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
1 个评论
Ahmed ElTahan
2016-3-25
Here is a function I have built to calculate it with added example. https://www.mathworks.com/matlabcentral/fileexchange/56142-output-estimation-difference-equation
采纳的回答
Samir A. Farag
2014-10-24
编辑：Walter Roberson
2017-2-22
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.
更多回答（1 个）
Matt J
2013-7-6
0 个投票
There is the filter() command. If you were looking for a symbolic solution, you might find something in the Symbolic Math Toolbox.
3 个评论
Azzi Abdelmalek
2013-7-6
Example
%y[n+2]-y[n+1]+0.25y[n]=u[n]
num=1
den=[1 -1 0.25]
n=0:0.1:5; % discrete time
x=heaviside(n) % input signal, in thise case heaviside signal
y=filter(num,den,x)
plot(n,y)
msh
2013-7-6
Samir A. Farag
2014-10-23
编辑：Walter Roberson
2017-2-22
% 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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