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
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Ahmed ElTahan
2016년 3월 25일
Here is a function I have built to calculate it with added example. https://www.mathworks.com/matlabcentral/fileexchange/56142-output-estimation-difference-equation
채택된 답변
Samir A. Farag
2014년 10월 24일
편집: Walter Roberson
2017년 2월 22일
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.
추가 답변 (1개)
Matt J
2013년 7월 6일
There is the filter() command. If you were looking for a symbolic solution, you might find something in the Symbolic Math Toolbox.
댓글 수: 3
Samir A. Farag
2014년 10월 23일
편집: Walter Roberson
2017년 2월 22일
% 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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