exp(-x) - sinx = 0

2014 1 10
2 个回答
更新时间：2014 1 11
1 次查看（30 天）

0 个投票

hi, i'm planning to reach the root of this function:
exp(-x) - sinx = 0;
here is my code:
------------------------------
x0 = input('please enter x0 ::: ');
eps = input('please enter steps ::: ');
% eps is the step
iterator = 0;
for i=0:eps:x0
x=x+exp(-x) - sin(x);
iterator = iteratio + 1;
end
disp('root ::: '); disp(x);
disp('iterate count ::: '); disp(iterator);
------------------------------
well i can't make it work. can you help me with that?

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回答（2 个）

Mischa Kim
Mischa Kim 2014-1-10

0 个投票

Try the fzero function. Unless, of course, you would like to do it on your own.
reza
reza 2014-1-10

0 个投票

Now it's working,
x0 = input('please enter x0 ::: '); eps = input('please enter steps ::: '); iterator = 0; x=0; iterator = 0; for i=0:eps:x0 x=x+exp(-x) - sin(x); iterator = iterator + 1; end disp('root ::: '); disp(x); disp('iterate count ::: '); disp(iterator);
thanks to all.

6 个评论
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Mischa Kim
Mischa Kim 2014-1-11
Just want to make sure you are getting the results you are looking for. What root-finding method are you using? For those kind of problems I'd recommend Newton-Raphson (if you prefer coding yourself). Also note that this function has an infinte number of roots. Here are two of them:
r1 = fzero(@(x) exp(-x) - sin(x), 0)
r1 =
0.5885
r2 = fzero(@(x) exp(-x) - sin(x), 2)
r2 =
3.0964
Youssef Khmou
Youssef Khmou 2014-1-11
that is good remark, so how, for example, we find the period of the solutions using only fzero as you illustrated above?
Mischa Kim
Mischa Kim 2014-1-11
Not sure I understand what you are asking. If it's about finding more than just a handful of roots, you could use a for -loop. For positive x-values the function (and therefore the roots) is dominated by the sine-term, which allows you to get pretty accurate starting values for the searches.
Youssef Khmou
Youssef Khmou 2014-1-11
编辑：Youssef Khmou 2014-1-11
yes, here is the result :
ct=1;
for n=0:100
F(ct)=fzero(@(x) exp(-x)-sin(x),n);
ct=ct+1;
end
stem(F)
can we conclude that there re 4 solutions?
Mischa Kim
Mischa Kim 2014-1-11
By solutions you mean roots? Here is the function plot:
Youssef Khmou
Youssef Khmou 2014-1-11
编辑：Youssef Khmou 2014-1-11
alright, infinite number of solutions with period of ~3.1
thanks

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提问:

reza
reza
2014-1-10

编辑：

Youssef Khmou
Youssef Khmou
2014-1-11

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