###### GS 2000/Math - Collins
Lab 3
Solution to Challenge

```The problem was to write a MATLAB script to solve the
Linear Non-Homogeneous DE:

x(n+1) = a x(n) + w(n)

The programming challenge was how to input w(n) since
it had to be defined for every value of n.

I came up with two different solutions, neither of which is totally
satisfying.

Solution 1   Define w(n) as a function:

w = input('Enter a function for w(n):','s');  % the 's' forces it to be a string
w = inline(w,'n');   % this makes a function out of what was typed

We could also use

w = input('Enter a function for w(n):','s');
.
.
.
x(n+1) = a*x(n) + eval(w);     % eval evaluates the expression in w

This form has the flexibility if we somehow wanted w to depend on x(n)
or other values.

Solution 2   Define the values of the vector w:

w = input('Enter a vector of 100 values for w:');

The user would have to type:  [1, 0, 0, 23, 2, etc. ] to get all
the values of w in.

I could have also put this in a loop:

for n = 1:100
w(n) = input(['Enter w(',int2str(n),'):']);   % int2str converts an
% integer into a string
% so it can be concatenated
% to other characters
end

Alternatively, I thought of only allowing w to change every
10 steps, so that the user only had to enter 10 values.

w = input('Enter 10 values for w:');
.
.
.
x(n+1) = a*x(n) + w(floor(n/10)+1);   % floor rounds down to
% the nearest integer

```
ccollins@math.utk.edu