Is MATLAB solving Difference equations ?

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Hi
I am wondering whether MATLAB is able to solve DIFFERENCE (recursive) equations, not differential ones. For example, difference equations as those frequently encountered in Economics.
Is a there a proxy method to do it?
Thanks

Accepted Answer

Samir A. Farag
Samir A. Farag on 24 Oct 2014
Edited: Walter Roberson on 22 Feb 2017
Let us solve this difference equation:
c(k+2)-1.3c(k+1)+0.4c(k)=r(k) % c(0)=0 and c(1)=0.
Where, c(k) represents the system output and r(k) the system input and both of them in discrete.
This example is solved by three MATLAB codes:
----------------
1-Solving the difference equation by obtaining the inverse z-transform of c(z) after substituting by the input at which you solve it and initial conditions:
delta=[1 zeros(1 , 5)]; num=[0 0 1]; den=conv([1 -1.3 0.4],[1 -1]);
c=filter(num , den , delta)
----------------------------
2- Solving the difference equation using filter function:
% c(k+2)-1.3c(k+1)+0.4c(k)=r(k) % c(0)=0 and c(1)=0.
num=[0 0 1]; den=[1 -1.3 0.4];
r=[1 ones(1,5)]; % input signal, in this case is unit step signal
c=filter(num , den , r)
---------
3-Solving the difference equation – at step input – using dstep function which used in case of zero initial condition:
k=0:5; num=[0 0 1]; den=[1 -1.3 0.4]; c=dstep(num,den, length(k))
---------------
When you run the three codes, you will find that all give the same results. Also, I solved this problem by hand and the results match that calculated by MATLAB. Let me know if you need it.
Mr. Eng. Samir A. Farag, Teaching Assistant at H.T.I, Egypt.

More Answers (1)

Matt J
Matt J on 6 Jul 2013
There is the filter() command. If you were looking for a symbolic solution, you might find something in the Symbolic Math Toolbox.
  3 Comments
msh
msh on 6 Jul 2013
I see your point, i will try to see whether fits my purpose. Thank you
Samir A. Farag
Samir A. Farag on 23 Oct 2014
Edited: Walter Roberson on 22 Feb 2017
% Mr. Azzi Abdelmalek, I have some notes on your answer.
%x(n+2)-1.3x(n+1)+0.4x(n)=u(n) % x(0)=0 and x(1)=0.
num=[0 0 1]; den=[1 -1 0.25];
k=0:1:5; % discrete time
% According to unit step definition, u(n)=1 for n>=0 and zero otherwise
% but using the heaviside function - and n is discrete and integer -
% contradicts this definition
% because it equals 0.5 - and not one - at n=0.
% So, to use k in discrete - and integre, i.e. 0, 1 , 2, .. etc,
% heaviside is not the proper function and you have to define it like my
% answer
x=[1 ones(1,5)]; % This yields outputs from y(0) to y(5)
y=filter(num,den,x)
% Also, the solution of difference equation is in discrete, so, to plot it,
use stem function
stem(k,y), grid
%Mr. Samir A. Farag, Teaching Assistant at H.T.I, Egypt

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