Is MATLAB solving Difference equations ?

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

[Ahmed ElTahan]

Here is a function I have built to calculate it with added example. https://www.mathworks.com/matlabcentral/fileexchange/56142-output-estimation-difference-equation

Answer 1

[Samir A. Farag]

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:

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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)

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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)

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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))

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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.

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[Charity Reed]

What is dstep?

Answer 2

[Matt J]

There is the filter() command. If you were looking for a symbolic solution, you might find something in the Symbolic Math Toolbox.

[Azzi Abdelmalek]

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]

I see your point, i will try to see whether fits my purpose. Thank you

[Samir A. Farag]

% 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