stem-plot difference of equations

2013 12 16
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更新时间：2013 12 31
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Here is the question
Find numerically and stem-plot the solutions of the difference equations [1<=k<=10]
a. y(k+1) - 3*k*y(k) = 0
b. y(y+1) - k*y(k) = 1
assume that y(1)=1
not sure if i am looking at this properly but here is what i was thinking. a and b do not have the same y values after 1 since in order to get 0 for the first one y(2) needs to be 3 while for equation b y(2) needs to be 2. So solve them differently and then plot? i am not sure which would be my x and y for stem plot as well. This looks simple but its confusing me not sure if am over thinking.
Thank you for your time

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Azzi Abdelmalek
Azzi Abdelmalek 2013-12-16
Your question is not clear. Do you want to solve two different equations or one system of two equations?
Tony
Tony 2013-12-16
that is the main question sorry if it was not but i am not sure if its suppose to be answered separate or together
Walter Roberson
Walter Roberson 2013-12-24
Are you sure that (b) should have y(y+1) on the left side, and not y(k+1) ??

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 采纳的回答

Walter Roberson
Walter Roberson 2013-12-16

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Once you have the set of values x1 with y1, and x2 with y2, you can use interp1() to interpolate each set of data over a common set of times; then you can stem().
For example,
y1_interp = interp1(x1, y1, 1:10)
y2_interp = interp1(x2, y2, 1:10)
plot(1:10, y1_interp, 1:10, y2_interp)

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Walter Roberson
Walter Roberson 2013-12-24
Write your equations as
ya(k+1) - 3*k*ya(k) = 0
yb(k+1) - k*yb(k) = 1
Then solve both equations against k = 1 to 10, producing ya and yb. Then
stem(1:10, ya)
and
stem(1:10, yb)
The question does not ask you to plot them on the same figure and does not ask you to calculate any relationship between the two. (The question as shown also does not ask you to do anything with the stem plots other than to create them.)
Tony
Tony 2013-12-30
编辑：Tony 2013-12-30
thank you sorry for the double post i was not sure if comments would get pushed up.
Last thing is just a coding error that i am not sure how to fix. for ya i get
ya =
1.0e+011 *
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0026 0.0714 2.1428
if i were to type ya(1) for example i would get 1 ya(2) 3 and so on but i get this when checking the values in the array. I do not get this error for yb
ya= zeros(size(11));
yb= zeros(size(11));
ya(1)=1;
yb(1)=1;
for k = 1:10;
ya(k+1) = (3)*(k)*ya(k)
yb(k+1) = k*yb(k)+ 1
end
figure, stem(1:11,ya), hold on,stem(1:11,yb)
Tony
Tony 2013-12-31
编辑：Tony 2013-12-31
edit actually doesn't seem to display properly with stem
second edit - its good thank you happy holiday
Walter Roberson
Walter Roberson 2013-12-31
At the command line give the command
format long g

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更多回答（1 个）

Youssef Khmou
Youssef Khmou 2013-12-24

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Tony, try this iterative method :
y1=zeros(10,1);
y2=zeros(10,1);
y1(1)=1;y2(1)=1; % initial conditions
for t=1:9
y1(t+1)=3*t*y1(t);
y2(t+1)=1+t*y2(t);
end
k=1:10;
figure, stem(k,y1), hold on,stem(k,y2,'r')

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