Solving difference equation with its initial conditions

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!

[John D'Errico]

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.

[Walter Roberson]

I would call this a recurrence equation, not a difference equation.

Answer 1

[Jan]

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).

[Ben Le]

Thank you so much, Jan!!!!

Answer 2

[Sindhuja Parimalarangan]

This link discusses solving recurrence equations using MATLAB. The discrete solution for "y" can be plotted using the stem function.