Solving difference equation with its initial conditions
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Hi,
Consider a difference equation:
8*y[n] - 6*y[n-1] + 2*y[n-2] = 1
with initial conditions
y[0]= 0 and y[-1]=2
How can I determine its plot y(n) in Matlab? Thank you in advance for your help!
2 Comments
John D'Errico
on 19 Feb 2017
Surely you can use a loop? Why not make an effort? You have the first two values, so a simple loop will suffice.
More importantly, you need to spend some time learning MATLAB. Read the getting started tutorials. It is apparent that you don't know how to even use indexing in MATLAB, nor how to use a for loop.
You will need to recognize that MATLAB does NOT allow zero or negative indices.
Accepted Answer
Jan
on 21 Feb 2017
Edited: Jan
on 21 Feb 2017
Resort the terms:
8*y[n] - 6*y[n-1] + 2*y[n-2] = 1
y[n] = (1 + 6*y[n-1] - 2*y[n-2]) / 8
or in Matlab:
y(n) = (1 + 6*y(n-1) - 2*y(n-2)) / 8;
Now the indices cannot start at -1, because in Matlab indices are greater than 0. This can be done by a simple translation:
y = zeros(1, 100); % Pre-allocate
y(1:2) = [2, 0];
for k = 3:100
y(k) = (1 + 6*y(k-1) - 2*y(k-2)) / 8;
end
Now you get the y[i] by y(i+2).
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