect to x is a*(sech(a*x)^2+sec(a*x)^2), which can never be zero assuming a is nonzero. This means there could never be any other root than at x=0 without violating the famous law of the mean of calculus.<br>
<br>
Roger Stafford

Sat, 14 Feb 2009 21:32:01 +0000
Re: How to solve transecedental equation using matlab
http://www.mathworks.com/matlabcentral/newsreader/view_thread/244498#628310
Matt Fig
Roger,<br>
Perhaps I missed something. <br>
We know tanh(a*x) has only one root, x = 0. But tan(a*x) has many roots because it is periodic, plotting tanh(a*x) and tan(a*x) on the same graph, we can see multiple intersection points.<br>
<br>
ezplot('tan(2*x)',[4*pi 4*pi])<br>
hold on<br>
ezplot('tanh(2*x)',[4*pi 4*pi])

Sat, 14 Feb 2009 21:33:02 +0000
Re: How to solve transecedental equation using matlab
http://www.mathworks.com/matlabcentral/newsreader/view_thread/244498#628311
Matt Fig
Roger,<br>
Perhaps I missed something. <br>
We know tanh(a*x) has only one root, x = 0. But tan(a*x) has many roots because it is periodic, plotting tanh(a*x) and tan(a*x) on the same graph, we can see multiple intersection points.<br>
<br>
ezplot('tan(2*x)',[4*pi 4*pi])<br>
hold on<br>
ezplot('tanh(2*x)',[4*pi 4*pi])

Sat, 14 Feb 2009 22:05:05 +0000
Re: How to solve transecedental equation using matlab
http://www.mathworks.com/matlabcentral/newsreader/view_thread/244498#628316
Roger Stafford
"Matt Fig" <spamanon@yahoo.com> wrote in message <gn7d8h$k2n$1@fred.mathworks.com>...<br>
>......<br>
> We know tanh(a*x) has only one root, x = 0. But tan(a*x) has many roots ......<br>
>......<br>
<br>
Yes, you caught me napping there, Matt. I was unconsciously restricting myself to the range abs(a*x) <= pi/2. There will actually be one root in each interval of width pi/abs(a) above and below that range and matlab is needed to find them. Of course there is antisymmetry here so only the positive roots need be actually computed. Unfortunately there are infinitely many of these.<br>
<br>
Roger Stafford